Defining and resolving seismic complexity through a unified source–path–site framework: the Vrancea intermediate-depth ground motions

Defining and resolving seismic complexity through a unified source–path–site framework: the Vrancea intermediate-depth ground motions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Defining and resolving seismic complexity through a unified source–path–site framework: the Vrancea intermediate-depth ground motions Anabella Cotovanu, Elisei Cojan, Radu Vacareanu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9267402/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Ground motions generated by the Vrancea intermediate-depth seismic source exhibit long-recognized intricate characteristics that challenge standard seismological interpretations. As a result, Vrancea earthquakes are frequently excluded from global comparative studies, being treated as exceptions for which conventional source, path, and site models fail to provide consistency. This study addresses this long-standing problem by defining and resolving the seismic complexity of Vrancea ground motions through a unified source–path–site framework. The proposed methodology systematically decomposes recorded ground-motion variability into source-, propagation-, and site-related contributions while explicitly accounting for the specific constraints imposed by limited recordings of major events and strong structural heterogeneities. Key seismic parameters that have remained debated or poorly constrained in the literature are re-evaluated, yielding physically consistent behaviors that satisfy general seismological requirements. Applied to the Vrancea seismic source, the framework demonstrates that the apparent anomalies commonly reported in previous studies do not reflect fundamentally different physical processes but instead arise from the pronounced complexity and strong interdependence of source, path, and site characteristics. Once treated coherently, Vrancea ground motions conform to general rules of seismic behavior. Beyond the regional case study, the proposed approach provides a transferable methodology for the analysis of complex seismic sources worldwide, particularly in tectonic settings characterized by sparse strong-motion data and non-standard ground-motion features. seismic complexity sparse strong-motion data source–path–site decomposition physically consistent seismic parameters Vrancea intermediate-depth earthquakes Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Increasing seismic reliability of elements at risk requires an accurate and physically consistent characterization of seismic action. Seismic hazard analyses depend on how well the properties of seismic sources and the propagation media are understood and represented. For example, the stochastic simulation of ground motions (Boore, 2003) relies on a wide range of parameters, including the properties of materials in the vicinity of the hypocenters (such as seismic velocities and densities), focal mechanisms, released energy, radiation patterns, spectral characteristics near the source, source and path durations, attenuation and scattering effects along the propagation path, as well as the definition and behavior of near-surface geological layers. Seismic hazard results are inputs for structural design and retrofit of buildings and structures, seismic risk assessment and management, and the evaluation of innovative design solutions or damage-mitigation strategies (Calofir, et al., 2024; Gheorghe & Vacareanu, 2026; Munteanu, et al., 2025; Nica, et al., 2022). Consequently, an accurate characterization of seismic ground motions directly contributes to improving seismic reliability (by extension, safety) and preparedness for major seismic events. For the estimation of seismic parameters from strong-motion databases, a variety of approaches have been employed, including inversion-based techniques such as the Generalized Inversion Technique (GIT), nonlinear and Bayesian inversion methods, empirical regression approaches, stochastic modeling, and spectral-ratio techniques. These direct, data-driven approaches are often further constrained by independent information derived from indirect methods, such as tomographic imaging, geological and geophysical models of the crust and upper mantle, and physically based bounds on seismic parameters. Most direct, data-driven approaches have been applied with greater confidence and success to shallow seismic sources and regions characterized by relatively homogeneous geological structures. In such settings, the underlying assumptions regarding source behavior, wave propagation, and site response are more easily satisfied. However, there are tectonic environments in which the application of these methods leads to results that are inconsistent with observed ground motions, statistically weak due to the limited availability of strong-motion recordings, or overly simplified through assumptions of spatially uniform behavior. In these cases, methodological simplifications - such as assuming similar seismic behavior across large regions or treating complex structures as homogeneous - do not sufficiently account for the pronounced heterogeneity of the system, thereby reducing the reliability of the resulting seismic parameters. The Vrancea intermediate-depth seismic source exemplifies a tectonic setting in which standard ground-motion analysis methods encounter persistent limitations. It is frequently excluded from global strong-motion analyses, or, when such methods are applied, they lead to parameter estimates that are either difficult to interpret consistently or so highly particular that they suggest behavior distinct from that observed in other seismic regions. Even when coherent results are obtained within a given methodological framework, their statistical reliability is constrained by the limited size of the Vrancea strong-motion database. For instance, Oth et al. (2007; 2008; 2009) employed stress-drop values approximately twenty times higher than commonly adopted reference values in their analyses to address the reported inconsistencies. Other studies (Popescu, et al., 2016; Radulian, 2017) highlight difficulties in applying source scaling relationships derived from small earthquakes to larger events, leading to the assumption of distinct source behaviors across different magnitude ranges. Similarly, for path attenuation, the literature adopts two contrasting sets of formulations, closely tied to different assumptions regarding geometrical scattering (Oncescu, et al., 1999; Sokolov, et al., 2005; Oth, et al., 2008) versus (Pavel, 2015; Pavel & Vacareanu, 2015; Pavel & Vacareanu, 2018). Uncertainties persist also with respect to site effects: the applicability of H/V spectral ratios has been questioned by Oth et al. (2009), while other studies continue to consider it reliable (Pavel, 2015). In addition, the thickness and characterization of near-surface stratification remain weakly constrained, and the characterization of linear and nonlinear site behavior is insufficiently documented. Even when the analysis moves away from detailed parameter-level descriptions toward probabilistic approaches that rely on statistically robust representations of seismic behavior, a fundamental limitation remains: the size of the available Vrancea strong-motion database. This limitation has been addressed by incorporating strong-motion recordings from other seismic regions to improve statistical robustness (Vacareanu, et al., 2014), with an unavoidable trade-off in terms of regional seismic specificity. A detailed discussion of Ground Motion Prediction Equations (GMPEs) for Vrancea for the last 30 years and their limitations is made in Aldea et al. (2022). This study aims to define the complexity of the interacting factors that govern strong ground motions in the region influenced by the Vrancea intermediate-depth seismic source and to reduce the ambiguity that has persisted in their interpretation. Addressing this problem requires the integration of information across multiple disciplinary domains, reflecting the inherently complex nature of the system. Through this process, the apparent multiplicity of contributing factors is shown to reduce to two primary factors underlying the observed ground-motion complexity: zonation and local site conditions. To achieve this reduction, a dedicated methodological framework is developed for the characterization of seismic ground motions in structurally complex settings under conditions of sparse strong-motion data. Within this framework, key seismic parameters that have remained debated in the literature (including anelastic attenuation, geometrical scattering, stress drop, and site behavior) are systematically re-evaluated and constrained in a physically consistent way. Beyond defining a methodology suited to regions characterized by sparse strong-motion databases and levels of complexity that do not conform to conventional source and site models, this study adopts a holistic treatment of earthquake ground-motion generation. Rather than isolating individual components, the analysis addresses source, path, and site effects simultaneously, seeking physical and scientific consistency across all contributing variables without resorting to special-case assumptions or deviations from established seismic principles. The study integrates a transdisciplinary analysis of the geologic and tectonic evolution of the region, which motivates the spatial zoning adopted in the analysis - an essential step for decoupling complex interactions and enabling focused interpretation where multiple effects are strongly intertwined. This is followed by an initial spectral comparison across the defined zones, providing a first-order indication of distinct ground-motion behavior and allowing the identification of potential deviations. Within this framework, the final stage of the study addresses the estimation and constraint of several seismic parameters that have remained debated in the literature, as outcomes of a coherent clarification of source–path–site complexity and in consistency with physical plausibility and historical observations. This endeavor addresses several long-standing scientific debates and reconciles results that have varied across studies and methodological approaches, which have often led to the conclusion that the Vrancea seismic source exhibits fundamentally different behavior. The present analysis demonstrates instead that the apparent anomalies arise from a high degree of complexity. When this complexity is treated coherently and in accordance with the specific characteristics of the source, path, and local site conditions, the Vrancea seismic source and the affected region are shown to conform to general seismological principles. The concrete outcomes of this study include: a methodological framework designed for complex settings with sparse strong-motion data; a geologically and tectonically motivated zoning supported by observational evidence; constrained characterization of path effects, namely anelastic attenuation and geometrical spreading; descriptions of local site conditions and their modification under strong shaking; envelope representations of site amplification; and, most importantly, a systematic structuring and definition of seismic complexity itself. 2. Vrancea intermediate-depth earthquakes Romania is among the European countries with the highest levels of seismic hazard, largely due to the influence of the Vrancea intermediate-depth seismic source. Located beneath the south-eastern bend of the Carpathian Arc, Vrancea represents a compact and isolated nested seismogenic volume characterized by intense and persistent seismic activity concentrated at depths of approximately 60–200 km (Ismail-Zadeh, et al., 2012; Manea, et al., 2011). This intermediate-depth seismicity dominates the national hazard, controlling seismic design requirements over more than two-thirds of the country. In a regional tectonic context, the Vrancea source is situated within a zone of complex continental convergence, at the junction of several major tectonic units: East European Platform, the Scythian Platform, the Moesian Platform, the North Dobrogea Orogen, and the Transylvanian Basin (Intra-Alpine Plate) (Radulian, 2014) (Fig. 1 ). The Vrancea source is commonly described as an intraslab seismic nest, in which large amounts of seismic energy are repeatedly released within a very limited mantle volume. The cumulative annual seismic energy release associated with Vrancea intermediate-depth earthquakes has been shown to be comparable to that of the entire Southern California region (Wenzel, et al., 1998). In a global perspective, Vrancea belongs to a very small class of highly active intermediate-depth seismic nests, alongside regions such as Bucaramanga (Colombia) and Hindu Kush (Afghanistan), and represents the only segment of the Carpathian orogenic system exhibiting sustained intermediate-depth seismicity (Manea, et al., 2011). From the beginning of the 20th century to the present, the Vrancea source has generated fourteen earthquakes with moment magnitudes M w ≥ 6.3 . Only four of these events were instrumentally recorded: March 4, 1977 ( M w 7.4, h ≈ 94 km ), August 30, 1986 ( M w 7.1, h ≈ 131 km ), and May 30–31, 1990 ( M w 6.9 and M w 6.3, h ≈ 91–87 km ). The largest event, the 1977 earthquake, was recorded within Romania at only a single station in Bucharest, highlighting the limited availability of reliable strong-motion data for major Vrancea earthquakes. The effects of these events extend beyond national borders, with macroseismic intensities of IV–VI MSK documented in neighboring regions such as Moldavia, Bulgaria, and Ukraine (Kronrod, et al., 2013; Aldea, et al., 2022). From a seismotectonic perspective, Vrancea intermediate-depth earthquakes cluster within a near-vertical lithospheric fragment descending into the mantle, separated from crustal seismicity by a relatively aseismic zone. Focal-mechanism solutions indicate a predominance of compressional reverse faulting with subvertical extension for the intermediate-depth events, in contrast to the extensional or strike-slip mechanisms that characterize the local crustal seismicity (Radulian, et al., 2018). The origin of the seismogenic body has been attributed to either a delaminated continental lithosphere or a remnant oceanic slab and lithospheric-instability scenarios, including delamination and gravitational or thermal instabilities (Sperner, et al., 2001; Cloetingh, et al., 2004; Knapp, et al., 2005). Recent evidence supports interpretations involving an oceanic lithospheric fragment undergoing dehydration-related processes (Ferrand & Manea, 2021). Regardless of the specific origin model, all proposed frameworks consistently indicate a high-velocity, high-density, and mechanically stressed body capable of sustaining persistent intermediate-depth seismicity within a limited volume, providing the physical basis for the strong and far-reaching effects observed during major Vrancea earthquakes. Recorded strong ground motions generated by the Vrancea intermediate-depth seismic source exhibit a combination of time-domain and spectral characteristics that distinguish them from those commonly observed in most seismic settings. In the time domain, the motions are marked by a strong initial pulse-like phase, during which a substantial fraction of the total seismic energy is released over a very short interval (about 50% of energy in less than 3 seconds), followed by a phase of gradual energy release extending over several tens of seconds (Cotovanu & Vacareanu, 2020b; Cotovanu & Vacareanu, 2021). This asymmetric energy distribution, characterized by an early high-amplitude pulse containing the peak ground acceleration (PGA) and a long tail of lower-amplitude motion, reflects the dominance of body-wave energy and the generally limited contribution of surface waves. From a spectral perspective, Vrancea strong-motion records are characterized by significant amplification at relatively long spectral periods. This feature is explicitly reflected in the Romanian seismic design code (MDRAP, 2014), which defines three spectral zones with corner periods of 0.7 s, 1.0 s, and 1.6 s - substantially longer than the relatively narrow amplification bands around 0.3–0.5 s more commonly observed in many seismic regions. The prevalence of long-period amplification has important implications for seismic design, as it extends the most severe seismic demand from low-rise to mid- and high-rise structures with very large displacement demands for the later and represents one of the defining features that differentiate the Vrancea source from more typical seismic environments. Furthermore, recorded motions indicate a magnitude-dependent redistribution of spectral energy: smaller Vrancea earthquakes tend to exhibit dominant energy at shorter periods, whereas larger-magnitude events progressively concentrate energy at longer periods - a physically expected trend that is strongly accentuated by local site conditions and examined in detail in subsequent sections. At a broader level, Vrancea ground motions reflect the combined influence of complex source properties, heterogeneous propagation paths, and highly variable local site conditions. Propagation effects are strongly controlled by pronounced lateral heterogeneity in the crust and upper mantle (Ismail-Zadeh, et al., 2012). Seismic refraction and tomographic investigations reveal substantial variations in crustal thickness, asthenospheric depth, and seismic velocities, particularly between foreland and back-arc regions, giving rise to markedly different attenuation behaviors depending on the propagation path. Local site conditions introduce an additional layer of complexity, especially in regions characterized by thick sedimentary sequences such as the Focsani Basin and the Dacian Basin (Fig. 1 ). In these areas, the depth to seismic bedrock varies from near-surface to several kilometers, rendering simplified site proxies of limited applicability. Observations indicate that long-period amplification is controlled not by shallow stratigraphy alone, but by the entire sedimentary package extending to deep geological interfaces. Consequently, local site effects cannot be decoupled from regional structure and path effects, and their influence varies spatially with basin geometry, impedance contrasts, and sedimentary evolution. The characteristics outlined above indicate that Vrancea intermediate-depth ground motions arise from the simultaneous interaction of multiple source-site-path factors. This intrinsic complexity is further compounded by the limited number of strong-motion recordings available for major Vrancea earthquakes, which constrains the statistical robustness of observational analyses and parameter estimation. As a result, many aspects of Vrancea ground-motion behavior have been investigated under conditions of sparse data, strong structural heterogeneity, and necessarily simplifying assumptions. These circumstances have led to a wide range of proposed models and interpretations, often emphasizing different components of the source-path-site system. The following section reviews the main debates that have emerged from these studies and discusses how methodological choices and data limitations have shaped the current understanding of Vrancea seismic behavior. 3. Debates in the literature The literature on Vrancea intermediate-depth ground motions reports differences across several parameters used in ground-motion analyses. Given the limited size and heterogeneity of the available strong-motion database, such differences are likely to occur and can be regarded as acceptable when estimates remain sufficiently close and within ranges that can be explained by the same underlying physical processes. For this reason, the present chapter does not attempt to address all parameters involved in previous studies, but focuses on those for which published results diverge beyond such explainable bounds and therefore require closer examination. The discussion addresses source-related properties through source spectral characteristics and stress drop, propagation effects through the heterogeneous structure of the crust and upper mantle and the associated anelastic attenuation and geometrical scattering formulations, and local ground conditions in relation to their diverse definitions, the transition between seismic bedrock and what we consider local site conditions. 3.1. Source spectral characteristics and stress drop In the literature, several source spectral shapes have been proposed, characterized by either one or two corner frequencies. The most widely adopted formulation is the ω² source model introduced by Brune (1970; 1971), which assumes a single corner frequency directly related to stress drop. In the context of Vrancea intermediate-depth earthquakes, most studies have employed source spectra with a single corner frequency. Exceptions are found in the works of Oncescu (1986) and Trifu (1987), who proposed spectral shapes with two corner frequencies, associating them with asperity-based rupture models. Similar spectral features were later reported by Trifu and Radulian (1989) and Radulian et al. (1991). In subsequent applications, including stochastic simulations (Boore, 2003) of Vrancea strong ground motions, Cotovanu and Vacareanu (2020a) observed that source models incorporating two corner frequencies may provide a closer representation of recorded motions. Nevertheless, likely due to the limited size of the available strong-motion database, attempts to determine two-corner frequency source models have not been pursued further. As a result, later studies have largely relied on single-corner frequency source spectra that have been widely tested at the global scale, from which statistical stability and parameter robustness can be indirectly transferred. In these models, the corner frequency is expressed either as a function of stress drop or directly as a function of seismic moment or moment magnitude. While these formulations generally provide satisfactory approximations, for Vrancea events they tend to reproduce either small-to-moderate or large events more effectively, depending on the underlying database. This discrepancy is most clearly reflected in the stress-drop values inferred from different studies. Early stress-drop estimates for major Vrancea intermediate-depth earthquakes were derived using rupture-area assumptions based on aftershock distributions. Räkers and Müller (1982) and Oncescu and Trifu (1987) assumed that the aftershock area coincides with the rupture area and obtained static stress-drop values of the order of 50 bar for the 1977 ( M w 7.4 ) and 1986 ( M w 7.1 ) earthquakes. These values became representative for early characterizations of Vrancea source properties and were subsequently adopted in later modeling studies. Using spectral methods, Gusev et al. (2002) estimated seismic moment and corner frequency from displacement spectra of long-range and teleseismic recordings. Employing Brune (1970; 1971) single-corner frequency source model, they obtained static stress-drop values of approximately 100–200 bar for large-magnitude events. Oncescu (1989) applied spectral methods to analog strong-motion recordings of the 1986 earthquake and obtained a static stress drop of about 850 bar, together with dynamic stress-drop values ranging between 950 and 1400 bar. A comprehensive investigation of Vrancea strong ground motions was carried out by Oth et al. (2007), Oth (2007) for the 1977, 1986, and 2004 ( M w considered in their paper 5.8) earthquakes using the empirical Green’s functions method and inversion techniques. Their results showed that the observed ground motions can be reproduced by rupture models involving small asperities associated with high stress drops, in the range of 300–1200 bar, and high particle velocities of 3.5–4.5 km/s. Although static stress drops for the 1977 and 2004 events were found to be two to three times larger than for the 1986 earthquake, the corresponding dynamic stress drops were similar for all three events, clustering around values of approximately 1000 bar. In parallel with source-parameter studies, stochastic ground-motion simulations for Vrancea earthquakes continued to rely on relatively low stress-drop values. Pavel and Vacareanu (2015) simulated ground motions for magnitudes 5, 6, and 7 using a stress drop of 50 bar and compared stochastic response spectra with GMPE-based predictions. They found that the agreement was satisfactory mainly for the magnitude-6 scenario and concluded that magnitude-dependent stress-drop values would provide a more appropriate representation of Vrancea ground motions. Similar conclusions were reached in Cotovanu (2018) and Cotovanu and Vacareanu (2020a), where stochastic simulations using SMSIM (Boore, 2003) and EXSIM (Motazedian & Atkinson, 2005) showed that low stress-drop values (around 50 bar) are unable to reproduce key features of the recorded strong-motion characteristics. High dynamic stress drops associated with rapid and efficient rupture processes were also noted by Radulian (2017). By comparing different datasets employed in studies of Vrancea source characteristics (Popescu, et al., 2016; Radulian & Popa, 1996; Oncescu, 1986), he observed an apparent increase in stress drop with increasing seismic moment for events up to magnitude 6, whereas such a trend is not evident for larger earthquakes. Madariaga (1976) provided a physical justification for the inverse relationship between corner frequency and source radius under the assumption of a circular rupture model. Corner frequencies were shown to be approximately one-half of those predicted by Brune’s (1970; 1971) formulation, implying corrections by a factor of eight to the corresponding stress-drop estimates. Building on this framework, Radulian (2017) examined the M₀ - radius dependence using different Vrancea datasets (Popescu, et al., 2016; 1996; Oncescu, 1986). When seismic moment is related consistently to source radius and, consequently, to corner frequency, the apparent discrepancies observed for the major events disappear. Taken together, the wide variety of stress-drop estimates reported for Vrancea reflects instability relative to differences in data and methodology. Within this context, stress drop often emerges as a corrective parameter rather than a directly constrained physical quantity. Although Oth et al. (2007; 2008; 2009) employed an approach that simultaneously considers multiple categories of parameters, stress drop remains the parameter through which consistency between model components was achieved. Similarly, Radulian (2017) examines stress-drop values across different magnitude ranges and notes a possible magnitude dependence, without extending this observation into a unified source parameterization. This situation raises a recurring question for the Vrancea intermediate-depth source: why do such corrective adjustments become significant here, while similar processes do not appear to exert a comparable influence on strong ground motions in other seismic regions where analogous methodologies are applied? More fundamentally, it remains unclear which physical aspects of the Vrancea source or propagation environment are implicitly absorbed by these corrections, given that comparable processes may exist elsewhere but with a much smaller impact on observed ground-motion characteristics. 3.2. Propagation path: structural heterogeneity, attenuation, and geometrical scattering The propagation of seismic waves from the Vrancea intermediate-depth source takes place within a heterogeneous crustal and upper-mantle environment (Ismail-Zadeh, et al., 2012). Three major projects have provided the primary constraints on the regional structure: the seismic refraction profiles VRANCEA1999 and VRANCEA2001, and the CALIXTO (Carpathian Arc Lithosphere X-Tomography) project (Hauser, et al., 2001; Hauser, et al., 2007; Landes, et al., 2004; Martin, et al., 2005; Martin, et al., 2006). Among others, these studies emphasized strong contrasts between the interior of the Carpathian Arc and the surrounding areas, particularly the Transylvanian Basin where the asthenosphere is located at significantly shallower depths (Fig. 2 ). Additional pronounced structural variability is observed in the vicinity of the Vrancea source, where in the Focsani Basin the geological strata are bent to depths larger than 30 km, of whom the first 8–10 km are composed from Neogene and Quaternary strata (Landes, et al., 2004; Hippolyte, et al., 1999). This area is prone to large topographic effects, consequently can record different characteristics. Small concentric basins with local influence can also be found at south of Carpathians chain (eg. SULR station area) (Manea, et al., 2020; Krezsek & Olariu, 2021; Matenco, et al., 2003). The northern and central sectors of the Moesian Platform - extending across southern Romania correspond to the Dacian Basin (Fig. 1 ). In contrast, the southern part of the platform, including northern Bulgaria, represents the more stable Moesian domain, characterized by a thinner sedimentary cover. Along this north-south section, the Danube valley marks the zone with the shallowest local site condition depths (Fig. 3 ). Bucharest, located roughly midway between the Southern Carpathians and the Danube, lies along the middle descending gradient of sediment thickness. One of the most challenging aspects in assessing seismic response across the Vrancea-affected area is the large variability in seismic bedrock depth - ranging from 3000 m to near-surface across much of the Moesian Platform (Manea, et al., 2020; Manea, et al., 2016), and from 800 m in the eastern parts of Romania (Juravle, 2009). Unlike in many other seismic regions, where shallow seismic bedrock allows for local site conditions to be reliably characterized through borehole recordings or standard geotechnical profiling, such methods are often impractical in the Vrancea context due to the deeply stratified and geologically complex subsurface. On this note, a direct consequence of the structural and geological complexity discussed above is reflected in the anelastic attenuation and scattering parameters. Russo et al. (2005) examined the variation in attenuation outside the Carpathian Chain and categorized the seismic stations into three distinct zones. The first group includes stations showing low attenuation, located in areas such as the Eastern European Platform, the Scythian Platform, and the northeastern sector of the Moesian Platform. The second group comprises stations with high attenuation, mainly situated near the Vrancea seismic zone and within the Transylvanian Basin. The third group includes stations with intermediate attenuation levels, but with significant variability depending on the seismic wave path—lower attenuation was observed for shallow events, while higher attenuation was associated with deeper events, particularly in the Focsani Basin area. Stations in the Bucharest region, along with other stations located further south, were excluded from the analysis due to inconsistent results attributed to strong local site effects. Bucharest, for instance, lies on a floodplain characterized by a complex mix of sediments, terraces, sand, and muddy alluvial deposits. Furthermore, six attenuation functions have been proposed in the literature for the propagation path from the Vrancea intermediate-depth source toward regions outside the Carpathian Arc: Oncescu et al. (1999) (O99), Sokolov et al. (2005) (S05), Oth et al. (2008) (O08), Pavel (2015) (P15), Pavel and Vacareanu (2015) (PV15), and Pavel and Vacareanu (2018) (PV18). These functions can be grouped into two categories based on the assumed geometrical scattering. The first group (O99, S05, and O08) is associated with stronger attenuation of spectral amplitudes at short periods and assumes geometrical spreading proportional to \(\:{R}^{-1}\) . The second group (P15, PV15, and PV18) primarily affects spectral amplitudes at longer periods and is derived assuming a weaker geometrical spreading proportional to \(\:{R}^{-0.5}\) . Oncescu et al. (1999) used a database of recordings from stations located outside the Carpathian Arc, including data from 19 earthquakes with magnitudes between 3.9 and 5.3, completed by recordings from the major events of 1990 ( M w 6.9 and M w 6.3 ), 1986 ( M w 7.1 ), and 1977 ( M w 7.4 ). They tested the Joint Source–Site Determination (JSSD) method for the characterization of both weak and strong ground motions generated by the Vrancea source. Within this framework, an attenuation relation of the form \(\:109\left(\pm\:14\right){f}^{0.81(\pm\:0.08)}\) was obtained using the INCERC station in Bucharest as a reference site, for which the transfer function was determined based on the geotechnical profile of Constantinescu and Enescu (1985). In this study, the determination of attenuation primarily served as a mean to analyze discrepancies observed in the recordings, and the authors emphasized the coupling between source and site effects, as well as the influence of rupture directivity on the perceived stress-drop values. In order to determine hard-rock spectral models for ground motions generated by Vrancea intermediate-depth earthquakes, Sokolov et al. (2005) approximated attenuation relations of the form \(\:{Q}_{0}{f}^{0.8}\) , based on the attenuation profiles proposed by Radulian et al. (2000). These relations were derived for several locations situated east and south of the Carpathian Arc, and for different hypocentral distance intervals (0–40 km, 0–110 km, and 100–200 km). Depending on the region and depth range, the parameter \(\:{Q}_{0}\) was estimated to take values of 100, 200, 400, or 500. Oth et al. (2008) employed a database of recordings from 55 earthquakes with magnitudes ranging between 4.0 and 7.1 and applied an adapted Generalized Inversion Technique (GIT) to separate source, path, and local site effects. As a constraint, they assumed that at a hypocentral distance of 90 km the total attenuation from all effects equals unity and that two regions characterized by different attenuation properties can be defined: Region 1, corresponding to the area outside the Carpathian Arc, and Region 2, corresponding to the epicentral region. Starting from initially assumed anelastic attenuation functions, similar to those proposed by Sokolov et al. (2005), an iterative procedure led to frequency-dependent attenuation relations of the form \(\:114{f}^{0.96}\) for Region 1 and \(\:72{f}^{0.12}\) for Region 2. The assumed constraint was addressed by Oth (2009; 2007), where a correction factor derived using the Empirical Green’s Function method was introduced. Pavel (2015) and Pavel and Vacareanu (2015; 2018) employed similar methodologies to determine anelastic attenuation and geometrical spreading using different strong-motion databases. In these analyses, three values of geometrical spreading \(\:({R}^{-0.5},{R}^{-0.7},\:{R}^{-1})\) were tested, with \(\:{R}^{-0.5}\) selected as the reference model. Regression analyses of Fourier Amplitude Spectra were then applied to derive frequency-dependent attenuation relations. The resulting models include \(\:165{f}^{1.2}\) (P15) and \(\:100{f}^{1.2}\) (PV15), the latter also incorporating regional subdivisions and estimates of the high-frequency decay parameter 𝜅. In Pavel and Vacareanu (2018), attenuation was further differentiated by azimuthal region, yielding \(\:115{f}^{1.25}\) for forearc regions and \(\:70{f}^{0.9}\) for the backarc region, while also accounting explicitly for local site conditions. Overall, the studies reviewed in this section highlight the existence of complex path effects and different attenuation formulations derived under distinct assumptions regarding regionalization, geometrical spreading, and data selection. Distinct zonations are adopted, ranging from two attenuation regions (Oth, et al., 2008), to station-based groupings (Sokolov, et al., 2005), and to azimuth-dependent zonations that evolve from multiple regions to a simplified forearc–backarc distinction (Pavel & Vacareanu, 2018). Consequently, multiple anelastic attenuation functions coexist in the literature, reflecting both the complexity of the propagation environment and the methodological choices adopted to manage it. 3.3. “Boundary” between the path and the local site conditions Path effects are considered to be phenomena that modify seismic waves along their travel path from the source to the local site conditions. Local site conditions are understood as the stratification above the bedrock. A first divergence in approach emerges regarding the interpretation of this boundary. Two types of bedrock are defined: engineering bedrock and seismic bedrock. Depending on the approach, the theoretic seismic bedrock is typically defined as the layer with shear wave velocity (Vs) values of 3000–3500 m/s and above, while engineering bedrock has values up to 760–800 m/s. The consideration of the “boundary” between local site conditions and path conditions is an essential aspect in analyses and applications, as the two domains exhibit different behaviors, particularly during major seismic events relevant for structural design. While path effects are dominated by attenuation and scattering, softer soils are associated with significant amplification effects and modifications to the spectral content of the ground motion, which can directly affect buildings depending on the correlation between the ground predominant periods and their natural periods. Thus, the way path effects are determined is directly influenced by how local site conditions are defined. Deep stratifications have the capacity to amplify seismic motion across a broad range of periods, depending not only on their physical configuration but also on how different earthquakes interact with them. Soil behavior is nonlinear, with stiffness and damping varying according to strain level. This means that the same stratigraphic profile may exhibit different dynamic responses depending on the characteristics of the seismic input, such as magnitude, depth, and spectral content. Consequently, the concept of "local site conditions" and the effective depth at which they are defined should not be treated as fixed. Instead, they represent a dynamic boundary, shaped by both the properties of the subsurface and the specific features of each seismic event. Also, the spectral content of seismic ground motion is closely linked to earthquake magnitude. Larger-magnitude events typically radiate more energy at longer periods due to the increased scale of the rupture and source geometry. This makes long-period waves more prominent in strong earthquakes, enhancing their ability to interact with deep soil profiles and excite resonant modes across a broad frequency range. On this note, further clarification is required on how the depth to the bedrock is practically determined, especially when local site conditions involve complex stratification and deep sedimentary basins. One approach to estimating this depth is provided by Manea et al. (2020), who used ambient vibration data to extract the fundamental frequency of resonance ( f₀ ) at multiple seismic stations across southeastern Romania. The f₀ value was identified from the horizontal-to-vertical (H/V) spectral ratio curve, based on the presence of a distinct and stable peak. Where such a peak was observed, it was interpreted as an indicator of a strong impedance contrast between the sedimentary layers and an underlying stiffer formation. Such contrasts are typically required for a clear resonant peak to emerge in the H/V curve. To refine these initial observations, Manea et al. (2020) performed a two-step inversion of Rayleigh-wave ellipticity to estimate subsurface vs profiles and assess the depth at which this impedance contrast occurs. The depth thus inferred was defined as the geophysical bedrock. These estimates were then interpolated spatially to construct a regional-scale model of bedrock depth variability, providing insight into the subsurface structure independent of fixed engineering or seismological thresholds. The fundamental frequency f₀ , as derived, reflects the presence of a strong seismic impedance contrast in the subsurface. While this contrast may coincide with the boundary between local site conditions and underlying bedrock, in terms of specific behavior this interpretation should be reflected in recorded ground motions. Without this validation, f₀ may be rather understood primarily as an indicator of a mechanical boundary, not necessarily as the depth of the entire sedimentary package relevant to site response. Moreover, in cases where seismic impedance increases gradually with depth, and no strong contrast is encountered near the surface, Rayleigh waves may propagate through multiple layers - regardless of their total thickness - until they reach a sufficiently sharp discontinuity that can generate a distinct resonant response. In such situations, the resulting f₀ may reflect a deeper transition, provided it exists, or remain undetectable if no major contrast is encountered. This further emphasizes the need to interpret f₀ in conjunction with earthquake recordings and other site response indicators. When comparing the f₀ distribution provided by Manea et al. (2020) with the geological configuration of the Moesian Platform, some questions arise regarding the interpretation of the identified geophysical bedrock in the context of local site effects. The central sector of the Moesian Platform, where lower f₀ values are mapped, appear to correspond stratigraphically to deeper units as the basin architecture suggests prolonged sediment accumulation (Fig. 3 ). Beyond the peri-Carpathian fault system begins the Dacian Basin where substantial Neogene sedimentation took place. The base of this sedimentary pile corresponds to the Pre-Paratethys denudation surface, an erosional unconformity overlying Mesozoic basement (Cretaceous, Jurassic, or even Triassic), as described by Matenco et al. (2003; 2016). Starting in the Miocene, the region experienced alternating lacustrine, marine, and fluvial environments associated with the Danube transformations, which led to the accumulation of progressively deposited sedimentary layers including clays, silts, sands, lignite, and salt-bearing horizons (Krezsek & Olariu, 2021). These successions are thick (often exceeding 2 km) and mechanically heterogeneous, with varying degrees of compaction and diagenesis. In this context, the stratification tends to be gradual, without sharp impedance contrasts. As such, the fundamental frequency ( f₀ ) values detected by Manea et al. (2020) in this region - often associated with deep interfaces (> 1000 m) - likely reflect internal lithological transitions rather than the base of the sedimentary sequence relevant for local site response. Towards the southern part of the Moesian Platform, where higher f₀ values are reported, the sedimentary succession becomes thinner. The continuous Neogene sequence observed in the basin center is no longer preserved. Instead, Cretaceous or older basement is overlain by Miocene, Pliocene, and Quaternary deposits. Here, the impedance contrast between the soft upper sediments and the rigid strata is well-defined, sharper. The entire sedimentary cover probably behaves as a seismic amplification unit, with clear local site effects. This situation corresponds more closely to classical models of site response, where a soft soil layer overlies stiff bedrock. As such, it remains unclear whether the depth to bedrock defined by f₀ in the northern part of the platform captures the effective lower limit of the sedimentary sequence relevant to site effects, or simply reflects a deeper lithological transition not strongly involved in the dynamic response of the upper soil layers during earthquakes. According to Jipa and Olariu (2009), coal-bearing layers - typically lignite - are present at the transition between the upper Pontian and lower Dacian units, often identified at depths of several hundred meters in the western and central parts of the Dacian Basin. These layers are commonly associated with coarsening-upward sequences and reflect a shift from brackish to continental environments. While coal itself has relatively low shear-wave velocities, its stratigraphic position within compacted and often well-cemented strata suggests a mechanically coherent interval. Consequently, the sedimentary package extending to or slightly below these coal-bearing layers may act more as a transmission medium than a resonant one, particularly in regions where no significant impedance contrast is located above. This reinforces the possibility that, in parts of the Moesian Platform where f₀ values are low and interpreted as indicative of deep impedance contrasts, the geophysical bedrock identified may lie below a thick, stiffened sedimentary sequence that contributes more to path effects than to local site amplification. Regardless of this discussion, several studies exist that characterize local conditions at different sites: from geological maps and lithological columns used for mapping the entire territory of Romania (Geological Institute of Romania, 2022) to complemented local studies conducted for various purposes (Jipa & Olariu, 2009; Stoica-Negulescu, 2016). In addition, there are studies that provide subsurface profiles including parameters such as density, P- and S-wave velocities, and in some cases even modulus reduction and damping curves (Bratosin, et al., 2009). Ideally, these studies should include the deep stratifications discussed previously. However, such deep characterizations are available only at very few locations, such as the INCERC site in Bucharest (Constantinescu & Enescu, 1985). Otherwise, site characterization has been performed rather using simplified v s30 -based profiles or H/V spectral ratios, which may or may not be representative, as argued by Oth (2007). The debates reviewed in this chapter show that the variability of parameters reported for Vrancea intermediate-depth ground motions reflects the combined effects of strong structural complexity, limited data availability, and the use of different definitions for source, path, and site parameters in the literature. Stress-drop estimates, attenuation formulations, and interpretations of local site conditions are therefore not contradictory in themselves, but arise from the strong coupling between model components and the assumptions adopted in different methodologies. 4. Zonation as a means of decomposing seismic complexity Starting from the premise that Vrancea ground motions follow generally applicable physical principles, yet appear inconsistent with standard modeling approaches, this chapter aims to define a balanced level of uniformity that enables simplification without hiding spatial variability and heterogeneity. Historically, several zonations have been proposed for the territory strongly affected by Vrancea earthquakes. The most stable and persistent subdivision divides Romania into two main regions: the interior of the Carpathian Arc (back-arc) and the exterior of the Carpathian Arc (forearc) (Vacareanu, et al., 2015). This distinction represents one of the earliest observed differences in seismic-wave attenuation, already evident in the first intensity maps constructed for major historical earthquakes. It has remained consistently reflected in successive generations of seismic design codes - The P100 series (MDRAP). Within the exterior of the Carpathian Arc, different levels of subdivision have been adopted depending on the objectives of the respective studies. Some works treat this region as a single unit (Pavel, 2015; Pavel & Vacareanu, 2015; Cotovanu & Vacareanu, 2021), while others distinguish the epicentral area from the remaining forearc region (Oth, et al., 2008). Additional studies consider the southern sector separately, focusing on the Moesian Platform (Manea, et al., 2020). Beyond these approaches, further zonations have been proposed based on azimuthal partitioning - initially into five regions (Pavel & Vacareanu, 2018) -, or on combined azimuthal and tectonic criteria (INFP; UTCB; URBAN-INCERC, 2016–2018). In the present study, a zonation is proposed based on geological, geophysical, tectonic, and topographic evidence (Matenco, et al., 2003; Jipa & Olariu, 2009; Juravle, 2009; Krezsek & Olariu, 2021), and most substantially on the work of Manea et al. (2016; 2020). As such, the zonation is defined without relying directly on recordings from major Vrancea earthquakes and serves as an independent pivot within the overall framework. A preliminary and qualitative verification of potential differences between the resulting strong-motion datasets is carried out through visual inspection. The proposed subdivision accounts for elements expected to exert a major influence on strong ground motions, including possible basin effects, as well as sedimentary stratification with the potential to exhibit site-specific or path-related behavior, and the presence of strong impedance contrasts. While shallow sources typically exert strong effects over areas of tens to hundreds of square kilometers, Vrancea earthquakes influence a local area of several tens of thousands of square kilometers and a regional area exceeding 100,000 square kilometers in Romania. Under these conditions, structural heterogeneity is unavoidable. The area of interest for seismic safety analyses is therefore broad and does not allow for a strictly incremental, locally focused approach. Instead, within an environment characterized by evident heterogeneity, a level of homogeneity sufficient for meaningful analysis must be identified. From this standpoint, the affected area can be firstly subdivided into three regions, governed primarily by the three major tectonic units (Fig. 2 ): the East European Plate, with an approximate thickness of 150 km, the Moesian Platform, with an approximate thickness of 130 km, and the Intra-Alpine Plate, with an approximate thickness of about 90 km (Besutiu, 2006; Ismail-Zadeh, et al., 2012). Considering the predominance of large intermediate-depth earthquakes within the depth range of approximately 90–150 km (Radulian, et al., 2019), a first and well-recognized distinction emerges. Seismic waves recorded within the Intra-Alpine Plate (the interior of the Carpathian Arc) are more likely to propagate through asthenospheric or more viscous media, leading to stronger attenuation and, consequently, different ground-motion characteristics compared to those observed outside the Carpathian Arc. Due to the scarcity of strong-motion recordings from major events in this area, the intra-Carpathian region is not considered in the present study. For the exterior of the Carpathian Arc, a first-order subdivision may be defined between the Moesian Platform and an eastern domain that includes both the East European Plate (EEP) and the Scythian Platform (Fig. 1 ). While tectonically distinct, these units are treated jointly due to data limitations. Based on the deep lithospheric structure inferred from the three major experiments discussed previously, this separation can be considered sufficiently homogeneous, except for the Focșani Basin, where lithospheric bending goes to depths of about 30 km and pronounced local topographic effects and internal variability are expected. By increasing the level of analysis to a slightly finer scale focused on near-surface stratification, additional features emerge that require closer consideration. In the Dobrogea Orogen, old stratigraphic units (Jurassic and Triassic) are encountered very close to the surface, overlain by only a few meters to several tens of meters of sediments. Within the southern part of Romania, corresponding to the Moesian Platform, two distinct stratigraphic trends can be identified (Fig. 3 ). In its northern half, from the Carpathians southward, sediment accumulation follows a chronological sequence that can be consistently linked to the long-term evolution of the Danube, including phases of migration and stagnation that resulted in progressive sediment deposition. In contrast, the southern half of the Moesian Platform does not exhibit this chronological sedimentary succession. Instead, this sector reflects a southward lateral shift (“slide”) of the Danube toward its present course, driven by topographic uplift associated with the formation of the Southern Carpathians (Matenco, et al., 2016). This process led to the deposition of relatively young sediments directly onto older stratigraphic units (Jurassic, Triassic, or Cretaceous), representing an evident stratigraphic discontinuity. This discontinuity suggests the presence of an impedance contrast that cannot be neglected in the interpretation of strong ground motions. From the perspective of sedimentary architecture, the Moesian Platform may be interpreted as a basin confined between the Carpathians and the Balkan Mountains. Within this configuration, the Dacian Basin represents a zone of stratified sediment accumulation resulting from the long-term evolution of the Danube River through successive depositional positions. This is followed by a relatively rapid southward sliding, characterized by a decrease in sediment thickness - from more than 1 km in the central part of the platform to only a few meters in the vicinity of the present-day Danube, where it assumes its role as a major fluvial system. The older East European Platform is characterized by deep sedimentary sequences without major stratigraphic discontinuities, showing a gradual decrease in sediment thickness from the Carpathian foredeep eastward. While a subdivision between the deeper foredeep and areas of thinner accumulation could be considered, the resulting differences are better interpreted as local site effects rather than path-related interconnectivity and should be accommodated without ambiguity within the general behavioral models. On this conceptualized foundation and based on the f₀ mapping of Manea et al. (2016; 2020), the analysis relies on a dataset of earthquakes with Mw > 5 , selected to ensure consistency with earlier studies (Pavel & Vacareanu, 2015; 2018; Craciun, et al., 2018). Seismic stations are grouped by geographical domain, f₀ intervals inferred, and magnitude class ( Mw 5–6 and Mw > 6 ). Based on the combined zonation criteria discussed above - tectonic setting, basin geometry, and near-surface stratification - the ground-motion recordings are classified into the following zonation categories (Fig. 4 ): North Moesia ridge – Carpathians Mountains, basin crest, convex geometry, corresponding to areas where f₀ > 1 Hz; North Moesia edge - steeply dipping flanks, concave geometry, with 0.15 Hz < f₀ < 1 Hz; Central Moesia accumulation – Dacian basin, deepest zone defined by f₀ < 0.15 Hz; South Moesia accumulation - up to the Danube, with 0.15 Hz < f₀ 0.5 Hz; Dobrogea Platform - distinct geomorphological features, with f₀ > 5 Hz; East of Carpathians (Moldavia region) - the East European and Scythian platforms; Focsani Basin - in the Central Moesia accumulation, but distinct due to large, local topographic effects and large sediment thicknesses. To provide a first-order illustration of how the proposed zonation is reflected in recorded ground motions, a preliminary comparative examination of response spectra was carried out using the strong-motion recordings associated with the earthquakes listed in Table 1 . For each recording, pseudo-acceleration response spectra were computed and subsequently normalized. Rather than focusing on absolute spectral amplitudes, this exploratory analysis emphasizes the shape of the response spectra, with particular attention given to spectral peaks associated with large amplifications. To this end, spectra were normalized with respect to their maximum spectral ordinate, allowing differences in spectral shape to be compared across sites and zonation categories with reduced sensitivity to earthquake magnitude. This choice is particularly relevant in the present context, as earthquakes of different magnitudes may preferentially excite different depths of stratified sedimentary packages. A direct comparison of unnormalized spectra, or spectra normalized to peak ground acceleration (PGA), would therefore tend to mix responses controlled by different stratigraphic levels, obscuring patterns related to zonation. Within each zonation category, in addition to computing the geometrical mean of normalized spectra, the number of spectral ordinates exceeding threshold of 0.75 relative to the number of recordings was rated across all periods, providing a simple measure of the persistence and width of high-amplification spectral intervals. These indicators are not intended as formal metrics, but as qualitative guides to highlight systematic differences between zones. The geometric mean of the normalized pseudo-spectral accelerations and the 0.75 ratio within each group of N recorded components was computed as: $$\:{PSA}_{norm,GM}\left(T\right)={\left(\prod\:_{i=1}^{N}\frac{{PSA}_{i}\left(T\right)}{max\:{PSA}_{i}\left(T\right)}\right)}^{1/N}$$ 1 $$\:{R}_{0.75}\left(T\right)=\frac{{N}_{\ge\:0.75}\left(T\right)}{N}$$ 2 where $$\:{N}_{\ge\:0.75}\left(T\right)=\sum\:_{i=1}^{N}\left\{\begin{array}{c}1,\:\frac{{PSA}_{i}\left(T\right)}{max\:{PSA}_{i}\left(T\right)}\ge\:0.75\:\\\:0,\:else\end{array}\right.$$ 3 The resulting spectral patterns offer an initial, visually guided indication of whether the proposed zonation captures meaningful differences in ground-motion behavior. The following observations are intentionally descriptive, serving to map variability rather than to explain it. The resulting spectral comparisons are illustrated in Figs. 5 and 6 . Figure 4 and Table 1 summarizes the stations and earthquakes included in analyses. For both the Mw 5–6 and Mw > 6 datasets, the Dobrogea region stands out clearly, characterized by a narrow amplification band and a spectral peak at approximately 0.1 s. This peak corresponds to the fundamental frequency identified in the f₀ mapping of Manea et al. (2020). For the larger-magnitude earthquakes, a similar peak is observed in the East region. In the case of Dobrogea, the persistence of this peak is consistent with the local site conditions, whereas in the eastern region, when compared to the other zones, its presence is more plausibly associated with lower attenuation at short periods. From this point of view, the eastern region appears, at this preliminary level of observation, to exhibit spectral characteristics closer to those of Dobrogea than to those of the remaining zones. Table 1 Vrancea intermediate-depth earthquakes used in the study grouped by magnitude class Date of earthquake Latitude Longitude Magnitude Depth Magnitude class 04.03.1977 45.77 26.76 7.4 94.0 Mw > 6 30.08.1986 45.52 26.49 7.1 131.0 30.05.1990 45.83 26.89 6.9 90.9 31.05.1990 45.85 26.91 6.4 86.9 27.10.2004 45.84 26.63 6.0 105.4 Mw 5–6 14.05.2005 45.64 26.53 5.5 148.5 18.06.2005 45.72 26.66 5.2 153.7 25.04.2009 45.68 26.62 5.4 109.6 06.10.2013 45.67 26.58 5.2 135.1 To enable an intra-dataset comparison, the Dobrogea region was selected as a reference (pivot) zone, owing to the presence of old seismic bedrock at very shallow depths and the absence of broad-band interference from local site conditions. An alternative reference could have been the North Moesia ridge; however, Dobrogea provides a more stable illustrative baseline. The North Moesia ridge is also characterized by shallow bedrock, but it represents a crest zone, where topographic effects may play a role. In addition, previous studies have suggested the presence of a low-velocity zone in the upper mantle beneath this area (Hauser, et al., 2001), which could further modify the recorded ground motions. Relative to the Dobrogea reference, and particularly for the Mw > 6 dataset, pronounced amplifications are observed in the period range of approximately 0.5–2.5 s, with the Focșani Basin and the South Moesia accumulation zone standing out most clearly. When examining the distribution of dominant spectral peaks - defined here as the ratio of peaks exceeding 0.75 of the maximum PSA - it is observed that the North Moesia ridge tends to lose energy in the short-period range of approximately 0.1–0.2 s. For large-magnitude earthquakes, a similar reduction is also apparent in both edge regions. This behavior is consistent with the presence of topographic effects, which are known to modify short-period ground motions in ridge and flank settings. In addition, the North Moesia edge exhibits a relatively broad amplification band, which may reflect a combination of local site conditions, topographic influences, or their joint interaction. By contrast, the South Moesia edge appears to concentrate amplification within a period range of approximately 0.35–0.5 s, suggesting the presence of a stratigraphic package that guides seismic energy within this interval. The two accumulation zones, Central Moesia and South Moesia, display broadly similar spectral behavior for moderate-magnitude earthquakes. However, for large-magnitude events, a clear divergence emerges between the two regions. In the South Moesia accumulation zone, larger earthquakes activate sedimentary packages that produce amplification extending up to periods of approximately 2 s. In contrast, the Central Moesia accumulation zone exhibits a response that is more similar to that of the North Moesia ridge, with the exception of a narrow period interval around 0.8–0.9 s, where some amplification is observed. This contrast suggests that the relative contribution of propagation effects and local site conditions varies with earthquake magnitude, suggesting a dynamic boundary between path-controlled and site-controlled behavior. Taken together, the proposed zonation successfully differentiates and highlights systematic differences in ground-motion behavior. The responses observed across the eight zones illustrate distinct manifestations of seismic effects, indicating that no zone can be meaningfully grouped with another without losing essential characteristics. Furthermore, averaging across zones (Fig. 5 ), for both magnitude ranges, hides these differences. In recognition of the variations highlighted by the proposed zonation, and of the additional limitations discussed throughout the paper, the following section introduces a framework aimed at assessing whether the apparent inconsistencies between Vrancea ground motions and standard modeling approaches are truly unique, or instead arise from previously undecomposed seismic complexity. 5. Framework for resolving seismic complexity under limited data conditions The conditions of the problem addressed in this section are the following. Reliable characterization of strong ground motions is required for seismic design and hazard definition, given the significant risk associated with Vrancea intermediate-depth earthquakes. However, the database of events with moment magnitude Mw > 6 consists of only four earthquakes, one of which is recorded at a single site (INCERC, Bucharest). In addition, the area strongly affected by Vrancea intermediate-depth earthquakes is substantially larger than the spatial scales typically considered in seismic mapping and hazard definition from a single seismic source. This inevitably introduces pronounced structural and site-related heterogeneity. While this heterogeneity has been classified through zonation and the underlying complexity has been explicitly defined in the previous chapter, this step further fragmented an already sparse strong-motion database. As a result, the primary challenge at this stage is not the identification of variability, but the fragility of the available data in the presence of clearly different ground-motion behavior between moderate-magnitude and large-magnitude event datasets, particularly with respect to local site conditions. In addition, two broad categories of parameters remain widely debated in the literature without convergence toward a common interpretation: source-related spectral shape, commonly linked to the stress-drop parameter, and path-related effects, represented by the combination of anelastic attenuation and geometrical scattering. To avoid circular reasoning, and in particular the use of stress drop as a free calibration parameter - which, as discussed previously, leads to unrealistically wide variability - stress drop is constrained in this framework to ranges consistent with general theoretical expectations. It is not treated as a Vrancea-unique dynamic parameter. Instead, the focus is placed on determining path-related parameters and on evaluating whether these, or other elements of the framework, reveal any genuine source uniqueness. This approach allows us to assess whether the apparent anomalies reported for Vrancea ground motions reflect truly distinctive physical processes, or whether they arise from previously undecomposed seismic complexity. The framework adopted in this study is defined as follows: (0) Zonation is introduced as a means of decomposing seismic complexity, providing a structured representation of heterogeneity without embedding ground-motion observations in its definition. (1) The database of major earthquakes ( Mw > 6 ) is too limited to sustain a minimum level of statistical robustness. To address this limitation, a complementary database of moderate-magnitude events ( Mw 5–6 ) is incorporated. For both datasets, characteristics are determined, and treated as dataset-specific attributes. (2) From the perspective of local site conditions, the two datasets exhibit significantly different behavior. This necessitates a uniformization of site effects without explicitly parameterizing them. This is achieved by defining an average ratio between the amplification patterns observed for large-magnitude events and those observed for moderate-magnitude events, and subsequently modifying the large-event dataset so that it reflects site-condition amplification characteristics consistent with those of the moderate-event dataset. The two datasets are then combined into a single database in which both event classes share aproximately the same reference site-condition behavior derived from the moderate-magnitude events. (3) Path-related parameters are determined and evaluated within this unified datasets. (4) Finally, the envelopes of amplification associated with local site conditions are analyzed, and additional factors potentially contributing to the observed variability of Vrancea ground motions are explored. The analysis is based on the decomposition of the total ground-motion spectrum at a site, following the formulation of Boore (2003), in which the observed motion is expressed as the product of source \(\:E({M}_{0},\:f)\) , path \(\:P(R,\:f)\) , site \(\:G\left(f\right)\) , and instrument contributions \(\:I\left(f\right)\) : $$\:Y\left({M}_{0},\:R,\:f\right)=E\left({M}_{0},\:f\right)P\left(R,\:f\right)G\left(f\right)I\left(f\right)$$ 4 Source parameters were defined according as following: density near source 3.45 g/cm 3 (Tondi, et al., 2009), velocity near source 4.60 km/s (Raykova & Panza, 2006) and radiation pattern 0.62 (Boore & Boatwright, 1984),. With respect to the source spectrum, a simplified Brune model (1970; 1971) with a single corner frequency was adopted. The stress-drop parameter was fixed at 100 bars, consistent with the value reported by Gusev et al. (2002) and with commonly accepted ranges in general seismological practice. A more detailed discussion of the stress-drop debate is provided in Chap. 3. Table 2 Database characteristics within each zonation category, for both moderate-magnitude and large-magnitude earthquakes Mw > 6 A. Nord >1 Hz B. Nord 0.15-1 Hz C. Central 0.5 Hz F. Dobrogea >5 Hz G. East H. Focsani basin Mean Mw 6.7 6.8 6.9 6.9 6.7 6.8 6.8 6.9 Mean R (km) 105.1 142.3 149.8 192.0 219.4 183.1 167.3 116.7 No. horizontal components 14 14 14 60 38 16 32 18 Equivalent M0 (dyne·cm) 2.3E + 26 3.2E + 26 4.4E + 26 4.1E + 26 2.6E + 26 2.7E + 26 3.2E + 26 3.9E + 26 Corner frequency fc (Hz) 0.21 0.18 0.16 0.17 0.20 0.20 0.18 0.17 Kappa 0.071 0.056 0.053 0.061 0.064 0.100 0.090 0.057 Mw 5–6 A. Nord >1 Hz B. Nord 0.15-1 Hz C. Central 0.5 Hz F. Dobrogea >5 Hz G. East H. Focsani basin Mean Mw 5.4 5.4 5.7 5.5 5.3 5.7 5.5 5.5 Mean R (km) 134.8 166.8 177.8 213.7 249.4 193.0 180.0 133.5 No. horizontal components 18 10 46 84 36 6 24 26 Equivalent M0 (dyne·cm) 3.5E + 24 3.3E + 24 9.4E + 24 5.6E + 24 2.5E + 24 1.1E + 25 5.0E + 24 5.8E + 24 Corner frequency fc (Hz) 0.97 0.99 0.67 0.82 1.09 0.65 0.85 0.81 Kappa 0.068 0.071 0.070 0.065 0.053 0.037 0.048 0.064 For each dataset and each zonation category, an equivalent moment magnitude was computed as the geometric mean of the magnitudes associated with the individual components within the group. This equivalent magnitude was then converted to seismic moment using the relationship proposed by Das et al. (2019) - \(\:lg\left({M}_{0}\right)\:=\:1.36{M}_{w}\:+17.2448\) . This choice requires clarification, as the moment-magnitude relationship of Hanks and Kanamori (1979), also employed in Boore (2003), is more commonly used. The alternative was not adopted superficially. The objective at this stage is not to analyze individual events or specific realizations of the database, but to characterize representative, generalized behavior at the level of each zone and dataset. For this reason, using particular seismic moment values and subsequently averaging them was avoided. The relation proposed by Das et al. (2019) was selected following a targeted search for a more reliable moment-magnitude formulation. While several global and local, Vrancea-specific, relations were considered, including Hanks and Kanamori (1979), Kanamori (1977), and Popescu et al. (2007; 2010), the local formulations are based on relatively limited datasets. As such, they do not provide a sufficiently robust basis to challenge the widely adopted Hanks and Kanamori (1979) relation. An important factor in the selection of Das et al. (2019) is that this relation provides a notably better approximation for the two major historical Vrancea earthquakes. Differences of approximately 1% for the 1986 event and 2% for the 1977 event are obtained, whereas substantially larger discrepancies are observed when using Hanks and Kanamori (1979) (about 37% and 29%, respectively), Kanamori (1977) (about 30% and 21%), or Popescu et al. (2007) (about 3% for 1986 and 9% for 1977). In addition, Das et al. (2019) provide a detailed discussion of the limitations of the Hanks and Kanamori (1979) relation, particularly with respect to the characteristics of the database on which it was derived and its assumed global applicability. Their generalized moment-magnitude scale was shown to perform consistently over a wide magnitude range ( Mw ≥ 4.5 ), across different focal depths and seismic regions. The scale is unsaturated and statistically more robust, making it better suited to the objectives of the present framework. From the path perspective, the following assumption was adopted: within each zonation category, for both moderate-magnitude and large-magnitude earthquakes, path-related characteristics vary with only hypocentral distance ( R ), but not in terms of the adopted attenuation model or geometrical scattering formulation. (1) The database For the spectral analysis, time-domain accelerograms processed by Craciun (2018) from seismic events in Table 1 were used. Historical recordings were available only in corrected form, while the remaining records were processed following the same procedure adopted by Pavel and Vacareanu (2015; 2018). Smoothed Fourier Amplitude Spectra (FAS) were computed for the horizontal components at 25 logarithmically spaced frequencies in the range 0.25–15 Hz, using a Konno–Ohmachi (1998) smoothing filter with a bandwidth of 0.2. For each database and each zone the geometrical mean of FAS were determined along with their equivalent moment magnitude, seismic moment, hipocentral distances, corner frequencies and kappa parameter. The high-frequency attenuation parameter 𝜅 was estimated for each zonation category from the decay of the Fourier Amplitude Spectra at high frequencies by regression in the frequency domain (Table 2 , Fig. 7 ). (2) “Uniformization” of site effects At this stage, the ratio between site-related amplifications derived from the large-magnitude dataset ( Mw > 6 ) and the moderate-magnitude dataset ( Mw 5–6 ), \(\:{A}_{M}/{A}_{m}\) , is defined (Fig. 8 ). To this end, an average FAS is first determined for each dataset and each zonation category after removing the effects of the source and geometrical scattering. Geometrical scattering is represented at this stage by an \(\:{R}^{-1}\:\) decay, consistent with the propagation of body waves in a homogeneous spherical medium. In addition, high-frequency diminution associated with local site conditions is removed using the \(\:k\) parameter determined for each zone. The reduced spectrum is thus expressed as: $$\:{Y}^{{\prime\:}}\left(R,f\right)=\frac{Y\left({M}_{0},R,f\right)}{E({M}_{0},f){R}^{-1}{e}^{-\pi\:kf}}$$ 5 where \(\:{Y}^{{\prime\:}}\left(R,f\right)\) represents the motion corrected for source and path effects, retaining predominantly the contribution of local site conditions. Because the two datasets exhibit different hipocentral distance distributions within each zonation category, the ratio \(\:{{Y}^{{\prime\:}}}_{M}\left({R}_{M},f\right)/{{Y}^{{\prime\:}}}_{m}\left({R}_{m},f\right)\) (between the large-magnitude and moderate-magnitude datasets) still contains a residual contribution from anelastic attenuation. In a first iteration, this effect is quantified using the attenuation model proposed by Oth et al. (2008), with \(\:Q\left(f\right)=114{f}^{0.96}\) . In a subsequent iteration, this correction is updated using the path attenuation functions determined independently for each zone (Fig. 8 ). Accordingly, the ratio of site amplifications between the two datasets is expressed as: $$\:\frac{{A}_{M}\left(f\right)}{{A}_{m}\left(f\right)}=\frac{{{Y}^{{\prime\:}}}_{M}\left({R}_{M},f\right)}{{{Y}^{{\prime\:}}}_{m}\left({R}_{m},f\right)}{e}^{\frac{\pi\:f({R}_{M}-{R}_{m})}{Q\left(f\right){c}_{Q}}}$$ 6 where \(\:{R}_{M}\) and \(\:{R}_{m}\) denote representative equivalen hipocentral distances for the large- and moderate-magnitude datasets, respectively, for each zone. For each zonation category, the large-magnitude dataset is further adjusted as: $$\:{{Y}^{{\prime\:}{\prime\:}}}_{M}\left(f\right)=\frac{{Y}_{M}\left({M}_{M0},{R}_{M},f\right)}{{E}_{M}({M}_{M0},f){(e}^{-\pi\:{k}_{M}f}{\left)\right(A}_{M}/{A}_{m})}$$ 7 while the moderate-magnitude dataset is expressed as: $$\:{{Y}^{{\prime\:}{\prime\:}}}_{m}\left(f\right)=\frac{{Y}_{m}\left({M}_{m0},{R}_{m},f\right)}{{E}_{m}({M}_{m0},f){(e}^{-\pi\:{k}_{m}f})}$$ 8 With this formulation, both datasets retain only path-related characteristics, while the site amplification is consistently represented by the conditions inferred from the moderate-magnitude dataset. At this stage, the two datasets become compatible and can be combined within each zonation category, allowing the estimation of path-related parameters without contamination from source effects or heterogeneous local site amplification. (3) Path-related parameters Having unified the datasets within each zonation category, anelastic attenuation was derived from the slope of the logarithmic Fourier adjusted Acceleration Spectra. Alternative formulations for geometrical scattering, ranging between \(\:{R}^{-0.5}\) and \(\:{R}^{-1}\) , were also explored, acknowledging the variability reported in the literature and to assess whether such choices could lead to improved attenuation estimates. However, the \(\:{R}^{-1}\) formulation, which is also supported by the physical plausibility, provided the most consistent results across all zones and was therefore retained. After the first iteration, the \(\:{A}_{M}/{A}_{m}\) ratio was recomputed using the attenuation relationships derived for each zone, and a second iteration was performed to assess the sensitivity of the results to differences in hypocentral distance. The estimates were found to be insensitive to the variations, both with respect to hypocentral distance and to reasonable stress-drop parameter modifications. (4) The envelopes of amplification associated with local site conditions As a final step, site-related amplification functions were isolated for both datasets and for each zonation category. The plausibility of these site amplifications provides an additional consistency check on the procedure and on the realism of the resulting parameters. This is rather an evalutaion of results final step. 6. Results Following the steps outlined in the previous chapter, this section presents the results obtained and highlights the internal coherence of the proposed framework. As a first step, the ratio between site amplification functions derived from the large-magnitude dataset ( Mw > 6 ) and the moderate-magnitude dataset ( Mw 5–6 ) was determined for each zonation category. Figure 8 shows that this ratio varies with values between approximately 0.5 and 6, depending on frequency and zone. Differences between the first and second iterations reach up to about 30% and follow the trend imposed by the difference between the attenuation model of Oth et al. (2008), used as the initial reference, and the attenuation functions obtained through the proposed procedure. For frequencies above approximately 5 Hz, the amplification ratio falls below unity in several zonation categories. Such behavior is observed in the Focșani Basin, Central Moesia accumulation, South Moesia accumulation, and the North Moesia edge. These regions are characterized by thick sedimentary successions, either associated with deep basin structures and/or with pronounced lithospheric bending related to the formation of the Carpathian orogen, which favor the accumulation of deep sediments. By contrast, no systematic reduction of the amplification ratio below unity is observed in the North Moesia ridge, South Moesia edge, Dobrogea Platform, or the East region. Except for the East region, these areas are characterized by relatively shallow local site conditions, typically limited to depths of the order of 100 m or less. In the East region, although sedimentary sequences locally reach several hundred meters in thickness, they are arranged in a laterally continuous and chronologically ordered manner, with a gradual thinning toward the east and without pronounced basin geometries capable of significantly distorting wave propagation. Following the uniformization of the two datasets with respect to local site amplification, anelastic attenuation functions were derived for each zonation category (Table 3 , Fig. 8 ). The only region for which a reliable attenuation function could not be independently determined is Dobrogea. Owing to the limited number of available recordings, the data did not allow a stable estimation of frequency-dependent attenuation for this zone. However, based on the similarities observed during the zonation analysis and the comparable spectral behavior identified at a preliminary level, the attenuation function derived for the East region was adopted for Dobrogea for the purpose of further evaluation. For all other zones, the determination of anelastic attenuation yields coefficients of determination ( \(\:R²\) ) exceeding 88%, indicating a good overall fit between the proposed attenuation models and the observed spectra. The highest \(\:R²\) value, approximately 98%, is obtained for the South Moesia accumulation zone, which also corresponds to the region with the largest number of available recordings. These results indicate that the attenuation estimates are statistically stable and can be considered reliable. Figure 8 highlights pronounced differences in attenuation behavior between the zonation categories. The lowest attenuation levels are observed for the North Moesia ridge, whereas higher overall attenuation characterizes the North Moesia edge and the South Moesia accumulation. The Focșani Basin exhibits the strongest frequency-dependent variability, indicating a particularly sensitive response to spectral content. These contrasts emphasize the strong structural heterogeneity of the Vrancea-affected region and provide a direct explanation for the wide range of attenuation parameters reported in previous studies based on non-zonated datasets. Table 3 Anelastic attenuation parameters derived for each zonation category Attenuation parameters \(\:{Q}_{0}{f}^{\alpha\:}\) A. Nord >1 Hz B. Nord 0.15-1 Hz C. Central 0.5 Hz F. Dobrogea >5 Hz G. East H. Focsani basin \(\:{Q}_{0}\) 476 90 143 118 200 286* 286 79 \(\:\alpha\:\) 1.44 0.96 1.31 1.09 1.16 1.49* 1.49 1.58 \(\:{R}^{2}\) 0.88 0.94 0.89 0.98 0.97 - 0.89 0.94 \(\:{c}_{Q}\:(km/s)\) 4.05 * as East With respect to the envelopes of site-related amplification derived for each zonation category (Fig. 9 ), the obtained results are physically plausible and consistent with both the recorded ground motions and the independent observations derived from stratigraphic information. A clear magnitude-dependent behavior is observed across several zones, indicating that an order of magnitude increase activates deeper stratigraphic packages. This behavior provides observational support for a dynamic boundary between path-controlled and site-controlled effects, rather than a fixed separation depth. Strong amplification at short periods - around 0.1 s, consistent to Manea et al. (2020) - is observed in both the Dobrogea Platform and the East region. In contrast, the Focșani Basin exhibits pronounced amplification at long periods (low frequencies), consistent with the activation of deep sedimentary structures. The North Moesia edge displays a comparatively weak dependence on earthquake magnitude, with similar amplification envelopes obtained for both moderate- and large-magnitude events. This behavior suggests a stratigraphic configuration that responds coherently over a wide range of input levels, without pronounced shifts in the frequency range of maximum amplification. For large-magnitude earthquakes, a clear distinction emerges between the Central Moesia accumulation and the South Moesia accumulation zones. Although these two regions cannot be analyzed jointly due to their different amplification levels, their amplification envelopes exhibit similar overall shapes, with peaks occurring at comparable periods. This similarity indicates that both zones likely involve stratigraphic packages of comparable nature, even though their overall amplification levels differ. In the Central Moesia accumulation zone, the absence of systematically larger long-period amplification relative to the South Moesia accumulation suggests that deeper site conditions are not more effectively activated in this region. Instead, the observed shift in amplification levels between the two zones indicates differences in the impedance structure rather than in the fundamental nature of the activated stratigraphy. In the intermediate period range of approximately 0.25–0.75 s, a similar amplification behavior is observed for the Central Moesia accumulation and the East region, pointing to the possible presence of comparable stratigraphic features across the two tectonic domains. In the South Moesia edge, large-magnitude earthquakes activate a stratigraphic package characterized by a fundamental frequency of approximately 2 Hz. This value is consistent with an average-ish fundamental frequencies reported by Manea et al. (2020). Taken together, the results obtained within the proposed framework are internally consistent, physically plausible, and non-unique in relation to global observations. They demonstrate that the wide range of parameter values reported in the literature for Vrancea intermediate-depth ground motions does not reflect the existence of different physical phenomena. Instead, it arises from the strong structural complexity and heterogeneity of the region, which, when not explicitly classified and decomposed, lead to apparently divergent parameter estimates. 7. Conclusions This study addresses and aims at solving a long-standing ambiguity in the interpretation of strong ground motions generated by the Vrancea intermediate-depth seismic source by explicitly defining, structuring, and decomposing seismic complexity. Rather than treating Vrancea as an anomalous case requiring source-specific adjustments, the analysis demonstrates that the apparent inconsistencies reported in the literature arise from unresolved heterogeneity acting simultaneously at the source, path, and site levels, compounded by sparse strong-motion data. The primary contribution of this work is the definition and validation of a general framework applicable to structurally complex regions with limited strong-motion databases, designed to robustly constrain parameters that are repeatedly identified as problematic in such settings. In the Vrancea case, these parameters include anelastic attenuation, geometrical scattering, stress drop, and local site conditions. The framework is not tuned to Vrancea-specific behavior; instead, it enforces physical plausibility and internal consistency across all model components. A central element of the framework is the explicit definition of seismic complexity through zonation, constructed independently of strong-motion recordings. Geological, tectonic, geophysical, and geomorphological information is used as a pivot for organizing heterogeneity, avoiding circular reasoning and preventing observational bias from being embedded in the grouping of data. This zonation enables the systematic decomposition of variability that otherwise manifests as instability in parameter estimation. Within this structure, the study provides constrained and physically consistent determinations of key path-related parameters, including frequency-dependent anelastic attenuation and geometrical scattering, and high-frequency attenuation parameter κ determined as a secondary outcome. The results demonstrate that the wide range of attenuation relations reported in the literature can be directly explained by spatial variability along propagation paths, rather than by source-specific anomalies. Once zonation is introduced, attenuation behavior becomes stable, statistically robust, and interpretable. Stress drop is deliberately not treated as a calibration parameter. By constraining it within ranges compatible with general seismological theory, the analysis avoids compensating unresolved path or site effects through source adjustments. The results show that no Vrancea-specific source physics are required once complexity is properly decomposed. A further contribution of this work is the explicit determination of site amplification envelopes for each zonation category. These envelopes provide generalized descriptions of local site behavior that can be directly used in applications such as GMPE development and seismic hazard assessment. The results demonstrate a clear magnitude-dependent activation of stratigraphic packages, supporting the concept of a dynamic boundary between path-controlled and site-controlled effects, rather than a fixed depth to seismic bedrock. To address the intrinsic limitation imposed by the scarcity of strong-motion recordings from large Vrancea earthquakes, the framework introduces a systematic “uniformization” of local site conditions between moderate- and large-magnitude datasets. By compensating for magnitude-dependent site amplification differences, the statistical power of the database is increased while preserving regional specificity. This approach allows moderate-magnitude events to be meaningfully integrated into the estimation of path-related parameters without contaminating results with incompatible site effects. The study also introduces a simple and transparent preliminary measure of spectral amplification persistence, defined as the rate of spectral ordinates exceeding 0.75 of the normalized peak amplitude across recordings. While intentionally non-parametric, this measure proves effective in highlighting high-amplification spectral intervals and in distinguishing systematic zonal behavior, providing an additional qualitative constraint on the interpretation of results. More broadly, the integration of transdisciplinary information from different fields - geology, tectonics, basin evolution, and seismology - proves essential for defining seismic complexity in a way that removes ambiguity rather than adding interpretative layers. Through this integration, several long-standing debates in the literature concerning source spectral characteristics, attenuation, and site effects are reconciled without invoking exceptional behavior. In conclusion, the Vrancea intermediate-depth seismic source does not challenge general seismological principles. It represents a case in which complexity is amplified and cannot be neglected. When this complexity is explicitly defined, structured, and consistently treated within a unified framework, the apparent anomalies disappear. The methodology presented here is transferable to other tectonic environments characterized by strong heterogeneity and sparse strong-motion data, offering a robust pathway toward physically consistent seismic characterization under limiting observational conditions. Declarations Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author contributions Anabella Cotovanu: Conceptualization, Methodology, Formal analysis, Investigation, Writing - Original Draft; Elisei Cojan: Visualization, Writing - Review & Editing; Radu Vacareanu: Supervision, Resources, Project administration, Writing - Review & Editing. Acknowledgement This research was funded by a grant of the Ministry Education and Research, CCCDI-UEFISCDI, project number PN-IV-P6-6.1-CoEx-2024-0102, within PNCDI IV. Data Availability The data that support the findings of this study are available from the corresponding author upon reasonable request. References Aldea, A., Vacareanu, R., Lungu, D., Pavel, F., & Arion, C. (2022). GMPEs for Romania’s Vrancea Intermediate Depth Seismic Source. In R. I. Vacareanu (Ed.), Progresses in European Earthquake Engineering and Seismology. ECEES 2022. Bucharest: Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. doi:https://doi.org/10.1007/978-3-031-15104-0_6 Besutiu, L. (2006). 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Radulian, M., Mândrescu, M., Panza, G., Popescu, E., & Utale, A. (2000). Characterization of seismogenic zones of Romania. In R. M. Panza G.F. (Ed.), Seismic Hazard of the Circum-Pannonian Region. (pp. 57–77). Birkhäuser, Basel.: Pageoph Topical Volumes. doi:https://doi.org/10.1007/978-3-0348-8415-0_4 Radulian, M., Trifu, C., & Cârbunar, F. (1991). Numerical simulation of the earthquake generation process. pure and applied geophysics, 136 , 499–514. doi:https://doi.org/10.1007/BF00878584 Räkers, E., & Müller, G. (1982). The Romanian earthquake of March 4, 1977. III. Improved focal model and moment determination. Journal of Geophysics, 50 , 143–150. Raykova, R., & Panza, G. (2006). Surface waves tomography and non-linear inversion in the southeast Carpathians. Physics of the Earth and Planetary Interiors, 157 (3–4), 164–180. doi:https://doi.org/10.1016/j.pepi.2006.03.019 Russo, R., Mocanu, V., Radulian, M., Popa, M., & Bonjer, K.-P. (2005). Seismic attenuation in the Carpathian bend zone and surroundings. Earth and Planetary Science Letters 237, 695–709 . Sokolov, V., Bonjer, K.-P., Oncescu, M., & Rizescu, M. (2005). Hard rock spectral models for intermediate-depth Vrancea, Romania, earthquakes. Bulletin of the Seismological Society of America (2005) 95 (5): 1749–1765 . Sperner, B., Lorenz, F., Bonjer, K., Hettel, S., Müller, B., & Wenzel, F. (2001). Slab Break-off – Abrupt Cut or Gradual Detachment? New Insights from the Vrancea Region (SE Carpathians, Romania). Terra Nova, 13:172–179 . Stoica-Negulescu, E. (2016). From Geophysics to Petroleum Systems within Geological Frame of Romania. Barcelona, Spain: International Conference and Exhibition. doi:https://doi.org/10.1190/ice2016-6491064.1 Tondi, R., Achauer, U., Landes, M., Daví, R., & Besutiu, L. (2009). Unveiling seismic and density structure beneath the Vrancea seismogenic zone, Romania. Journal of Geophysical Research, 114 (B11307), 1–17. doi: https://doi.org/10.1029/2008JB005992 Trifu, C.-I. (1987). Depth distribution of local stress inhomogeneities in the Vrancea Region, Romania. Journal of Geophisical Research, 92 (B13), 13878–13886. doi: https://doi.org/10.1029/JB092iB13p13878 Trifu, C.-I., & Radulian, M. (1989). Asperity distribution and percolation as fundamentals of an earthquake cycle. Physics of the Earth and Planetary Interiors, 58 (4), 277–288. doi:https://doi.org/10.1016/0031-9201(89)90100-3 Vacareanu, R., Demetriu, S., Lungu, D., Pavel, F., Arion, C., Iancovici, M.,. .. Neagu, C. (2014). Empirical ground motion model for Vrancea intermediate-depth seismic source. EARTHQUAKES AND STRUCTURES, 6 (2), 141–161. doi:https://doi.org/10.12989/eas.2014.6.2.141 Vacareanu, R., Radulian, M., Iancovici, M., Pavel, F., & Neagu, C. (2015). Fore-Arc and Back-Arc Ground Motion Prediction Model for Vrancea Intermediate Depth Seismic Source. Journal of Earthquake Engineering, 19 (3), 535–562. doi:https://doi.org/10.1080/13632469.2014.990653 Wenzel, F., Lungu, D., & Novak, O. (1998). Vrancea Earthquakes: Tectonics, Hazard and Risk Mitigation. Dordrecht/Boston/London: Kluwer Acad. Publ. Wyk de Vries, B., Byrne, P., Delcamp, A., Einarson, P., Göğüş, O., Guilbaud, M.-N.,. .. Vye, E. (2018). A global framework for the Earth: putting geological sciences in context. Global and Planetary Change, 171 , 293–321. doi:https://doi.org/10.1016/j.gloplacha.2017.12.019 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 04 Apr, 2026 Editor invited by journal 03 Apr, 2026 Editor assigned by journal 03 Apr, 2026 First submitted to journal 31 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9267402","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":617597123,"identity":"91b73cfc-2cb1-4b99-977a-6511c855280d","order_by":0,"name":"Anabella Cotovanu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIiWNgGAWjYHACNgaGAgskPnsDMVoMJEAMRohangOMhDSha5FIwK+Ff3bzswcfDCTkGdgPH3/wsc0uz+Dm6/QHPxjuyeHSInHnmLnhDAMJwwaetMTGmW3JxQa3czc29jAUG+O05kaCmTSPgQRjgwSPYTPPGebEDUAtDTwMCYm4XCd/I/2b9B8DCXuolvrEDTfPbmz8g0eLwY0cM2mg9xMhWioOJ264wbuxGZ8thjdyyg17DCSS24B+mTmj4njizDO5G2fLGCTg9IvcjfRtD35U2Nj2sx8+8OGDQXVi3/GzGz6+qUjAGWJwwIbmYIIaRsEoGAWjYBTgAQAzmVhpn5bHDgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-1710-9056","institution":"Technical University of Civil Engineering of Bucharest: Universitatea Tehnica de Constructii Bucuresti","correspondingAuthor":true,"prefix":"","firstName":"Anabella","middleName":"","lastName":"Cotovanu","suffix":""},{"id":617597124,"identity":"1ffd2402-6dc8-4cfb-8a8f-2951cb2f10ab","order_by":1,"name":"Elisei Cojan","email":"","orcid":"","institution":"Ferdinand I Military Technical Academy: Academia Tehnica Militara Ferdinand I","correspondingAuthor":false,"prefix":"","firstName":"Elisei","middleName":"","lastName":"Cojan","suffix":""},{"id":617597125,"identity":"18f6aec7-d991-4179-af99-0f4e0632a31b","order_by":2,"name":"Radu Vacareanu","email":"","orcid":"","institution":"Technical University of Civil Engineering of Bucharest: Universitatea Tehnica de Constructii Bucuresti","correspondingAuthor":false,"prefix":"","firstName":"Radu","middleName":"","lastName":"Vacareanu","suffix":""}],"badges":[],"createdAt":"2026-03-30 13:12:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9267402/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9267402/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106835481,"identity":"d8a19c3c-08d0-47fa-9a10-19a5c2b3e77a","added_by":"auto","created_at":"2026-04-14 02:00:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":4920198,"visible":true,"origin":"","legend":"\u003cp\u003eMap of the major morphostructural units of Romania, after Juravle (2009); the approximate extent of the Dacia and Focsani basins based on Jipa and Olariu (2009)and Borleanu et al. (2011), with Focșani basin contours indicating sedimentary layer depth in meters; the distribution of Vrancea earthquake epicenters (Radulian, et al., 2019); and the location of the sections presented in Fig. 3\u003c/p\u003e","description":"","filename":"Fig.1.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/327e7c49d62169f99034421d.png"},{"id":106960530,"identity":"2a891125-6ea5-4b94-8ba7-fd495ada304e","added_by":"auto","created_at":"2026-04-15 09:21:38","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":4459387,"visible":true,"origin":"","legend":"\u003cp\u003eSimplified cross-sections of the main tectonic units, including the asthenosphere, lithospheric mantle, and major crustal layers after Matenco et al. (2010) and Wyk de Vries et al. (2018), and the hypocenters of Vrancea earthquakes (Radulian, et al., 2019)\u003c/p\u003e","description":"","filename":"Fig.2.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/74995faac3946c0edde373a8.png"},{"id":106960333,"identity":"4d70f5d0-19d7-461b-85b7-0b621ffcd7b6","added_by":"auto","created_at":"2026-04-15 09:20:16","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":5334033,"visible":true,"origin":"","legend":"\u003cp\u003eSimplified cross-sections along three representative Carpathians–foreland profiles (as shown in Fig. 1), after Matenco et al. (2010), complemented in Section A from A` with Juravle (2009) and in Section B the Dobrogea sector with Munteanu et al. (Munteanu, et al., 2012)\u003c/p\u003e","description":"","filename":"Fig.3.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/9f6917e9e183eb32ef45c42e.png"},{"id":106835483,"identity":"8e834083-4708-4a9d-95f8-52747a07f49b","added_by":"auto","created_at":"2026-04-14 02:00:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2557141,"visible":true,"origin":"","legend":"\u003cp\u003eZonation based on the combined criteria adopted in this study, including the f₀ mapping, tectonic setting, basin geometry, near-surface stratification, and the seismic stations used in the analysis\u003c/p\u003e","description":"","filename":"Fig.4.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/625e2690fed28bdc8228ccf9.png"},{"id":106961085,"identity":"6d216f4a-d992-4aef-af26-a5d864d8893d","added_by":"auto","created_at":"2026-04-15 09:24:12","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":4512418,"visible":true,"origin":"","legend":"\u003cp\u003eThe geometric mean of the normalized PSA within each zone and magnitude class, and the ratio of each relative to F. Dobrogea geometric mean of the normalized PSA\u003c/p\u003e","description":"","filename":"Fig.5.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/820bde8fbd4955f6b4af3f1c.png"},{"id":106835485,"identity":"12ffa7f9-83e3-4e01-bb7d-f211eb527a2a","added_by":"auto","created_at":"2026-04-14 02:00:59","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":5316638,"visible":true,"origin":"","legend":"\u003cp\u003eThe 0.75 ratio - number of spectral ordinates exceeding threshold of 0.75 relative to the number of recording within each zone and magnitude class\u003c/p\u003e","description":"","filename":"Fig.6.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/3f750fd3d65d70deba492f0d.png"},{"id":106835489,"identity":"748d8bc9-8d3c-4824-bbe7-28a2f217e802","added_by":"auto","created_at":"2026-04-14 02:00:59","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2646228,"visible":true,"origin":"","legend":"\u003cp\u003eThe 0.75 ratio - number of spectral ordinates exceeding threshold of 0.75 relative to the number of recording within each zone and magnitude class\u003c/p\u003e","description":"","filename":"Fig.7.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/162a36599f4b370226a2f132.png"},{"id":106961342,"identity":"102bd1f3-36a3-4aff-8a0e-5a8f1b2b2ab5","added_by":"auto","created_at":"2026-04-15 09:25:07","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":1477831,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend.\u003c/p\u003e","description":"","filename":"Fig.8.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/23e4c64878cd9f5f5db4be86.png"},{"id":106835486,"identity":"97bb317c-b076-4927-a97a-ec162e9a7320","added_by":"auto","created_at":"2026-04-14 02:00:59","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":4195844,"visible":true,"origin":"","legend":"\u003cp\u003eEnvelopes of frequency and period dependent site-related amplification derived for each zonation category, for both moderate-magnitude and large-magnitude earthquakes\u003c/p\u003e","description":"","filename":"Fig.9.png","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/fdc7253107ba7f518d3e4cbc.png"},{"id":106963392,"identity":"a4002115-a341-4ef6-9b16-c13d3bb5acdc","added_by":"auto","created_at":"2026-04-15 09:44:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":36573254,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9267402/v1/77b8fcdc-819e-4a24-990b-e8fed134f909.pdf"}],"financialInterests":"","formattedTitle":"Defining and resolving seismic complexity through a unified source–path–site framework: the Vrancea intermediate-depth ground motions","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIncreasing seismic reliability of elements at risk requires an accurate and physically consistent characterization of seismic action. Seismic hazard analyses depend on how well the properties of seismic sources and the propagation media are understood and represented. For example, the stochastic simulation of ground motions (Boore, 2003) relies on a wide range of parameters, including the properties of materials in the vicinity of the hypocenters (such as seismic velocities and densities), focal mechanisms, released energy, radiation patterns, spectral characteristics near the source, source and path durations, attenuation and scattering effects along the propagation path, as well as the definition and behavior of near-surface geological layers.\u003c/p\u003e \u003cp\u003eSeismic hazard results are inputs for structural design and retrofit of buildings and structures, seismic risk assessment and management, and the evaluation of innovative design solutions or damage-mitigation strategies (Calofir, et al., 2024; Gheorghe \u0026amp; Vacareanu, 2026; Munteanu, et al., 2025; Nica, et al., 2022). Consequently, an accurate characterization of seismic ground motions directly contributes to improving seismic reliability (by extension, safety) and preparedness for major seismic events.\u003c/p\u003e \u003cp\u003eFor the estimation of seismic parameters from strong-motion databases, a variety of approaches have been employed, including inversion-based techniques such as the Generalized Inversion Technique (GIT), nonlinear and Bayesian inversion methods, empirical regression approaches, stochastic modeling, and spectral-ratio techniques. These direct, data-driven approaches are often further constrained by independent information derived from indirect methods, such as tomographic imaging, geological and geophysical models of the crust and upper mantle, and physically based bounds on seismic parameters.\u003c/p\u003e \u003cp\u003eMost direct, data-driven approaches have been applied with greater confidence and success to shallow seismic sources and regions characterized by relatively homogeneous geological structures. In such settings, the underlying assumptions regarding source behavior, wave propagation, and site response are more easily satisfied. However, there are tectonic environments in which the application of these methods leads to results that are inconsistent with observed ground motions, statistically weak due to the limited availability of strong-motion recordings, or overly simplified through assumptions of spatially uniform behavior. In these cases, methodological simplifications - such as assuming similar seismic behavior across large regions or treating complex structures as homogeneous - do not sufficiently account for the pronounced heterogeneity of the system, thereby reducing the reliability of the resulting seismic parameters.\u003c/p\u003e \u003cp\u003eThe Vrancea intermediate-depth seismic source exemplifies a tectonic setting in which standard ground-motion analysis methods encounter persistent limitations. It is frequently excluded from global strong-motion analyses, or, when such methods are applied, they lead to parameter estimates that are either difficult to interpret consistently or so highly particular that they suggest behavior distinct from that observed in other seismic regions. Even when coherent results are obtained within a given methodological framework, their statistical reliability is constrained by the limited size of the Vrancea strong-motion database.\u003c/p\u003e \u003cp\u003eFor instance, Oth et al. (2007; 2008; 2009) employed stress-drop values approximately twenty times higher than commonly adopted reference values in their analyses to address the reported inconsistencies. Other studies (Popescu, et al., 2016; Radulian, 2017) highlight difficulties in applying source scaling relationships derived from small earthquakes to larger events, leading to the assumption of distinct source behaviors across different magnitude ranges. Similarly, for path attenuation, the literature adopts two contrasting sets of formulations, closely tied to different assumptions regarding geometrical scattering (Oncescu, et al., 1999; Sokolov, et al., 2005; Oth, et al., 2008) versus (Pavel, 2015; Pavel \u0026amp; Vacareanu, 2015; Pavel \u0026amp; Vacareanu, 2018). Uncertainties persist also with respect to site effects: the applicability of H/V spectral ratios has been questioned by Oth et al. (2009), while other studies continue to consider it reliable (Pavel, 2015). In addition, the thickness and characterization of near-surface stratification remain weakly constrained, and the characterization of linear and nonlinear site behavior is insufficiently documented.\u003c/p\u003e \u003cp\u003eEven when the analysis moves away from detailed parameter-level descriptions toward probabilistic approaches that rely on statistically robust representations of seismic behavior, a fundamental limitation remains: the size of the available Vrancea strong-motion database. This limitation has been addressed by incorporating strong-motion recordings from other seismic regions to improve statistical robustness (Vacareanu, et al., 2014), with an unavoidable trade-off in terms of regional seismic specificity. A detailed discussion of Ground Motion Prediction Equations (GMPEs) for Vrancea for the last 30 years and their limitations is made in Aldea et al. (2022).\u003c/p\u003e \u003cp\u003eThis study aims to define the complexity of the interacting factors that govern strong ground motions in the region influenced by the Vrancea intermediate-depth seismic source and to reduce the ambiguity that has persisted in their interpretation. Addressing this problem requires the integration of information across multiple disciplinary domains, reflecting the inherently complex nature of the system.\u003c/p\u003e \u003cp\u003eThrough this process, the apparent multiplicity of contributing factors is shown to reduce to two primary factors underlying the observed ground-motion complexity: zonation and local site conditions. To achieve this reduction, a dedicated methodological framework is developed for the characterization of seismic ground motions in structurally complex settings under conditions of sparse strong-motion data. Within this framework, key seismic parameters that have remained debated in the literature (including anelastic attenuation, geometrical scattering, stress drop, and site behavior) are systematically re-evaluated and constrained in a physically consistent way.\u003c/p\u003e \u003cp\u003eBeyond defining a methodology suited to regions characterized by sparse strong-motion databases and levels of complexity that do not conform to conventional source and site models, this study adopts a holistic treatment of earthquake ground-motion generation. Rather than isolating individual components, the analysis addresses source, path, and site effects simultaneously, seeking physical and scientific consistency across all contributing variables without resorting to special-case assumptions or deviations from established seismic principles.\u003c/p\u003e \u003cp\u003eThe study integrates a transdisciplinary analysis of the geologic and tectonic evolution of the region, which motivates the spatial zoning adopted in the analysis - an essential step for decoupling complex interactions and enabling focused interpretation where multiple effects are strongly intertwined. This is followed by an initial spectral comparison across the defined zones, providing a first-order indication of distinct ground-motion behavior and allowing the identification of potential deviations. Within this framework, the final stage of the study addresses the estimation and constraint of several seismic parameters that have remained debated in the literature, as outcomes of a coherent clarification of source\u0026ndash;path\u0026ndash;site complexity and in consistency with physical plausibility and historical observations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis endeavor addresses several long-standing scientific debates and reconciles results that have varied across studies and methodological approaches, which have often led to the conclusion that the Vrancea seismic source exhibits fundamentally different behavior. The present analysis demonstrates instead that the apparent anomalies arise from a high degree of complexity. When this complexity is treated coherently and in accordance with the specific characteristics of the source, path, and local site conditions, the Vrancea seismic source and the affected region are shown to conform to general seismological principles.\u003c/p\u003e \u003cp\u003eThe concrete outcomes of this study include: a methodological framework designed for complex settings with sparse strong-motion data; a geologically and tectonically motivated zoning supported by observational evidence; constrained characterization of path effects, namely anelastic attenuation and geometrical spreading; descriptions of local site conditions and their modification under strong shaking; envelope representations of site amplification; and, most importantly, a systematic structuring and definition of seismic complexity itself.\u003c/p\u003e"},{"header":"2. Vrancea intermediate-depth earthquakes","content":"\u003cp\u003eRomania is among the European countries with the highest levels of seismic hazard, largely due to the influence of the Vrancea intermediate-depth seismic source. Located beneath the south-eastern bend of the Carpathian Arc, Vrancea represents a compact and isolated nested seismogenic volume characterized by intense and persistent seismic activity concentrated at depths of approximately 60\u0026ndash;200 km (Ismail-Zadeh, et al., 2012; Manea, et al., 2011). This intermediate-depth seismicity dominates the national hazard, controlling seismic design requirements over more than two-thirds of the country.\u003c/p\u003e \u003cp\u003eIn a regional tectonic context, the Vrancea source is situated within a zone of complex continental convergence, at the junction of several major tectonic units: East European Platform, the Scythian Platform, the Moesian Platform, the North Dobrogea Orogen, and the Transylvanian Basin (Intra-Alpine Plate) (Radulian, 2014) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe Vrancea source is commonly described as an intraslab seismic nest, in which large amounts of seismic energy are repeatedly released within a very limited mantle volume. The cumulative annual seismic energy release associated with Vrancea intermediate-depth earthquakes has been shown to be comparable to that of the entire Southern California region (Wenzel, et al., 1998). In a global perspective, Vrancea belongs to a very small class of highly active intermediate-depth seismic nests, alongside regions such as Bucaramanga (Colombia) and Hindu Kush (Afghanistan), and represents the only segment of the Carpathian orogenic system exhibiting sustained intermediate-depth seismicity (Manea, et al., 2011).\u003c/p\u003e \u003cp\u003eFrom the beginning of the 20th century to the present, the Vrancea source has generated fourteen earthquakes with moment magnitudes \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026ge; 6.3\u003c/em\u003e. Only four of these events were instrumentally recorded: March 4, 1977 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.4, h\u0026thinsp;\u0026asymp;\u0026thinsp;94 km\u003c/em\u003e), August 30, 1986 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.1, h\u0026thinsp;\u0026asymp;\u0026thinsp;131 km\u003c/em\u003e), and May 30\u0026ndash;31, 1990 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e6.9 and M\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e6.3, h\u0026thinsp;\u0026asymp;\u0026thinsp;91\u0026ndash;87 km\u003c/em\u003e). The largest event, the 1977 earthquake, was recorded within Romania at only a single station in Bucharest, highlighting the limited availability of reliable strong-motion data for major Vrancea earthquakes. The effects of these events extend beyond national borders, with macroseismic intensities of IV\u0026ndash;VI MSK documented in neighboring regions such as Moldavia, Bulgaria, and Ukraine (Kronrod, et al., 2013; Aldea, et al., 2022).\u003c/p\u003e \u003cp\u003eFrom a seismotectonic perspective, Vrancea intermediate-depth earthquakes cluster within a near-vertical lithospheric fragment descending into the mantle, separated from crustal seismicity by a relatively aseismic zone. Focal-mechanism solutions indicate a predominance of compressional reverse faulting with subvertical extension for the intermediate-depth events, in contrast to the extensional or strike-slip mechanisms that characterize the local crustal seismicity (Radulian, et al., 2018). The origin of the seismogenic body has been attributed to either a delaminated continental lithosphere or a remnant oceanic slab and lithospheric-instability scenarios, including delamination and gravitational or thermal instabilities (Sperner, et al., 2001; Cloetingh, et al., 2004; Knapp, et al., 2005). Recent evidence supports interpretations involving an oceanic lithospheric fragment undergoing dehydration-related processes (Ferrand \u0026amp; Manea, 2021). Regardless of the specific origin model, all proposed frameworks consistently indicate a high-velocity, high-density, and mechanically stressed body capable of sustaining persistent intermediate-depth seismicity within a limited volume, providing the physical basis for the strong and far-reaching effects observed during major Vrancea earthquakes.\u003c/p\u003e \u003cp\u003eRecorded strong ground motions generated by the Vrancea intermediate-depth seismic source exhibit a combination of time-domain and spectral characteristics that distinguish them from those commonly observed in most seismic settings. In the time domain, the motions are marked by a strong initial pulse-like phase, during which a substantial fraction of the total seismic energy is released over a very short interval (about 50% of energy in less than 3 seconds), followed by a phase of gradual energy release extending over several tens of seconds (Cotovanu \u0026amp; Vacareanu, 2020b; Cotovanu \u0026amp; Vacareanu, 2021). This asymmetric energy distribution, characterized by an early high-amplitude pulse containing the peak ground acceleration (PGA) and a long tail of lower-amplitude motion, reflects the dominance of body-wave energy and the generally limited contribution of surface waves.\u003c/p\u003e \u003cp\u003eFrom a spectral perspective, Vrancea strong-motion records are characterized by significant amplification at relatively long spectral periods. This feature is explicitly reflected in the Romanian seismic design code (MDRAP, 2014), which defines three spectral zones with corner periods of 0.7 s, 1.0 s, and 1.6 s - substantially longer than the relatively narrow amplification bands around 0.3\u0026ndash;0.5 s more commonly observed in many seismic regions. The prevalence of long-period amplification has important implications for seismic design, as it extends the most severe seismic demand from low-rise to mid- and high-rise structures with very large displacement demands for the later and represents one of the defining features that differentiate the Vrancea source from more typical seismic environments. Furthermore, recorded motions indicate a magnitude-dependent redistribution of spectral energy: smaller Vrancea earthquakes tend to exhibit dominant energy at shorter periods, whereas larger-magnitude events progressively concentrate energy at longer periods - a physically expected trend that is strongly accentuated by local site conditions and examined in detail in subsequent sections.\u003c/p\u003e \u003cp\u003eAt a broader level, Vrancea ground motions reflect the combined influence of complex source properties, heterogeneous propagation paths, and highly variable local site conditions. Propagation effects are strongly controlled by pronounced lateral heterogeneity in the crust and upper mantle (Ismail-Zadeh, et al., 2012). Seismic refraction and tomographic investigations reveal substantial variations in crustal thickness, asthenospheric depth, and seismic velocities, particularly between foreland and back-arc regions, giving rise to markedly different attenuation behaviors depending on the propagation path.\u003c/p\u003e \u003cp\u003eLocal site conditions introduce an additional layer of complexity, especially in regions characterized by thick sedimentary sequences such as the Focsani Basin and the Dacian Basin (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In these areas, the depth to seismic bedrock varies from near-surface to several kilometers, rendering simplified site proxies of limited applicability. Observations indicate that long-period amplification is controlled not by shallow stratigraphy alone, but by the entire sedimentary package extending to deep geological interfaces. Consequently, local site effects cannot be decoupled from regional structure and path effects, and their influence varies spatially with basin geometry, impedance contrasts, and sedimentary evolution.\u003c/p\u003e \u003cp\u003eThe characteristics outlined above indicate that Vrancea intermediate-depth ground motions arise from the simultaneous interaction of multiple source-site-path factors. This intrinsic complexity is further compounded by the limited number of strong-motion recordings available for major Vrancea earthquakes, which constrains the statistical robustness of observational analyses and parameter estimation. As a result, many aspects of Vrancea ground-motion behavior have been investigated under conditions of sparse data, strong structural heterogeneity, and necessarily simplifying assumptions. These circumstances have led to a wide range of proposed models and interpretations, often emphasizing different components of the source-path-site system. The following section reviews the main debates that have emerged from these studies and discusses how methodological choices and data limitations have shaped the current understanding of Vrancea seismic behavior.\u003c/p\u003e"},{"header":"3. Debates in the literature","content":"\u003cp\u003eThe literature on Vrancea intermediate-depth ground motions reports differences across several parameters used in ground-motion analyses. Given the limited size and heterogeneity of the available strong-motion database, such differences are likely to occur and can be regarded as acceptable when estimates remain sufficiently close and within ranges that can be explained by the same underlying physical processes. For this reason, the present chapter does not attempt to address all parameters involved in previous studies, but focuses on those for which published results diverge beyond such explainable bounds and therefore require closer examination.\u003c/p\u003e \u003cp\u003eThe discussion addresses source-related properties through source spectral characteristics and stress drop, propagation effects through the heterogeneous structure of the crust and upper mantle and the associated anelastic attenuation and geometrical scattering formulations, and local ground conditions in relation to their diverse definitions, the transition between seismic bedrock and what we consider local site conditions.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Source spectral characteristics and stress drop\u003c/h2\u003e \u003cp\u003eIn the literature, several source spectral shapes have been proposed, characterized by either one or two corner frequencies. The most widely adopted formulation is the ω\u0026sup2; source model introduced by Brune (1970; 1971), which assumes a single corner frequency directly related to stress drop. In the context of Vrancea intermediate-depth earthquakes, most studies have employed source spectra with a single corner frequency. Exceptions are found in the works of Oncescu (1986) and Trifu (1987), who proposed spectral shapes with two corner frequencies, associating them with asperity-based rupture models. Similar spectral features were later reported by Trifu and Radulian (1989) and Radulian et al. (1991). In subsequent applications, including stochastic simulations (Boore, 2003) of Vrancea strong ground motions, Cotovanu and Vacareanu (2020a) observed that source models incorporating two corner frequencies may provide a closer representation of recorded motions.\u003c/p\u003e \u003cp\u003eNevertheless, likely due to the limited size of the available strong-motion database, attempts to determine two-corner frequency source models have not been pursued further. As a result, later studies have largely relied on single-corner frequency source spectra that have been widely tested at the global scale, from which statistical stability and parameter robustness can be indirectly transferred. In these models, the corner frequency is expressed either as a function of stress drop or directly as a function of seismic moment or moment magnitude. While these formulations generally provide satisfactory approximations, for Vrancea events they tend to reproduce either small-to-moderate or large events more effectively, depending on the underlying database. This discrepancy is most clearly reflected in the stress-drop values inferred from different studies.\u003c/p\u003e \u003cp\u003eEarly stress-drop estimates for major Vrancea intermediate-depth earthquakes were derived using rupture-area assumptions based on aftershock distributions. R\u0026auml;kers and M\u0026uuml;ller (1982) and Oncescu and Trifu (1987) assumed that the aftershock area coincides with the rupture area and obtained static stress-drop values of the order of 50 bar for the 1977 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.4\u003c/em\u003e) and 1986 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.1\u003c/em\u003e) earthquakes. These values became representative for early characterizations of Vrancea source properties and were subsequently adopted in later modeling studies.\u003c/p\u003e \u003cp\u003eUsing spectral methods, Gusev et al. (2002) estimated seismic moment and corner frequency from displacement spectra of long-range and teleseismic recordings. Employing Brune (1970; 1971) single-corner frequency source model, they obtained static stress-drop values of approximately 100\u0026ndash;200 bar for large-magnitude events.\u003c/p\u003e \u003cp\u003eOncescu (1989) applied spectral methods to analog strong-motion recordings of the 1986 earthquake and obtained a static stress drop of about 850 bar, together with dynamic stress-drop values ranging between 950 and 1400 bar.\u003c/p\u003e \u003cp\u003eA comprehensive investigation of Vrancea strong ground motions was carried out by Oth et al. (2007), Oth (2007) for the 1977, 1986, and 2004 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e considered in their paper 5.8) earthquakes using the empirical Green\u0026rsquo;s functions method and inversion techniques. Their results showed that the observed ground motions can be reproduced by rupture models involving small asperities associated with high stress drops, in the range of 300\u0026ndash;1200 bar, and high particle velocities of 3.5\u0026ndash;4.5 km/s. Although static stress drops for the 1977 and 2004 events were found to be two to three times larger than for the 1986 earthquake, the corresponding dynamic stress drops were similar for all three events, clustering around values of approximately 1000 bar.\u003c/p\u003e \u003cp\u003eIn parallel with source-parameter studies, stochastic ground-motion simulations for Vrancea earthquakes continued to rely on relatively low stress-drop values. Pavel and Vacareanu (2015) simulated ground motions for magnitudes 5, 6, and 7 using a stress drop of 50 bar and compared stochastic response spectra with GMPE-based predictions. They found that the agreement was satisfactory mainly for the magnitude-6 scenario and concluded that magnitude-dependent stress-drop values would provide a more appropriate representation of Vrancea ground motions. Similar conclusions were reached in Cotovanu (2018) and Cotovanu and Vacareanu (2020a), where stochastic simulations using SMSIM (Boore, 2003) and EXSIM (Motazedian \u0026amp; Atkinson, 2005) showed that low stress-drop values (around 50 bar) are unable to reproduce key features of the recorded strong-motion characteristics.\u003c/p\u003e \u003cp\u003eHigh dynamic stress drops associated with rapid and efficient rupture processes were also noted by Radulian (2017). By comparing different datasets employed in studies of Vrancea source characteristics (Popescu, et al., 2016; Radulian \u0026amp; Popa, 1996; Oncescu, 1986), he observed an apparent increase in stress drop with increasing seismic moment for events up to magnitude 6, whereas such a trend is not evident for larger earthquakes.\u003c/p\u003e \u003cp\u003eMadariaga (1976) provided a physical justification for the inverse relationship between corner frequency and source radius under the assumption of a circular rupture model. Corner frequencies were shown to be approximately one-half of those predicted by Brune\u0026rsquo;s (1970; 1971) formulation, implying corrections by a factor of eight to the corresponding stress-drop estimates. Building on this framework, Radulian (2017) examined the M₀ - radius dependence using different Vrancea datasets (Popescu, et al., 2016; 1996; Oncescu, 1986). When seismic moment is related consistently to source radius and, consequently, to corner frequency, the apparent discrepancies observed for the major events disappear.\u003c/p\u003e \u003cp\u003eTaken together, the wide variety of stress-drop estimates reported for Vrancea reflects instability relative to differences in data and methodology. Within this context, stress drop often emerges as a corrective parameter rather than a directly constrained physical quantity. Although Oth et al. (2007; 2008; 2009) employed an approach that simultaneously considers multiple categories of parameters, stress drop remains the parameter through which consistency between model components was achieved. Similarly, Radulian (2017) examines stress-drop values across different magnitude ranges and notes a possible magnitude dependence, without extending this observation into a unified source parameterization.\u003c/p\u003e \u003cp\u003eThis situation raises a recurring question for the Vrancea intermediate-depth source: why do such corrective adjustments become significant here, while similar processes do not appear to exert a comparable influence on strong ground motions in other seismic regions where analogous methodologies are applied? More fundamentally, it remains unclear which physical aspects of the Vrancea source or propagation environment are implicitly absorbed by these corrections, given that comparable processes may exist elsewhere but with a much smaller impact on observed ground-motion characteristics.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Propagation path: structural heterogeneity, attenuation, and geometrical scattering\u003c/h2\u003e \u003cp\u003eThe propagation of seismic waves from the Vrancea intermediate-depth source takes place within a heterogeneous crustal and upper-mantle environment (Ismail-Zadeh, et al., 2012). Three major projects have provided the primary constraints on the regional structure: the seismic refraction profiles VRANCEA1999 and VRANCEA2001, and the CALIXTO (Carpathian Arc Lithosphere X-Tomography) project (Hauser, et al., 2001; Hauser, et al., 2007; Landes, et al., 2004; Martin, et al., 2005; Martin, et al., 2006). Among others, these studies emphasized strong contrasts between the interior of the Carpathian Arc and the surrounding areas, particularly the Transylvanian Basin where the asthenosphere is located at significantly shallower depths (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAdditional pronounced structural variability is observed in the vicinity of the Vrancea source, where in the \u003cb\u003eFocsani Basin\u003c/b\u003e the geological strata are bent to depths larger than 30 km, of whom the first 8\u0026ndash;10 km are composed from Neogene and Quaternary strata (Landes, et al., 2004; Hippolyte, et al., 1999). This area is prone to large topographic effects, consequently can record different characteristics. Small concentric basins with local influence can also be found at south of Carpathians chain (eg. SULR station area) (Manea, et al., 2020; Krezsek \u0026amp; Olariu, 2021; Matenco, et al., 2003).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe northern and central sectors of the Moesian Platform - extending across southern Romania correspond to the Dacian Basin (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In contrast, the southern part of the platform, including northern Bulgaria, represents the more stable Moesian domain, characterized by a thinner sedimentary cover. Along this north-south section, the Danube valley marks the zone with the shallowest local site condition depths (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Bucharest, located roughly midway between the Southern Carpathians and the Danube, lies along the middle descending gradient of sediment thickness.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOne of the most challenging aspects in assessing seismic response across the Vrancea-affected area is the large variability in seismic bedrock depth - ranging from 3000 m to near-surface across much of the Moesian Platform (Manea, et al., 2020; Manea, et al., 2016), and from 800 m in the eastern parts of Romania (Juravle, 2009). Unlike in many other seismic regions, where shallow seismic bedrock allows for local site conditions to be reliably characterized through borehole recordings or standard geotechnical profiling, such methods are often impractical in the Vrancea context due to the deeply stratified and geologically complex subsurface.\u003c/p\u003e \u003cp\u003eOn this note, a direct consequence of the structural and geological complexity discussed above is reflected in the anelastic attenuation and scattering parameters.\u003c/p\u003e \u003cp\u003eRusso et al. (2005) examined the variation in attenuation outside the Carpathian Chain and categorized the seismic stations into three distinct zones. The first group includes stations showing low attenuation, located in areas such as the Eastern European Platform, the Scythian Platform, and the northeastern sector of the Moesian Platform. The second group comprises stations with high attenuation, mainly situated near the Vrancea seismic zone and within the Transylvanian Basin. The third group includes stations with intermediate attenuation levels, but with significant variability depending on the seismic wave path\u0026mdash;lower attenuation was observed for shallow events, while higher attenuation was associated with deeper events, particularly in the Focsani Basin area. Stations in the Bucharest region, along with other stations located further south, were excluded from the analysis due to inconsistent results attributed to strong local site effects. Bucharest, for instance, lies on a floodplain characterized by a complex mix of sediments, terraces, sand, and muddy alluvial deposits.\u003c/p\u003e \u003cp\u003eFurthermore, six attenuation functions have been proposed in the literature for the propagation path from the Vrancea intermediate-depth source toward regions outside the Carpathian Arc: Oncescu et al. (1999) (O99), Sokolov et al. (2005) (S05), Oth et al. (2008) (O08), Pavel (2015) (P15), Pavel and Vacareanu (2015) (PV15), and Pavel and Vacareanu (2018) (PV18). These functions can be grouped into two categories based on the assumed geometrical scattering. The first group (O99, S05, and O08) is associated with stronger attenuation of spectral amplitudes at short periods and assumes geometrical spreading proportional to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-1}\\)\u003c/span\u003e\u003c/span\u003e. The second group (P15, PV15, and PV18) primarily affects spectral amplitudes at longer periods and is derived assuming a weaker geometrical spreading proportional to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-0.5}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eOncescu et al. (1999) used a database of recordings from stations located outside the Carpathian Arc, including data from 19 earthquakes with magnitudes between 3.9 and 5.3, completed by recordings from the major events of 1990 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e6.9\u003c/em\u003e and \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e6.3\u003c/em\u003e), 1986 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.1\u003c/em\u003e), and 1977 (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e7.4\u003c/em\u003e). They tested the Joint Source\u0026ndash;Site Determination (JSSD) method for the characterization of both weak and strong ground motions generated by the Vrancea source. Within this framework, an attenuation relation of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:109\\left(\\pm\\:14\\right){f}^{0.81(\\pm\\:0.08)}\\)\u003c/span\u003e\u003c/span\u003e was obtained using the INCERC station in Bucharest as a reference site, for which the transfer function was determined based on the geotechnical profile of Constantinescu and Enescu (1985). In this study, the determination of attenuation primarily served as a mean to analyze discrepancies observed in the recordings, and the authors emphasized the coupling between source and site effects, as well as the influence of rupture directivity on the perceived stress-drop values.\u003c/p\u003e \u003cp\u003eIn order to determine hard-rock spectral models for ground motions generated by Vrancea intermediate-depth earthquakes, Sokolov et al. (2005) approximated attenuation relations of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{0}{f}^{0.8}\\)\u003c/span\u003e\u003c/span\u003e, based on the attenuation profiles proposed by Radulian et al. (2000). These relations were derived for several locations situated east and south of the Carpathian Arc, and for different hypocentral distance intervals (0\u0026ndash;40 km, 0\u0026ndash;110 km, and 100\u0026ndash;200 km). Depending on the region and depth range, the parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{0}\\)\u003c/span\u003e\u003c/span\u003e was estimated to take values of 100, 200, 400, or 500.\u003c/p\u003e \u003cp\u003eOth et al. (2008) employed a database of recordings from 55 earthquakes with magnitudes ranging between 4.0 and 7.1 and applied an adapted Generalized Inversion Technique (GIT) to separate source, path, and local site effects. As a constraint, they assumed that at a hypocentral distance of 90 km the total attenuation from all effects equals unity and that two regions characterized by different attenuation properties can be defined: Region 1, corresponding to the area outside the Carpathian Arc, and Region 2, corresponding to the epicentral region. Starting from initially assumed anelastic attenuation functions, similar to those proposed by Sokolov et al. (2005), an iterative procedure led to frequency-dependent attenuation relations of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:114{f}^{0.96}\\)\u003c/span\u003e\u003c/span\u003e for Region 1 and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:72{f}^{0.12}\\)\u003c/span\u003e\u003c/span\u003e for Region 2. The assumed constraint was addressed by Oth (2009; 2007), where a correction factor derived using the Empirical Green\u0026rsquo;s Function method was introduced.\u003c/p\u003e \u003cp\u003ePavel (2015) and Pavel and Vacareanu (2015; 2018) employed similar methodologies to determine anelastic attenuation and geometrical spreading using different strong-motion databases. In these analyses, three values of geometrical spreading \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({R}^{-0.5},{R}^{-0.7},\\:{R}^{-1})\\)\u003c/span\u003e\u003c/span\u003e were tested, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-0.5}\\)\u003c/span\u003e\u003c/span\u003e selected as the reference model. Regression analyses of Fourier Amplitude Spectra were then applied to derive frequency-dependent attenuation relations. The resulting models include \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:165{f}^{1.2}\\)\u003c/span\u003e\u003c/span\u003e (P15) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:100{f}^{1.2}\\)\u003c/span\u003e\u003c/span\u003e (PV15), the latter also incorporating regional subdivisions and estimates of the high-frequency decay parameter \u0026#120581;. In Pavel and Vacareanu (2018), attenuation was further differentiated by azimuthal region, yielding \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:115{f}^{1.25}\\)\u003c/span\u003e\u003c/span\u003e for forearc regions and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:70{f}^{0.9}\\)\u003c/span\u003e\u003c/span\u003e for the backarc region, while also accounting explicitly for local site conditions.\u003c/p\u003e \u003cp\u003eOverall, the studies reviewed in this section highlight the existence of complex path effects and different attenuation formulations derived under distinct assumptions regarding regionalization, geometrical spreading, and data selection. Distinct zonations are adopted, ranging from two attenuation regions (Oth, et al., 2008), to station-based groupings (Sokolov, et al., 2005), and to azimuth-dependent zonations that evolve from multiple regions to a simplified forearc\u0026ndash;backarc distinction (Pavel \u0026amp; Vacareanu, 2018). Consequently, multiple anelastic attenuation functions coexist in the literature, reflecting both the complexity of the propagation environment and the methodological choices adopted to manage it.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. \u0026ldquo;Boundary\u0026rdquo; between the path and the local site conditions\u003c/h2\u003e \u003cp\u003ePath effects are considered to be phenomena that modify seismic waves along their travel path from the source to the local site conditions. Local site conditions are understood as the stratification above the bedrock. A first divergence in approach emerges regarding the interpretation of this boundary. Two types of bedrock are defined: engineering bedrock and seismic bedrock. Depending on the approach, the theoretic seismic bedrock is typically defined as the layer with shear wave velocity (Vs) values of 3000\u0026ndash;3500 m/s and above, while engineering bedrock has values up to 760\u0026ndash;800 m/s. The consideration of the \u0026ldquo;boundary\u0026rdquo; between local site conditions and path conditions is an essential aspect in analyses and applications, as the two domains exhibit different behaviors, particularly during major seismic events relevant for structural design. While path effects are dominated by attenuation and scattering, softer soils are associated with significant amplification effects and modifications to the spectral content of the ground motion, which can directly affect buildings depending on the correlation between the ground predominant periods and their natural periods. Thus, the way path effects are determined is directly influenced by how local site conditions are defined.\u003c/p\u003e \u003cp\u003eDeep stratifications have the capacity to amplify seismic motion across a broad range of periods, depending not only on their physical configuration but also on how different earthquakes interact with them. Soil behavior is nonlinear, with stiffness and damping varying according to strain level. This means that the same stratigraphic profile may exhibit different dynamic responses depending on the characteristics of the seismic input, such as magnitude, depth, and spectral content. Consequently, the concept of \"local site conditions\" and the effective depth at which they are defined should not be treated as fixed. Instead, they represent a dynamic boundary, shaped by both the properties of the subsurface and the specific features of each seismic event.\u003c/p\u003e \u003cp\u003eAlso, the spectral content of seismic ground motion is closely linked to earthquake magnitude. Larger-magnitude events typically radiate more energy at longer periods due to the increased scale of the rupture and source geometry. This makes long-period waves more prominent in strong earthquakes, enhancing their ability to interact with deep soil profiles and excite resonant modes across a broad frequency range.\u003c/p\u003e \u003cp\u003eOn this note, further clarification is required on how the depth to the bedrock is practically determined, especially when local site conditions involve complex stratification and deep sedimentary basins. One approach to estimating this depth is provided by Manea et al. (2020), who used ambient vibration data to extract the fundamental frequency of resonance (\u003cem\u003ef₀\u003c/em\u003e) at multiple seismic stations across southeastern Romania. The \u003cem\u003ef₀\u003c/em\u003e value was identified from the horizontal-to-vertical (H/V) spectral ratio curve, based on the presence of a distinct and stable peak. Where such a peak was observed, it was interpreted as an indicator of a strong impedance contrast between the sedimentary layers and an underlying stiffer formation. Such contrasts are typically required for a clear resonant peak to emerge in the H/V curve. To refine these initial observations, Manea et al. (2020) performed a two-step inversion of Rayleigh-wave ellipticity to estimate subsurface vs profiles and assess the depth at which this impedance contrast occurs. The depth thus inferred was defined as the geophysical bedrock. These estimates were then interpolated spatially to construct a regional-scale model of bedrock depth variability, providing insight into the subsurface structure independent of fixed engineering or seismological thresholds.\u003c/p\u003e \u003cp\u003eThe fundamental frequency \u003cem\u003ef₀\u003c/em\u003e, as derived, reflects the presence of a strong seismic impedance contrast in the subsurface. While this contrast may coincide with the boundary between local site conditions and underlying bedrock, in terms of specific behavior this interpretation should be reflected in recorded ground motions. Without this validation, \u003cem\u003ef₀\u003c/em\u003e may be rather understood primarily as an indicator of a mechanical boundary, not necessarily as the depth of the entire sedimentary package relevant to site response. Moreover, in cases where seismic impedance increases gradually with depth, and no strong contrast is encountered near the surface, Rayleigh waves may propagate through multiple layers - regardless of their total thickness - until they reach a sufficiently sharp discontinuity that can generate a distinct resonant response. In such situations, the resulting \u003cem\u003ef₀\u003c/em\u003e may reflect a deeper transition, provided it exists, or remain undetectable if no major contrast is encountered. This further emphasizes the need to interpret \u003cem\u003ef₀\u003c/em\u003e in conjunction with earthquake recordings and other site response indicators.\u003c/p\u003e \u003cp\u003eWhen comparing the \u003cem\u003ef₀\u003c/em\u003e distribution provided by Manea et al. (2020) with the geological configuration of the Moesian Platform, some questions arise regarding the interpretation of the identified geophysical bedrock in the context of local site effects. The central sector of the Moesian Platform, where lower \u003cem\u003ef₀\u003c/em\u003e values are mapped, appear to correspond stratigraphically to deeper units as the basin architecture suggests prolonged sediment accumulation (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Beyond the peri-Carpathian fault system begins the Dacian Basin where substantial Neogene sedimentation took place. The base of this sedimentary pile corresponds to the Pre-Paratethys denudation surface, an erosional unconformity overlying Mesozoic basement (Cretaceous, Jurassic, or even Triassic), as described by Matenco et al. (2003; 2016). Starting in the Miocene, the region experienced alternating lacustrine, marine, and fluvial environments associated with the Danube transformations, which led to the accumulation of progressively deposited sedimentary layers including clays, silts, sands, lignite, and salt-bearing horizons (Krezsek \u0026amp; Olariu, 2021). These successions are thick (often exceeding 2 km) and mechanically heterogeneous, with varying degrees of compaction and diagenesis. In this context, the stratification tends to be gradual, without sharp impedance contrasts. As such, the fundamental frequency (\u003cem\u003ef₀\u003c/em\u003e) values detected by Manea et al. (2020) in this region - often associated with deep interfaces (\u0026gt;\u0026thinsp;1000 m) - likely reflect internal lithological transitions rather than the base of the sedimentary sequence relevant for local site response.\u003c/p\u003e \u003cp\u003eTowards the southern part of the Moesian Platform, where higher f₀ values are reported, the sedimentary succession becomes thinner. The continuous Neogene sequence observed in the basin center is no longer preserved. Instead, Cretaceous or older basement is overlain by Miocene, Pliocene, and Quaternary deposits. Here, the impedance contrast between the soft upper sediments and the rigid strata is well-defined, sharper. The entire sedimentary cover probably behaves as a seismic amplification unit, with clear local site effects. This situation corresponds more closely to classical models of site response, where a soft soil layer overlies stiff bedrock.\u003c/p\u003e \u003cp\u003eAs such, it remains unclear whether the depth to bedrock defined by \u003cem\u003ef₀\u003c/em\u003e in the northern part of the platform captures the effective lower limit of the sedimentary sequence relevant to site effects, or simply reflects a deeper lithological transition not strongly involved in the dynamic response of the upper soil layers during earthquakes. According to Jipa and Olariu (2009), coal-bearing layers - typically lignite - are present at the transition between the upper Pontian and lower Dacian units, often identified at depths of several hundred meters in the western and central parts of the Dacian Basin. These layers are commonly associated with coarsening-upward sequences and reflect a shift from brackish to continental environments. While coal itself has relatively low shear-wave velocities, its stratigraphic position within compacted and often well-cemented strata suggests a mechanically coherent interval. Consequently, the sedimentary package extending to or slightly below these coal-bearing layers may act more as a transmission medium than a resonant one, particularly in regions where no significant impedance contrast is located above. This reinforces the possibility that, in parts of the Moesian Platform where \u003cem\u003ef₀\u003c/em\u003e values are low and interpreted as indicative of deep impedance contrasts, the geophysical bedrock identified may lie below a thick, stiffened sedimentary sequence that contributes more to path effects than to local site amplification.\u003c/p\u003e \u003cp\u003eRegardless of this discussion, several studies exist that characterize local conditions at different sites: from geological maps and lithological columns used for mapping the entire territory of Romania (Geological Institute of Romania, 2022) to complemented local studies conducted for various purposes (Jipa \u0026amp; Olariu, 2009; Stoica-Negulescu, 2016). In addition, there are studies that provide subsurface profiles including parameters such as density, P- and S-wave velocities, and in some cases even modulus reduction and damping curves (Bratosin, et al., 2009). Ideally, these studies should include the deep stratifications discussed previously. However, such deep characterizations are available only at very few locations, such as the INCERC site in Bucharest (Constantinescu \u0026amp; Enescu, 1985). Otherwise, site characterization has been performed rather using simplified \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003es30\u003c/em\u003e\u003c/sub\u003e-based profiles or H/V spectral ratios, which may or may not be representative, as argued by Oth (2007).\u003c/p\u003e \u003cp\u003eThe debates reviewed in this chapter show that the variability of parameters reported for Vrancea intermediate-depth ground motions reflects the combined effects of strong structural complexity, limited data availability, and the use of different definitions for source, path, and site parameters in the literature. Stress-drop estimates, attenuation formulations, and interpretations of local site conditions are therefore not contradictory in themselves, but arise from the strong coupling between model components and the assumptions adopted in different methodologies.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Zonation as a means of decomposing seismic complexity","content":"\u003cp\u003eStarting from the premise that Vrancea ground motions follow generally applicable physical principles, yet appear inconsistent with standard modeling approaches, this chapter aims to define a balanced level of uniformity that enables simplification without hiding spatial variability and heterogeneity.\u003c/p\u003e \u003cp\u003eHistorically, several zonations have been proposed for the territory strongly affected by Vrancea earthquakes. The most stable and persistent subdivision divides Romania into two main regions: the interior of the Carpathian Arc (back-arc) and the exterior of the Carpathian Arc (forearc) (Vacareanu, et al., 2015). This distinction represents one of the earliest observed differences in seismic-wave attenuation, already evident in the first intensity maps constructed for major historical earthquakes. It has remained consistently reflected in successive generations of seismic design codes - The P100 series (MDRAP).\u003c/p\u003e \u003cp\u003eWithin the exterior of the Carpathian Arc, different levels of subdivision have been adopted depending on the objectives of the respective studies. Some works treat this region as a single unit (Pavel, 2015; Pavel \u0026amp; Vacareanu, 2015; Cotovanu \u0026amp; Vacareanu, 2021), while others distinguish the epicentral area from the remaining forearc region (Oth, et al., 2008). Additional studies consider the southern sector separately, focusing on the Moesian Platform (Manea, et al., 2020). Beyond these approaches, further zonations have been proposed based on azimuthal partitioning - initially into five regions (Pavel \u0026amp; Vacareanu, 2018) -, or on combined azimuthal and tectonic criteria (INFP; UTCB; URBAN-INCERC, 2016\u0026ndash;2018).\u003c/p\u003e \u003cp\u003eIn the present study, a zonation is proposed based on geological, geophysical, tectonic, and topographic evidence (Matenco, et al., 2003; Jipa \u0026amp; Olariu, 2009; Juravle, 2009; Krezsek \u0026amp; Olariu, 2021), and most substantially on the work of Manea et al. (2016; 2020). As such, the zonation is defined without relying directly on recordings from major Vrancea earthquakes and serves as an independent pivot within the overall framework. A preliminary and qualitative verification of potential differences between the resulting strong-motion datasets is carried out through visual inspection. The proposed subdivision accounts for elements expected to exert a major influence on strong ground motions, including possible basin effects, as well as sedimentary stratification with the potential to exhibit site-specific or path-related behavior, and the presence of strong impedance contrasts.\u003c/p\u003e \u003cp\u003eWhile shallow sources typically exert strong effects over areas of tens to hundreds of square kilometers, Vrancea earthquakes influence a local area of several tens of thousands of square kilometers and a regional area exceeding 100,000 square kilometers in Romania. Under these conditions, structural heterogeneity is unavoidable. The area of interest for seismic safety analyses is therefore broad and does not allow for a strictly incremental, locally focused approach. Instead, within an environment characterized by evident heterogeneity, a level of homogeneity sufficient for meaningful analysis must be identified.\u003c/p\u003e \u003cp\u003eFrom this standpoint, the affected area can be firstly subdivided into three regions, governed primarily by the three major tectonic units (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e): the East European Plate, with an approximate thickness of 150 km, the Moesian Platform, with an approximate thickness of 130 km, and the Intra-Alpine Plate, with an approximate thickness of about 90 km (Besutiu, 2006; Ismail-Zadeh, et al., 2012). Considering the predominance of large intermediate-depth earthquakes within the depth range of approximately 90\u0026ndash;150 km (Radulian, et al., 2019), a first and well-recognized distinction emerges. Seismic waves recorded within the Intra-Alpine Plate (the interior of the Carpathian Arc) are more likely to propagate through asthenospheric or more viscous media, leading to stronger attenuation and, consequently, different ground-motion characteristics compared to those observed outside the Carpathian Arc. Due to the scarcity of strong-motion recordings from major events in this area, the intra-Carpathian region is not considered in the present study.\u003c/p\u003e \u003cp\u003eFor the exterior of the Carpathian Arc, a first-order subdivision may be defined between the Moesian Platform and an eastern domain that includes both the East European Plate (EEP) and the Scythian Platform (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). While tectonically distinct, these units are treated jointly due to data limitations. Based on the deep lithospheric structure inferred from the three major experiments discussed previously, this separation can be considered sufficiently homogeneous, except for the Focșani Basin, where lithospheric bending goes to depths of about 30 km and pronounced local topographic effects and internal variability are expected.\u003c/p\u003e \u003cp\u003eBy increasing the level of analysis to a slightly finer scale focused on near-surface stratification, additional features emerge that require closer consideration. In the Dobrogea Orogen, old stratigraphic units (Jurassic and Triassic) are encountered very close to the surface, overlain by only a few meters to several tens of meters of sediments.\u003c/p\u003e \u003cp\u003eWithin the southern part of Romania, corresponding to the Moesian Platform, two distinct stratigraphic trends can be identified (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In its northern half, from the Carpathians southward, sediment accumulation follows a chronological sequence that can be consistently linked to the long-term evolution of the Danube, including phases of migration and stagnation that resulted in progressive sediment deposition. In contrast, the southern half of the Moesian Platform does not exhibit this chronological sedimentary succession. Instead, this sector reflects a southward lateral shift (\u0026ldquo;slide\u0026rdquo;) of the Danube toward its present course, driven by topographic uplift associated with the formation of the Southern Carpathians (Matenco, et al., 2016). This process led to the deposition of relatively young sediments directly onto older stratigraphic units (Jurassic, Triassic, or Cretaceous), representing an evident stratigraphic discontinuity. This discontinuity suggests the presence of an impedance contrast that cannot be neglected in the interpretation of strong ground motions.\u003c/p\u003e \u003cp\u003eFrom the perspective of sedimentary architecture, the Moesian Platform may be interpreted as a basin confined between the Carpathians and the Balkan Mountains. Within this configuration, the Dacian Basin represents a zone of stratified sediment accumulation resulting from the long-term evolution of the Danube River through successive depositional positions. This is followed by a relatively rapid southward sliding, characterized by a decrease in sediment thickness - from more than 1 km in the central part of the platform to only a few meters in the vicinity of the present-day Danube, where it assumes its role as a major fluvial system.\u003c/p\u003e \u003cp\u003eThe older East European Platform is characterized by deep sedimentary sequences without major stratigraphic discontinuities, showing a gradual decrease in sediment thickness from the Carpathian foredeep eastward. While a subdivision between the deeper foredeep and areas of thinner accumulation could be considered, the resulting differences are better interpreted as local site effects rather than path-related interconnectivity and should be accommodated without ambiguity within the general behavioral models.\u003c/p\u003e \u003cp\u003eOn this conceptualized foundation and based on the \u003cem\u003ef₀\u003c/em\u003e mapping of Manea et al. (2016; 2020), the analysis relies on a dataset of earthquakes with \u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;5\u003c/em\u003e, selected to ensure consistency with earlier studies (Pavel \u0026amp; Vacareanu, 2015; 2018; Craciun, et al., 2018). Seismic stations are grouped by geographical domain, \u003cem\u003ef₀\u003c/em\u003e intervals inferred, and magnitude class (\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e and \u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e).\u003c/p\u003e \u003cp\u003eBased on the combined zonation criteria discussed above - tectonic setting, basin geometry, and near-surface stratification - the ground-motion recordings are classified into the following zonation categories (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eNorth Moesia ridge \u0026ndash; Carpathians Mountains, basin crest, convex geometry, corresponding to areas where \u003cem\u003ef₀\u003c/em\u003e \u0026gt; 1 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eNorth Moesia edge - steeply dipping flanks, concave geometry, with 0.15 Hz\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ef₀\u003c/em\u003e \u0026lt; 1 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCentral Moesia accumulation \u0026ndash; Dacian basin, deepest zone defined by \u003cem\u003ef₀\u003c/em\u003e \u0026lt; 0.15 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSouth Moesia accumulation - up to the Danube, with 0.15 Hz\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ef₀\u003c/em\u003e \u0026lt; 0.5 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSouth Moesia edge - approximately south of the Danube, with \u003cem\u003ef₀\u003c/em\u003e \u0026gt; 0.5 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eDobrogea Platform - distinct geomorphological features, with \u003cem\u003ef₀\u003c/em\u003e \u0026gt; 5 Hz;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eEast of Carpathians (Moldavia region) - the East European and Scythian platforms;\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFocsani Basin - in the Central Moesia accumulation, but distinct due to large, local topographic effects and large sediment thicknesses.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eTo provide a first-order illustration of how the proposed zonation is reflected in recorded ground motions, a preliminary comparative examination of response spectra was carried out using the strong-motion recordings associated with the earthquakes listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFor each recording, pseudo-acceleration response spectra were computed and subsequently normalized. Rather than focusing on absolute spectral amplitudes, this exploratory analysis emphasizes the shape of the response spectra, with particular attention given to spectral peaks associated with large amplifications. To this end, spectra were normalized with respect to their maximum spectral ordinate, allowing differences in spectral shape to be compared across sites and zonation categories with reduced sensitivity to earthquake magnitude. This choice is particularly relevant in the present context, as earthquakes of different magnitudes may preferentially excite different depths of stratified sedimentary packages. A direct comparison of unnormalized spectra, or spectra normalized to peak ground acceleration (PGA), would therefore tend to mix responses controlled by different stratigraphic levels, obscuring patterns related to zonation.\u003c/p\u003e \u003cp\u003eWithin each zonation category, in addition to computing the geometrical mean of normalized spectra, the number of spectral ordinates exceeding threshold of 0.75 relative to the number of recordings was rated across all periods, providing a simple measure of the persistence and width of high-amplification spectral intervals. These indicators are not intended as formal metrics, but as qualitative guides to highlight systematic differences between zones.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe geometric mean of the normalized pseudo-spectral accelerations and the 0.75 ratio within each group of N recorded components was computed as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{PSA}_{norm,GM}\\left(T\\right)={\\left(\\prod\\:_{i=1}^{N}\\frac{{PSA}_{i}\\left(T\\right)}{max\\:{PSA}_{i}\\left(T\\right)}\\right)}^{1/N}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{R}_{0.75}\\left(T\\right)=\\frac{{N}_{\\ge\\:0.75}\\left(T\\right)}{N}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{N}_{\\ge\\:0.75}\\left(T\\right)=\\sum\\:_{i=1}^{N}\\left\\{\\begin{array}{c}1,\\:\\frac{{PSA}_{i}\\left(T\\right)}{max\\:{PSA}_{i}\\left(T\\right)}\\ge\\:0.75\\:\\\\\\:0,\\:else\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe resulting spectral patterns offer an initial, visually guided indication of whether the proposed zonation captures meaningful differences in ground-motion behavior. The following observations are intentionally descriptive, serving to map variability rather than to explain it. The resulting spectral comparisons are illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the stations and earthquakes included in analyses.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor both the \u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e and \u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e datasets, the Dobrogea region stands out clearly, characterized by a narrow amplification band and a spectral peak at approximately 0.1 s. This peak corresponds to the fundamental frequency identified in the \u003cem\u003ef₀\u003c/em\u003e mapping of Manea et al. (2020). For the larger-magnitude earthquakes, a similar peak is observed in the East region. In the case of Dobrogea, the persistence of this peak is consistent with the local site conditions, whereas in the eastern region, when compared to the other zones, its presence is more plausibly associated with lower attenuation at short periods. From this point of view, the eastern region appears, at this preliminary level of observation, to exhibit spectral characteristics closer to those of Dobrogea than to those of the remaining zones.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVrancea intermediate-depth earthquakes used in the study grouped by magnitude class\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDate of earthquake\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLatitude\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLongitude\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMagnitude\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDepth\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMagnitude class\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e04.03.1977\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e94.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30.08.1986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e131.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30.05.1990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e31.05.1990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e86.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27.10.2004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e105.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14.05.2005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e148.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18.06.2005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e153.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25.04.2009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e109.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e06.10.2013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e135.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo enable an intra-dataset comparison, the Dobrogea region was selected as a reference (pivot) zone, owing to the presence of old seismic bedrock at very shallow depths and the absence of broad-band interference from local site conditions. An alternative reference could have been the North Moesia ridge; however, Dobrogea provides a more stable illustrative baseline. The North Moesia ridge is also characterized by shallow bedrock, but it represents a crest zone, where topographic effects may play a role. In addition, previous studies have suggested the presence of a low-velocity zone in the upper mantle beneath this area (Hauser, et al., 2001), which could further modify the recorded ground motions.\u003c/p\u003e \u003cp\u003eRelative to the Dobrogea reference, and particularly for the \u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e dataset, pronounced amplifications are observed in the period range of approximately 0.5\u0026ndash;2.5 s, with the Focșani Basin and the South Moesia accumulation zone standing out most clearly.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen examining the distribution of dominant spectral peaks - defined here as the ratio of peaks exceeding 0.75 of the maximum PSA - it is observed that the North Moesia ridge tends to lose energy in the short-period range of approximately 0.1\u0026ndash;0.2 s. For large-magnitude earthquakes, a similar reduction is also apparent in both edge regions. This behavior is consistent with the presence of topographic effects, which are known to modify short-period ground motions in ridge and flank settings. In addition, the North Moesia edge exhibits a relatively broad amplification band, which may reflect a combination of local site conditions, topographic influences, or their joint interaction. By contrast, the South Moesia edge appears to concentrate amplification within a period range of approximately 0.35\u0026ndash;0.5 s, suggesting the presence of a stratigraphic package that guides seismic energy within this interval.\u003c/p\u003e \u003cp\u003eThe two accumulation zones, Central Moesia and South Moesia, display broadly similar spectral behavior for moderate-magnitude earthquakes. However, for large-magnitude events, a clear divergence emerges between the two regions. In the South Moesia accumulation zone, larger earthquakes activate sedimentary packages that produce amplification extending up to periods of approximately 2 s. In contrast, the Central Moesia accumulation zone exhibits a response that is more similar to that of the North Moesia ridge, with the exception of a narrow period interval around 0.8\u0026ndash;0.9 s, where some amplification is observed. This contrast suggests that the relative contribution of propagation effects and local site conditions varies with earthquake magnitude, suggesting a dynamic boundary between path-controlled and site-controlled behavior.\u003c/p\u003e \u003cp\u003eTaken together, the proposed zonation successfully differentiates and highlights systematic differences in ground-motion behavior. The responses observed across the eight zones illustrate distinct manifestations of seismic effects, indicating that no zone can be meaningfully grouped with another without losing essential characteristics. Furthermore, averaging across zones (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), for both magnitude ranges, hides these differences. In recognition of the variations highlighted by the proposed zonation, and of the additional limitations discussed throughout the paper, the following section introduces a framework aimed at assessing whether the apparent inconsistencies between Vrancea ground motions and standard modeling approaches are truly unique, or instead arise from previously undecomposed seismic complexity.\u003c/p\u003e"},{"header":"5. Framework for resolving seismic complexity under limited data conditions","content":"\u003cp\u003eThe conditions of the problem addressed in this section are the following. Reliable characterization of strong ground motions is required for seismic design and hazard definition, given the significant risk associated with Vrancea intermediate-depth earthquakes. However, the database of events with moment magnitude \u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e consists of only four earthquakes, one of which is recorded at a single site (INCERC, Bucharest). In addition, the area strongly affected by Vrancea intermediate-depth earthquakes is substantially larger than the spatial scales typically considered in seismic mapping and hazard definition from a single seismic source. This inevitably introduces pronounced structural and site-related heterogeneity. While this heterogeneity has been classified through zonation and the underlying complexity has been explicitly defined in the previous chapter, this step further fragmented an already sparse strong-motion database. As a result, the primary challenge at this stage is not the identification of variability, but the fragility of the available data in the presence of clearly different ground-motion behavior between moderate-magnitude and large-magnitude event datasets, particularly with respect to local site conditions.\u003c/p\u003e \u003cp\u003eIn addition, two broad categories of parameters remain widely debated in the literature without convergence toward a common interpretation: source-related spectral shape, commonly linked to the stress-drop parameter, and path-related effects, represented by the combination of anelastic attenuation and geometrical scattering.\u003c/p\u003e \u003cp\u003eTo avoid circular reasoning, and in particular the use of stress drop as a free calibration parameter - which, as discussed previously, leads to unrealistically wide variability - stress drop is constrained in this framework to ranges consistent with general theoretical expectations. It is not treated as a Vrancea-unique dynamic parameter. Instead, the focus is placed on determining path-related parameters and on evaluating whether these, or other elements of the framework, reveal any genuine source uniqueness. This approach allows us to assess whether the apparent anomalies reported for Vrancea ground motions reflect truly distinctive physical processes, or whether they arise from previously undecomposed seismic complexity.\u003c/p\u003e \u003cp\u003eThe framework adopted in this study is defined as follows:\u003c/p\u003e \u003cp\u003e(0) Zonation is introduced as a means of decomposing seismic complexity, providing a structured representation of heterogeneity without embedding ground-motion observations in its definition.\u003c/p\u003e \u003cp\u003e(1) The database of major earthquakes (\u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e) is too limited to sustain a minimum level of statistical robustness. To address this limitation, a complementary database of moderate-magnitude events (\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e) is incorporated. For both datasets, characteristics are determined, and treated as dataset-specific attributes.\u003c/p\u003e \u003cp\u003e(2) From the perspective of local site conditions, the two datasets exhibit significantly different behavior. This necessitates a uniformization of site effects without explicitly parameterizing them. This is achieved by defining an average ratio between the amplification patterns observed for large-magnitude events and those observed for moderate-magnitude events, and subsequently modifying the large-event dataset so that it reflects site-condition amplification characteristics consistent with those of the moderate-event dataset. The two datasets are then combined into a single database in which both event classes share aproximately the same reference site-condition behavior derived from the moderate-magnitude events.\u003c/p\u003e \u003cp\u003e(3) Path-related parameters are determined and evaluated within this unified datasets.\u003c/p\u003e \u003cp\u003e(4) Finally, the envelopes of amplification associated with local site conditions are analyzed, and additional factors potentially contributing to the observed variability of Vrancea ground motions are explored.\u003c/p\u003e \u003cp\u003eThe analysis is based on the decomposition of the total ground-motion spectrum at a site, following the formulation of Boore (2003), in which the observed motion is expressed as the product of source \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E({M}_{0},\\:f)\\)\u003c/span\u003e\u003c/span\u003e, path \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P(R,\\:f)\\)\u003c/span\u003e\u003c/span\u003e, site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G\\left(f\\right)\\)\u003c/span\u003e\u003c/span\u003e, and instrument contributions \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:I\\left(f\\right)\\)\u003c/span\u003e\u003c/span\u003e:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:Y\\left({M}_{0},\\:R,\\:f\\right)=E\\left({M}_{0},\\:f\\right)P\\left(R,\\:f\\right)G\\left(f\\right)I\\left(f\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSource parameters were defined according as following: density near source 3.45 g/cm\u003csup\u003e3\u003c/sup\u003e (Tondi, et al., 2009), velocity near source 4.60 km/s (Raykova \u0026amp; Panza, 2006) and radiation pattern 0.62 (Boore \u0026amp; Boatwright, 1984),. With respect to the source spectrum, a simplified Brune model (1970; 1971) with a single corner frequency was adopted. The stress-drop parameter was fixed at 100 bars, consistent with the value reported by Gusev et al. (2002) and with commonly accepted ranges in general seismological practice. A more detailed discussion of the stress-drop debate is provided in Chap.\u0026nbsp;3.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDatabase characteristics within each zonation category, for both moderate-magnitude and large-magnitude earthquakes\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA. Nord \u0026gt;1 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB. Nord 0.15-1 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC. Central \u0026lt;0.15 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD. Central 0.15\u0026ndash;0.5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eE. South \u0026gt;0.5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eF. Dobrogea \u0026gt;5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eG. East\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eH. Focsani basin\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean Mw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean R (km)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e105.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e142.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e149.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e192.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e219.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e183.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e167.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e116.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. horizontal components\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEquivalent M0 (dyne\u0026middot;cm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.3E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.2E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.4E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.1E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.6E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.7E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.2E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.9E\u0026thinsp;+\u0026thinsp;26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorner frequency fc (Hz)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKappa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA. Nord \u0026gt;1 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB. Nord 0.15-1 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC. Central \u0026lt;0.15 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD. Central 0.15\u0026ndash;0.5 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eE. South \u0026gt;0.5 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eF. Dobrogea \u0026gt;5 Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eG. East\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eH. Focsani basin\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean Mw\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean R (km)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e134.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e166.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e177.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e213.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e249.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e193.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e180.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e133.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. horizontal components\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEquivalent M0 (dyne\u0026middot;cm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.5E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.3E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.4E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.6E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.5E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.1E\u0026thinsp;+\u0026thinsp;25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.0E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.8E\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorner frequency fc (Hz)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKappa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.064\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor each dataset and each zonation category, an equivalent moment magnitude was computed as the geometric mean of the magnitudes associated with the individual components within the group. This equivalent magnitude was then converted to seismic moment using the relationship proposed by Das et al. (2019) - \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:lg\\left({M}_{0}\\right)\\:=\\:1.36{M}_{w}\\:+17.2448\\)\u003c/span\u003e\u003c/span\u003e. This choice requires clarification, as the moment-magnitude relationship of Hanks and Kanamori (1979), also employed in Boore (2003), is more commonly used. The alternative was not adopted superficially. The objective at this stage is not to analyze individual events or specific realizations of the database, but to characterize representative, generalized behavior at the level of each zone and dataset. For this reason, using particular seismic moment values and subsequently averaging them was avoided.\u003c/p\u003e \u003cp\u003eThe relation proposed by Das et al. (2019) was selected following a targeted search for a more reliable moment-magnitude formulation. While several global and local, Vrancea-specific, relations were considered, including Hanks and Kanamori (1979), Kanamori (1977), and Popescu et al. (2007; 2010), the local formulations are based on relatively limited datasets. As such, they do not provide a sufficiently robust basis to challenge the widely adopted Hanks and Kanamori (1979) relation.\u003c/p\u003e \u003cp\u003eAn important factor in the selection of Das et al. (2019) is that this relation provides a notably better approximation for the two major historical Vrancea earthquakes. Differences of approximately 1% for the 1986 event and 2% for the 1977 event are obtained, whereas substantially larger discrepancies are observed when using Hanks and Kanamori (1979) (about 37% and 29%, respectively), Kanamori (1977) (about 30% and 21%), or Popescu et al. (2007) (about 3% for 1986 and 9% for 1977). In addition, Das et al. (2019) provide a detailed discussion of the limitations of the Hanks and Kanamori (1979) relation, particularly with respect to the characteristics of the database on which it was derived and its assumed global applicability. Their generalized moment-magnitude scale was shown to perform consistently over a wide magnitude range (\u003cem\u003eMw\u0026thinsp;\u0026ge;\u0026thinsp;4.5\u003c/em\u003e), across different focal depths and seismic regions. The scale is unsaturated and statistically more robust, making it better suited to the objectives of the present framework.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFrom the path perspective, the following assumption was adopted: within each zonation category, for both moderate-magnitude and large-magnitude earthquakes, path-related characteristics vary with only hypocentral distance (\u003cem\u003eR\u003c/em\u003e), but not in terms of the adopted attenuation model or geometrical scattering formulation.\u003c/p\u003e \u003cp\u003e(1) The database\u003c/p\u003e \u003cp\u003eFor the spectral analysis, time-domain accelerograms processed by Craciun (2018) from seismic events in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e were used. Historical recordings were available only in corrected form, while the remaining records were processed following the same procedure adopted by Pavel and Vacareanu (2015; 2018). Smoothed Fourier Amplitude Spectra (FAS) were computed for the horizontal components at 25 logarithmically spaced frequencies in the range 0.25\u0026ndash;15 Hz, using a Konno\u0026ndash;Ohmachi (1998) smoothing filter with a bandwidth of 0.2.\u003c/p\u003e \u003cp\u003eFor each database and each zone the geometrical mean of FAS were determined along with their equivalent moment magnitude, seismic moment, hipocentral distances, corner frequencies and kappa parameter. The high-frequency attenuation parameter \u0026#120581; was estimated for each zonation category from the decay of the Fourier Amplitude Spectra at high frequencies by regression in the frequency domain (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e(2) \u0026ldquo;Uniformization\u0026rdquo; of site effects\u003c/p\u003e \u003cp\u003eAt this stage, the ratio between site-related amplifications derived from the large-magnitude dataset (\u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e) and the moderate-magnitude dataset (\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{M}/{A}_{m}\\)\u003c/span\u003e\u003c/span\u003e, is defined (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). To this end, an average FAS is first determined for each dataset and each zonation category after removing the effects of the source and geometrical scattering. Geometrical scattering is represented at this stage by an \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-1}\\:\\)\u003c/span\u003e\u003c/span\u003edecay, consistent with the propagation of body waves in a homogeneous spherical medium. In addition, high-frequency diminution associated with local site conditions is removed using the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e parameter determined for each zone.\u003c/p\u003e \u003cp\u003eThe reduced spectrum is thus expressed as:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{Y}^{{\\prime\\:}}\\left(R,f\\right)=\\frac{Y\\left({M}_{0},R,f\\right)}{E({M}_{0},f){R}^{-1}{e}^{-\\pi\\:kf}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}^{{\\prime\\:}}\\left(R,f\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the motion corrected for source and path effects, retaining predominantly the contribution of local site conditions.\u003c/p\u003e \u003cp\u003eBecause the two datasets exhibit different hipocentral distance distributions within each zonation category, the ratio \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{Y}^{{\\prime\\:}}}_{M}\\left({R}_{M},f\\right)/{{Y}^{{\\prime\\:}}}_{m}\\left({R}_{m},f\\right)\\)\u003c/span\u003e\u003c/span\u003e (between the large-magnitude and moderate-magnitude datasets) still contains a residual contribution from anelastic attenuation. In a first iteration, this effect is quantified using the attenuation model proposed by Oth et al. (2008), with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\left(f\\right)=114{f}^{0.96}\\)\u003c/span\u003e\u003c/span\u003e. In a subsequent iteration, this correction is updated using the path attenuation functions determined independently for each zone (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAccordingly, the ratio of site amplifications between the two datasets is expressed as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\frac{{A}_{M}\\left(f\\right)}{{A}_{m}\\left(f\\right)}=\\frac{{{Y}^{{\\prime\\:}}}_{M}\\left({R}_{M},f\\right)}{{{Y}^{{\\prime\\:}}}_{m}\\left({R}_{m},f\\right)}{e}^{\\frac{\\pi\\:f({R}_{M}-{R}_{m})}{Q\\left(f\\right){c}_{Q}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{M}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{m}\\)\u003c/span\u003e\u003c/span\u003e denote representative equivalen hipocentral distances for the large- and moderate-magnitude datasets, respectively, for each zone.\u003c/p\u003e \u003cp\u003eFor each zonation category, the large-magnitude dataset is further adjusted as:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{{Y}^{{\\prime\\:}{\\prime\\:}}}_{M}\\left(f\\right)=\\frac{{Y}_{M}\\left({M}_{M0},{R}_{M},f\\right)}{{E}_{M}({M}_{M0},f){(e}^{-\\pi\\:{k}_{M}f}{\\left)\\right(A}_{M}/{A}_{m})}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhile the moderate-magnitude dataset is expressed as:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:{{Y}^{{\\prime\\:}{\\prime\\:}}}_{m}\\left(f\\right)=\\frac{{Y}_{m}\\left({M}_{m0},{R}_{m},f\\right)}{{E}_{m}({M}_{m0},f){(e}^{-\\pi\\:{k}_{m}f})}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWith this formulation, both datasets retain only path-related characteristics, while the site amplification is consistently represented by the conditions inferred from the moderate-magnitude dataset. At this stage, the two datasets become compatible and can be combined within each zonation category, allowing the estimation of path-related parameters without contamination from source effects or heterogeneous local site amplification.\u003c/p\u003e \u003cp\u003e(3) Path-related parameters\u003c/p\u003e \u003cp\u003eHaving unified the datasets within each zonation category, anelastic attenuation was derived from the slope of the logarithmic Fourier adjusted Acceleration Spectra. Alternative formulations for geometrical scattering, ranging between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-0.5}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-1}\\)\u003c/span\u003e\u003c/span\u003e, were also explored, acknowledging the variability reported in the literature and to assess whether such choices could lead to improved attenuation estimates. However, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{-1}\\)\u003c/span\u003e\u003c/span\u003e formulation, which is also supported by the physical plausibility, provided the most consistent results across all zones and was therefore retained.\u003c/p\u003e \u003cp\u003eAfter the first iteration, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{M}/{A}_{m}\\)\u003c/span\u003e\u003c/span\u003e ratio was recomputed using the attenuation relationships derived for each zone, and a second iteration was performed to assess the sensitivity of the results to differences in hypocentral distance. The estimates were found to be insensitive to the variations, both with respect to hypocentral distance and to reasonable stress-drop parameter modifications.\u003c/p\u003e \u003cp\u003e(4) The envelopes of amplification associated with local site conditions\u003c/p\u003e \u003cp\u003eAs a final step, site-related amplification functions were isolated for both datasets and for each zonation category. The plausibility of these site amplifications provides an additional consistency check on the procedure and on the realism of the resulting parameters. This is rather an evalutaion of results final step.\u003c/p\u003e"},{"header":"6. Results","content":"\u003cp\u003eFollowing the steps outlined in the previous chapter, this section presents the results obtained and highlights the internal coherence of the proposed framework.\u003c/p\u003e \u003cp\u003eAs a first step, the ratio between site amplification functions derived from the large-magnitude dataset (\u003cem\u003eMw\u0026thinsp;\u0026gt;\u0026thinsp;6\u003c/em\u003e) and the moderate-magnitude dataset (\u003cem\u003eMw 5\u0026ndash;6\u003c/em\u003e) was determined for each zonation category. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows that this ratio varies with values between approximately 0.5 and 6, depending on frequency and zone. Differences between the first and second iterations reach up to about 30% and follow the trend imposed by the difference between the attenuation model of Oth et al. (2008), used as the initial reference, and the attenuation functions obtained through the proposed procedure.\u003c/p\u003e \u003cp\u003eFor frequencies above approximately 5 Hz, the amplification ratio falls below unity in several zonation categories. Such behavior is observed in the Focșani Basin, Central Moesia accumulation, South Moesia accumulation, and the North Moesia edge. These regions are characterized by thick sedimentary successions, either associated with deep basin structures and/or with pronounced lithospheric bending related to the formation of the Carpathian orogen, which favor the accumulation of deep sediments. By contrast, no systematic reduction of the amplification ratio below unity is observed in the North Moesia ridge, South Moesia edge, Dobrogea Platform, or the East region. Except for the East region, these areas are characterized by relatively shallow local site conditions, typically limited to depths of the order of 100 m or less. In the East region, although sedimentary sequences locally reach several hundred meters in thickness, they are arranged in a laterally continuous and chronologically ordered manner, with a gradual thinning toward the east and without pronounced basin geometries capable of significantly distorting wave propagation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFollowing the uniformization of the two datasets with respect to local site amplification, anelastic attenuation functions were derived for each zonation category (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). The only region for which a reliable attenuation function could not be independently determined is Dobrogea. Owing to the limited number of available recordings, the data did not allow a stable estimation of frequency-dependent attenuation for this zone. However, based on the similarities observed during the zonation analysis and the comparable spectral behavior identified at a preliminary level, the attenuation function derived for the East region was adopted for Dobrogea for the purpose of further evaluation. For all other zones, the determination of anelastic attenuation yields coefficients of determination (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\u0026sup2;\\)\u003c/span\u003e\u003c/span\u003e) exceeding 88%, indicating a good overall fit between the proposed attenuation models and the observed spectra. The highest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\u0026sup2;\\)\u003c/span\u003e\u003c/span\u003e value, approximately 98%, is obtained for the South Moesia accumulation zone, which also corresponds to the region with the largest number of available recordings. These results indicate that the attenuation estimates are statistically stable and can be considered reliable.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e highlights pronounced differences in attenuation behavior between the zonation categories. The lowest attenuation levels are observed for the North Moesia ridge, whereas higher overall attenuation characterizes the North Moesia edge and the South Moesia accumulation. The Focșani Basin exhibits the strongest frequency-dependent variability, indicating a particularly sensitive response to spectral content. These contrasts emphasize the strong structural heterogeneity of the Vrancea-affected region and provide a direct explanation for the wide range of attenuation parameters reported in previous studies based on non-zonated datasets.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAnelastic attenuation parameters derived for each zonation category\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAttenuation parameters\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{0}{f}^{\\alpha\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA. Nord \u0026gt;1 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB. Nord 0.15-1 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC. Central \u0026lt;0.15 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD. Central 0.15\u0026ndash;0.5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eE. South \u0026gt;0.5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eF. Dobrogea \u0026gt;5 Hz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eG. East\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eH. Focsani basin\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{0}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e286*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.49*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{Q}\\:(km/s)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e* as East\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWith respect to the envelopes of site-related amplification derived for each zonation category (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e), the obtained results are physically plausible and consistent with both the recorded ground motions and the independent observations derived from stratigraphic information. A clear magnitude-dependent behavior is observed across several zones, indicating that an order of magnitude increase activates deeper stratigraphic packages. This behavior provides observational support for a dynamic boundary between path-controlled and site-controlled effects, rather than a fixed separation depth.\u003c/p\u003e \u003cp\u003eStrong amplification at short periods - around 0.1 s, consistent to Manea et al. (2020) - is observed in both the Dobrogea Platform and the East region. In contrast, the Focșani Basin exhibits pronounced amplification at long periods (low frequencies), consistent with the activation of deep sedimentary structures. The North Moesia edge displays a comparatively weak dependence on earthquake magnitude, with similar amplification envelopes obtained for both moderate- and large-magnitude events. This behavior suggests a stratigraphic configuration that responds coherently over a wide range of input levels, without pronounced shifts in the frequency range of maximum amplification.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor large-magnitude earthquakes, a clear distinction emerges between the Central Moesia accumulation and the South Moesia accumulation zones. Although these two regions cannot be analyzed jointly due to their different amplification levels, their amplification envelopes exhibit similar overall shapes, with peaks occurring at comparable periods. This similarity indicates that both zones likely involve stratigraphic packages of comparable nature, even though their overall amplification levels differ. In the Central Moesia accumulation zone, the absence of systematically larger long-period amplification relative to the South Moesia accumulation suggests that deeper site conditions are not more effectively activated in this region. Instead, the observed shift in amplification levels between the two zones indicates differences in the impedance structure rather than in the fundamental nature of the activated stratigraphy.\u003c/p\u003e \u003cp\u003eIn the intermediate period range of approximately 0.25\u0026ndash;0.75 s, a similar amplification behavior is observed for the Central Moesia accumulation and the East region, pointing to the possible presence of comparable stratigraphic features across the two tectonic domains.\u003c/p\u003e \u003cp\u003eIn the South Moesia edge, large-magnitude earthquakes activate a stratigraphic package characterized by a fundamental frequency of approximately 2 Hz. This value is consistent with an average-ish fundamental frequencies reported by Manea et al. (2020).\u003c/p\u003e \u003cp\u003eTaken together, the results obtained within the proposed framework are internally consistent, physically plausible, and non-unique in relation to global observations. They demonstrate that the wide range of parameter values reported in the literature for Vrancea intermediate-depth ground motions does not reflect the existence of different physical phenomena. Instead, it arises from the strong structural complexity and heterogeneity of the region, which, when not explicitly classified and decomposed, lead to apparently divergent parameter estimates.\u003c/p\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis study addresses and aims at solving a long-standing ambiguity in the interpretation of strong ground motions generated by the Vrancea intermediate-depth seismic source by explicitly defining, structuring, and decomposing seismic complexity. Rather than treating Vrancea as an anomalous case requiring source-specific adjustments, the analysis demonstrates that the apparent inconsistencies reported in the literature arise from unresolved heterogeneity acting simultaneously at the source, path, and site levels, compounded by sparse strong-motion data.\u003c/p\u003e \u003cp\u003eThe primary contribution of this work is the definition and validation of a general framework applicable to structurally complex regions with limited strong-motion databases, designed to robustly constrain parameters that are repeatedly identified as problematic in such settings. In the Vrancea case, these parameters include anelastic attenuation, geometrical scattering, stress drop, and local site conditions. The framework is not tuned to Vrancea-specific behavior; instead, it enforces physical plausibility and internal consistency across all model components.\u003c/p\u003e \u003cp\u003eA central element of the framework is the explicit definition of seismic complexity through zonation, constructed independently of strong-motion recordings. Geological, tectonic, geophysical, and geomorphological information is used as a pivot for organizing heterogeneity, avoiding circular reasoning and preventing observational bias from being embedded in the grouping of data. This zonation enables the systematic decomposition of variability that otherwise manifests as instability in parameter estimation.\u003c/p\u003e \u003cp\u003eWithin this structure, the study provides constrained and physically consistent determinations of key path-related parameters, including frequency-dependent anelastic attenuation and geometrical scattering, and high-frequency attenuation parameter κ determined as a secondary outcome. The results demonstrate that the wide range of attenuation relations reported in the literature can be directly explained by spatial variability along propagation paths, rather than by source-specific anomalies. Once zonation is introduced, attenuation behavior becomes stable, statistically robust, and interpretable.\u003c/p\u003e \u003cp\u003eStress drop is deliberately not treated as a calibration parameter. By constraining it within ranges compatible with general seismological theory, the analysis avoids compensating unresolved path or site effects through source adjustments. The results show that no Vrancea-specific source physics are required once complexity is properly decomposed.\u003c/p\u003e \u003cp\u003eA further contribution of this work is the explicit determination of site amplification envelopes for each zonation category. These envelopes provide generalized descriptions of local site behavior that can be directly used in applications such as GMPE development and seismic hazard assessment. The results demonstrate a clear magnitude-dependent activation of stratigraphic packages, supporting the concept of a dynamic boundary between path-controlled and site-controlled effects, rather than a fixed depth to seismic bedrock.\u003c/p\u003e \u003cp\u003eTo address the intrinsic limitation imposed by the scarcity of strong-motion recordings from large Vrancea earthquakes, the framework introduces a systematic \u0026ldquo;uniformization\u0026rdquo; of local site conditions between moderate- and large-magnitude datasets. By compensating for magnitude-dependent site amplification differences, the statistical power of the database is increased while preserving regional specificity. This approach allows moderate-magnitude events to be meaningfully integrated into the estimation of path-related parameters without contaminating results with incompatible site effects.\u003c/p\u003e \u003cp\u003eThe study also introduces a simple and transparent preliminary measure of spectral amplification persistence, defined as the rate of spectral ordinates exceeding 0.75 of the normalized peak amplitude across recordings. While intentionally non-parametric, this measure proves effective in highlighting high-amplification spectral intervals and in distinguishing systematic zonal behavior, providing an additional qualitative constraint on the interpretation of results.\u003c/p\u003e \u003cp\u003eMore broadly, the integration of transdisciplinary information from different fields - geology, tectonics, basin evolution, and seismology - proves essential for defining seismic complexity in a way that removes ambiguity rather than adding interpretative layers. Through this integration, several long-standing debates in the literature concerning source spectral characteristics, attenuation, and site effects are reconciled without invoking exceptional behavior.\u003c/p\u003e \u003cp\u003eIn conclusion, the Vrancea intermediate-depth seismic source does not challenge general seismological principles. It represents a case in which complexity is amplified and cannot be neglected. When this complexity is explicitly defined, structured, and consistently treated within a unified framework, the apparent anomalies disappear. The methodology presented here is transferable to other tectonic environments characterized by strong heterogeneity and sparse strong-motion data, offering a robust pathway toward physically consistent seismic characterization under limiting observational conditions.\u003c/p\u003e"},{"header":"Declarations","content":" \u003cp\u003e \u003cstrong\u003eCompeting interests\u003c/strong\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e \u003cp\u003eAnabella Cotovanu: Conceptualization, Methodology, Formal analysis, Investigation, Writing - Original Draft; Elisei Cojan: Visualization, Writing - Review \u0026amp; Editing; Radu Vacareanu: Supervision, Resources, Project administration, Writing - Review \u0026amp; Editing.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e \u003cp\u003eThis research was funded by a grant of the Ministry Education and Research, CCCDI-UEFISCDI, project number PN-IV-P6-6.1-CoEx-2024-0102, within PNCDI IV.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAldea, A., Vacareanu, R., Lungu, D., Pavel, F., \u0026amp; Arion, C. 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A global framework for the Earth: putting geological sciences in context. \u003cem\u003eGlobal and Planetary Change, 171\u003c/em\u003e, 293\u0026ndash;321. doi:https://doi.org/10.1016/j.gloplacha.2017.12.019\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"seismic complexity, sparse strong-motion data, source–path–site decomposition, physically consistent seismic parameters, Vrancea intermediate-depth earthquakes","lastPublishedDoi":"10.21203/rs.3.rs-9267402/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9267402/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGround motions generated by the Vrancea intermediate-depth seismic source exhibit long-recognized intricate characteristics that challenge standard seismological interpretations. As a result, Vrancea earthquakes are frequently excluded from global comparative studies, being treated as exceptions for which conventional source, path, and site models fail to provide consistency. This study addresses this long-standing problem by defining and resolving the seismic complexity of Vrancea ground motions through a unified source\u0026ndash;path\u0026ndash;site framework.\u003c/p\u003e \u003cp\u003eThe proposed methodology systematically decomposes recorded ground-motion variability into source-, propagation-, and site-related contributions while explicitly accounting for the specific constraints imposed by limited recordings of major events and strong structural heterogeneities. Key seismic parameters that have remained debated or poorly constrained in the literature are re-evaluated, yielding physically consistent behaviors that satisfy general seismological requirements.\u003c/p\u003e \u003cp\u003eApplied to the Vrancea seismic source, the framework demonstrates that the apparent anomalies commonly reported in previous studies do not reflect fundamentally different physical processes but instead arise from the pronounced complexity and strong interdependence of source, path, and site characteristics. Once treated coherently, Vrancea ground motions conform to general rules of seismic behavior. Beyond the regional case study, the proposed approach provides a transferable methodology for the analysis of complex seismic sources worldwide, particularly in tectonic settings characterized by sparse strong-motion data and non-standard ground-motion features.\u003c/p\u003e","manuscriptTitle":"Defining and resolving seismic complexity through a unified source–path–site framework: the Vrancea intermediate-depth ground motions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-14 02:00:54","doi":"10.21203/rs.3.rs-9267402/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2026-04-04T16:32:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Bulletin of Earthquake Engineering","date":"2026-04-03T10:16:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-03T05:06:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Bulletin of Earthquake Engineering","date":"2026-04-01T03:19:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-earthquake-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"beee","sideBox":"Learn more about [Bulletin of Earthquake Engineering](https://www.springer.com/journal/10518)","snPcode":"10518","submissionUrl":"https://submission.nature.com/new-submission/10518/3","title":"Bulletin of Earthquake Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"bff81789-3649-401e-b543-47baaa429e9f","owner":[],"postedDate":"April 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-14T02:00:54+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-14 02:00:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9267402","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9267402","identity":"rs-9267402","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}