Pore pressure prediction based on elastic parameters derived from seismic prestack multiwave inversion

Pore pressure prediction based on elastic parameters derived from seismic prestack multiwave inversion | 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 Article Pore pressure prediction based on elastic parameters derived from seismic prestack multiwave inversion Yutan Dou, Fei Li, Yonggang Wang, Mengbo Zhang, Guanghong Du, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5250630/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Pore pressure prediction is one of the major geological tasks related to oil and gas exploration and development. In this research, highly accurate elastic parameters, such as P- and S-wave impedance and density from seismic prestack multiwave joint inversion, are obtained and then innovatively converted to the burial depth domain. Moreover, based on the formation pressure measurements of wells with acoustic full-waveform logging data, a second-order polynomial is applied for △H/H and H via the least-square method. Finally, the pore pressure is calculated using the modified Liu’s pore pressure model. The pore pressure prediction method, which incorporates accurately calculated elastic parameters, S-wave impedance, and density, is found to have a higher prediction accuracy than methods based solely on P-wave impedance; it also provides enhanced resolution for pore pressure prediction in thin reservoirs. The presented method is particularly suitable for tight gas fields. pore pressure multiwave pressure prediction prestack multiwave joint inversion elastic parameter tight gas field Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1 Introduction Pore pressure is important for the successful exploration and production of hydrocarbons, and accordingly, its prediction is a major geological task. During the drilling process, accurate pore pressure prediction plays a vital role in improving drilling safety and efficiency and reducing costs. To develop oil and gas reservoirs safely, efficiently, and reasonably, it is necessary to develop a reasonable calculation method for pore pressure prediction 1 – 3 . In the 1960s, scholars began to study pore pressure prediction using seismic velocity 4 . Due to the limited level of research at that time, there were significant errors in the test results, and it was not until many years later that substantial progress was made. In recent years, with the continuous innovation of testing technology, new drilling, logging, and seismic technologies have rapidly improved the accuracy of pore pressure prediction. The gradual development of pore pressure prediction can be divided into three stages. The first stage was from 1968 to 2003, during which most seismic techniques were based on P-wave velocity data. Eaton 5 , 6 developed equations to predict geopressure magnitudes from well log and drilling parameter data. The present study relies on normal compaction trend lines. Through comprehensive research on logging, drilling, seismic and other data in the Gulf of Mexico and other regions, Fillippone 7 , 8 proposed two sets of simple and practical pore pressure calculation formulas that do not rely on normal compaction trend lines. Good results have been achieved in practical applications in areas such as the Gulf of Mexico. However, the accuracy of this method depends on the P-wave velocity data. Eberhart-Phillips 9 used multivariate analysis to investigate the influence of the effective pressure Pe, porosity phi, and clay content C on the compressional velocity Vp and shear velocity Vs of sandstones. However, these three parameters phi, C, and Pe are too simplified, which affects the prediction accuracy. Based on the work of many predecessors, Liu 10 more deeply studied the physical relation between the formation pressure and interval velocity and reasonably improved two models of pressure prediction. Then, the distribution of abnormal formation pressures in the Paleogene in the northern sag of the Liaoxi Depression was determined by excellent inversion of the seismic data. Liu's method has made significant improvements compared to Fillippone's method. After a large number of on-site case studies, Bowers 11 proposed that the porosity of formation rocks generally does not change with changes in effective rock stress due to the influence of different pressurization methods and stress evolution on formation rocks. In a sense, the proposal of this research theory has improved the pressure prediction method of the unloading curve to a certain extent. Since 2003, a large number of scholars have introduced Poisson's ratio into the process of pore pressure prediction. Xia 12 analyzed the actual situation of using directional wells extensively in offshore drilling. In addition, how to use offshore directional well logging data to predict formation pressure in drilling areas is discussed in detail. In the process of calculating the seismic pressure, he approximated the effective stress as an exponent of Poisson's ratio. By introducing the S-wave velocity, Wang’s method 13 reduced the multiplicity of the pressure forecast and improved the accuracy. Based on the analysis of the formation pressure anomaly in the Wufeng-Longmaxi Formation, the abnormal formation pressure was attributed to horizontal and vertical forces, and the Poisson’s ratio formation pressure prediction method was developed based on the Poisson’s ratio calculation using seismic parameters. It has been proven that this prediction method is suitable for predicting the shale gas formation pressure in the Wufeng-Longmaxi Formations 14 . The third stage began after the rise of neural networks. The basic steps of predicting pore pressure in this context are to use various logging curves for pressure prediction, to use multiple regression measurements to predict pressure curves, or to use neural networks of different depths to fit pressure curves 15 – 18 . However, due to the black box nature of neural networks, the physical meaning of this pressure prediction method is not very clear. For methods that rely on normal compaction trend lines, the prediction accuracy depends on plotting an accurate normal compaction trend, especially for deeply buried formations. However, the normal compaction trend in these theories can only be identified empirically, which leads to the intrinsic subjective uncertainty of such methods, and their applicability is limited to cases in which enough information is available to identify the normal compaction trend. The methods, which are independent of the normal compaction trend, predict pore pressure via seismic pore pressure modeling. Such methods are much more feasible and, in particular, applicable to areas that are subjected to preliminary exploration. The most representative methods are Liu's method and Fillippone's method. Liu's method is responsible fora greater amount of progress compared to Fillippone's method due to the introduction of Poisson's ratio, but the disadvantage is that it is assumed to be a constant. In general, the current seismic pore pressure models are all ultimately based on correlations with the P-wave velocity and ignore the S-wave velocity and density 19 . Therefore, such modeling methods fail to offer sufficient prediction accuracy and high resolution. This research focuses on the predrilling pore pressure prediction of tight gas reservoirs. The seismic pore pressure prediction model developed by Liu's method is modified. Then, reliable high-resolution elastic parameters (including the P- and S-wave impedance and density data) are obtained via prestack multiwave joint inversion of prestack multiwave multicomponent seismic data (PP and PS wave data). Finally, an accurate predrilling seismic pore prediction method based on prestack multiwave parameters was developed for tight gas reservoirs. 2 Method The workflow for pore pressure prediction based on prestack multiwave parameters (Fig. 1 ) is described below. Step 1: Obtain n ( n ≥ 3) limited-offset stacks of PP and PS (converted wave) after amplitude-preserving processing, and align them; subsequently, perform the prestack PP-PS simultaneous joint inversion to obtain the elastic parameter data of \(P_{{imp}}^{T}\) (P-wave impedance), \(S_{{imp}}^{T}\) (S-wave impedance), and \({\rho ^{\text{T}}}\) (density) in the time domain. Step 2: Correct the velocity model based on the velocity spectrum according to the calibrated well-logging velocity model. Then, convert the elastic parameter data obtained above into the burial depth domain using the corrected velocity model with the ground surface as the datum. Therefore, \(P_{{imp}}^{D}\) (P-wave impedance), \(S_{{imp}}^{D}\) (S-wave impedance), and \({\rho ^{\text{D}}}\) (density) in the measured depth domain are obtained. The time‒depth conversion presented above is different from that of conventional methods. Specifically, the datum of the conventional time‒depth conversion is the sea level, and thus, the obtained depth is the altitude. In contrast, the datum of the presented time‒depth conversion is the ground surface, and the depth here refers to the measured depth. Accordingly, the converted data are in the measured depth domain. This step lays the foundation for estimating the overburden pressure. Step 3: Calculate the overburden pressure \({P_{ov}}\) using the obtained density data. Specifically, integrate \({\rho ^{\text{D}}}\) in the depth domain along the burial depth to obtain the overburden pressure: $${P_{ov}}=\int_{0}^{{{H_0}}} {{\rho ^{\text{D}}}\left( H \right)} gdh$$ 1 where \({H_0}\) is the depth of the observation point from the ground surface; g is the gravitational acceleration; and is the burial depth. Step 4: Calculate the effective stress of the rock framework \({P_e}\) according to the P- and S- wave impedance and density. In the seismic formation pressure Model I (SFPM-I) proposed by Liu 10 , the effective stress of the rock framework is expressed as: $${P_e}=\frac{{1{\text{+}}\sigma }}{{3{\text{-}}3\sigma }} \cdot \rho \cdot {V_p}^{2} \cdot {{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}$$ 2 where \(\sigma\) is Poisson's ratio; \({V_p}\) is the P-wave velocity; \(\rho\) is the density; and \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) is the compaction deformation per unit thickness. Liu defines \(\sigma\) in Eq. 2 as a constant (equal to 0.12), which makes Eq. 2 a univariate quadratic function of the P-wave velocity \({V_p}\) . However, in this research \(\sigma\) is kept a variable and Eq. 2 is rewritten as: $${P_e}={{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} {{\rho ^{\text{D}}}}}} \right. \kern-0pt} {{\rho ^{\text{D}}}}} \cdot {{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}$$ 3 Then, the effective stress of the rock framework \({P_e}\) is calculated using Eq. 3 . Step 5: Calculate the pore pressure \({P_p}\) by subtracting the rock framework effective stress from the overburden pressure: $${P_p}={P_{ov}} - {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} {{\rho ^{\text{D}}}}}} \right. \kern-0pt} {{\rho ^{\text{D}}}}} \cdot {{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}$$ 4 where \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) is a variable dependent on various factors, such as depth, lithology, and sedimentary burial history, which are, in most cases, difficult to calculate directly. The solution of this research is as follows. First, based on the measured pressure of multiple wells with available acoustic full-waveform well logging data, calculate the overburden pressure profiles of these wells; then, substitute the computed \({P_{ov}}\) , and measured \({P_p}\) , \(P_{{imp}}^{{\text{D}}}\) , \(S_{{imp}}^{{\text{D}}}\) , and \({\rho ^{\text{D}}}\) into Eq. 4 to determine \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) at these wells; finally, perform the second-order polynomial fitting between \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) and H via the least square method based on the measured formation pressure data and the calculated \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) of the wells: $${{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}=a{H^2}+bH+c$$ 5 where a , b and c are the fitting coefficients. Based on the built second-order polynomial relationship, the P- and S-wave impedances, and the density, the effective stress of the rock framework is calculated using Eq. 3 . The modified pore pressure presented in this research is: $${P_p}={P_{ov}} - {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} {{\rho ^{\text{D}}}}}} \right. \kern-0pt} {{\rho ^{\text{D}}}}} \cdot \left( {a{H^2}+bH+c} \right)+D$$ 6 where D is an empirical constant specific to the area of interest. The corresponding pore pressure coefficient formula k can be written as: $$k={{\left( {{P_{ov}} - {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} {{\rho ^{\text{D}}}}}} \right. \kern-0pt} {{\rho ^{\text{D}}}}} \cdot \left( {a{H^2}+bH+c} \right)+D} \right)} \mathord{\left/ {\vphantom {{\left( {{P_{ov}} - {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} \mathord{\left/ {\vphantom {{\left( {P{{_{{imp}}^{{\text{D}}}}^2} - \frac{4}{3}S{{_{{imp}}^{{\text{D}}}}^2}} \right)} {{\rho ^{\text{D}}}}}} \right. \kern-0pt} {{\rho ^{\text{D}}}}} \cdot \left( {a{H^2}+bH+c} \right)+D} \right)} {{P_w}}}} \right. \kern-0pt} {{P_w}}}$$ 7 where \({P_w}\) is the hydrostatic pressure. Ultimately, the calculated pore pressure can be corrected according to the pressure measurements obtained from drilling, after which the pore pressure (coefficient) can be mapped. 3 Applications The Sulige area of the Ordos Basin is located at the border of Shaanxi, Gansu and Inner Mongolia provinces in China, with desert, grassland, and hilly areas on the surface. The terrain is relatively flat, with an altitude of 1200–1500 meters. The sedimentary strata mainly include the Ordovician in the lower Paleozoic, the Permian in the upper Paleozoic, and the Carboniferous; the Cretaceous, Jurassic, Triassic, and the Tertiary and Quaternary strata of the Mesozoic. In 2000, the discovery of the Sulige gas field in the Upper Paleozoic Permian H8 and S1 formations of the Sulige region revealed abundant natural gas resources in the area. H8 is currently the main reservoir series developed by Sulige, with quartz sandstone as the main reservoir and locally developed lithic quartz sandstone. The porosity of the reservoir is low, the permeability is low, and the physical properties are relatively poor. The continuity of the sand layer is poor, and the gas storage enrichment area is affected by the tight lithological zone. The pore pressure coefficient of the Paleozoic formations in this area is generally 0.76–0.95 (abnormal underpressure) 20 , 21 . The method presented above is applied to this area for validation. 3.1 Multiwave resolution analysis AVO analysis technology is a technique that studies gas bearing properties based on the variation in amplitude with offset. The application of PP-wave AVO technology is quite extensive, and the amplitude of PP-wave reflection at the top of gas-bearing sandstone in the Sulige area increases with increasing offset, mostly belonging to the third type of AVO. PS-wave AVO is more complex, but its ability to identify gas-bearing layers in the local area is better than that of PP-waves. Figure 2 shows the PP-wave gather profile of (a, b) and the PS-wave gather profile of (c, d). On the PP-wave gather profile, the H8 reflection of well S44 shows an increasing trend, while the H8 reflection of well S51 remains basically unchanged. On the PS-wave gather profile, the H8 reflections of wells S44 and S51 are initially enhanced and then weakened, but the gradient change in well S44 is greater. The gas test results are S44 > S51. In summary, if the reflection amplitude at the top of the reservoir on the PP-wave gather profile increases significantly with increasing offset and the reflection amplitude gradient on the PS-wave gather profile changes greatly, the stacked profile shows a "bright spot" feature, then the thickness of the reservoir sand body is large, and the gas content is good; this proves that the resolution of PS-waves in gas-bearing reservoirs is greater than that of PP-waves. For tight sandstone, multiwave data can improve the resolution ability for favorable reservoirs. 3.2 Prestack PP + PS simultaneous joint inversion It is difficult to directly clarify the distribution of effective reservoirs using conventional reservoir prediction techniques and guide later exploration and development work. In theory, multicomponent seismic exploration technology has unique advantages in solving complex structures, complex lithology oil and gas reservoirs, and anisotropic research. Therefore, this topic has received increasing research, and many oil companies have begun to conduct experiments on this technology. Currently, this technology is mostly used for offshore hydrocarbon exploration worldwide and has achieved good results. The Colorado School of Mines in the United States and the University of Calgary in Canada have accumulated certain achievements in this research 22 . However, there is relatively little research on onshore oil and gas exploration, and some good application effects have not yet been reported 23 – 27 . Multiwave data are used in this work to study tight and thin sand bodies in local areas. (1) PP-PS wave data alignment The processes of Pre-stack PP + PS simultaneous joint inversion and PP-wave pre-stack simultaneous inversion are basically the same; the difference is that the input data include not only PP-wave offset stacking data but also PS-wave offset stacking data in the PP domain. The primary issue in inversion is to align the PP-wave with the PS-wave data, which compresses the PS-wave from the PS domain to the PP domain. An accurate Vp/Vs ratio is derived from the PP prestack inversion, which is then used to transform the PS-wave offset stacking data to the PP domain. Subsequently, according to the reflection marker horizon, horizon compression is performed for the PS-wave data to obtain the optimal matched PP and PS wave profiles. Figure 3 shows the PP-PS-aligned stacked profiles (PP domain). The PP-wave seismic profile and the PS-wave seismic profile are similar in terms of large wave group characteristics, but there are differences in many internal details. In fact, this is exactly the AVO feature that we are striving to find, and the addition of PS-wave data has increased the recognition ability of favorable reservoirs. (2) Prestack PP + PS simultaneous joint inversion The multiwave survey line L1 is selected to perform the prestack PP + PS simultaneous joint inversion using seven selected limited-offset stacks of PP and PS stacks. Perform PP-PS wave data alignment. Furthermore, the PP and PS limited-offset stacks and corresponding angle wavelets are input to generate the vertical variation trends of various parameters (P-wave impedance, density, and Vp/Vs) and the lateral constraint ranges. An optimal group of parameters is identified via quality control. The simultaneous joint inversion of PP and PS wave data is performed based on the Knott-Zoeppritz equation. Simultaneous joint inversion can obtain the P- and S-wave impedance and density, which are more robust and have high resolution 25 , 26 . Figure 4 shows P-wave prestack inversion (a) and multiwave joint inversion (b) for the Poisson's ratio profiles of Line S10. The consistency between the Poisson's ratio profile obtained from the multiwave joint inversion and the gas testing results is much greater than that obtained from the P-wave prestack inversion. Multiwave joint inversion overcomes the problem of multiple solutions for single P-wave detection of sand bodies and fluids and improves the accuracy of seismic reservoir prediction. Figure 5 shows the P- and S-wave impedances and density of Line L1 derived from PP + PS pre-stack simultaneous joint inversion. At CDP 7488 of Well SuX1 in Fig. 2 , the P-wave impedance of the H8 reservoir is low (11182 g/cc*m/s), the S-wave impedance is high (6145.6 g/cc*m/s), and the density is low (2.46 g/cc). 3.3 Conversion from the time domain to the burial depth domain Fine well-seismic calibration is carried out for wells SuX1, SuX2, and SuX3, which are crossed by Line L1, to generate the velocity model. Afterward, the developed velocity model is adopted to calibrate the velocity model originating from the velocity spectrum. Finally, the P- and S-wave impedances and density are converted to the measured burial depth domain (Fig. 6 ), with the ground surface set as the depth datum. 3.4 Second-order polynomial fitting between △H/H and H using data from multiple wells \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) is a complex variable influenced by multiple factors, such as H , lithology, and sedimentary burial history. Establishing the relationship between \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) and H is a complex process, and in general, fitting methods are used to establish empirical relationships to connect the relationships between these variables. Based on the pore pressure measurements and measured or calculated elastic parameters ( \({P_p}\) , \(P_{{imp}}^{{\text{D}}}\) , \(S_{{imp}}^{{\text{D}}}\) , \({\rho ^{\text{D}}}\) , and \({P_{ov}}\) ) of the target interval, \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) values are obtained for the H8 reservoirs of wells SuX1, SuX2, SuX3, SuX4, SuX5, SuX6, and SuX7, which possess acoustic full-waveform logging data. Next, a second-order polynomial correlation between \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) and H is derived for the study area via least-square-method fitting based on the measured pore pressure data and computed \({{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}\) values of the wells and correction of the calculated pore pressure according to the measured pressure: $${{\Delta H} \mathord{\left/ {\vphantom {{\Delta H} H}} \right. \kern-0pt} H}={\text{-8}}{\text{.957745}} \times {\text{1}}{{\text{0}}^{ - 14}}{H^2}+{\text{5}}{\text{.7128389325}} \times {\text{1}}{{\text{0}}^{ - 10}}H{\text{-1}}{\text{.1755738181174 }} \times {\text{1}}{{\text{0}}^{ - 7}}{\text{ }}$$ 8 3.5 Pore pressure (coefficient) mapping Figure 7 shows pore pressure/pressure coefficient maps predicted by different methods. Using Eqs. 6 , 7 , and 8 , the pore pressure (coefficient) can be mapped across the study area, in which D is empirically set to -27 MPa. The maps are presented in Fig. 7 (a) and 7(b). The pore pressure and pressure coefficients are 29.77 MPa and 0.92, respectively, at CDP 7488, which is also the location of Well SuX1. Moreover, the measured pore pressure and pressure coefficient are 29.52 MPa and 0.91, respectively. Hence, the prediction is in good agreement with the measurement and thus satisfactory. The resulting 2-D profiles have high resolution, which suggests improved pore pressure prediction performance for thin reservoirs. Figure 7 (c) shows the pore pressure predicted by Liu’s methods. The resolution of the pressure profile is significantly lower than that of the method proposed in this paper. Due to the addition of multiwave data and the improvement of pressure prediction methods, the pore pressure prediction method presented in this research is particularly suitable for thin tight gas reservoirs. 4 Discussion The conventional pore pressure prediction method is not suitable for low-porosity and low-permeability formations because although the acoustic time difference has a certain indicative effect on abnormally high pressure, the response is weak, and the magnitude of abnormally high pressure does not show a direct relationship with the deviation degree of the acoustic time difference. However, abnormally high pressure in low-porosity and low-permeability formations is difficult to accurately reflect during drilling, resulting in inaccurate reference data from conventional prediction methods and further leading to distorted prediction results. The seismic velocity is the key to accurately calculating the seismic pressure. When conditions permit, incorporating multiwave data as much as possible can help accurately predict the seismic pore pressure; this is particularly crucial for tight gas reservoirs. The pore pressure calculation model should introduce the shear wave velocity as much as possible to improve the prediction accuracy. The additional information provided by the S-wave velocity may help to reduce the ambiguity between variations in pore pressure and variations in lithology and fluid content 28 . 5 Conclusions Pore pressure prediction based on seismic wave velocities has become the main methodology for predrilling pore pressure prediction. The calculation of elastic parameters, conversion to the burial depth domain, and selection of prediction models are key to obtaining pore pressure prediction results. (1) The elastic parameter datasets of the P- and S-wave impedance and density derived from PP + PS prestack simultaneous joint inversion are robust and have high resolution, which favors subsequent seismic pore pressure prediction. (2) The pore pressure model proposed by Liu’s method is modified by incorporating the S-wave velocity and density terms, which improves the prediction accuracy and resolution. (3) Predrilling seismic pore pressure modeling (prediction), based on prestack multiwave elastic parameters, can generate highly accurate estimates and is particularly suitable for tight gas fields. Declarations Acknowledgements This paper is based on work supported by China National Petroleum Corporation "14th Five-Year Plan" forward-looking basic major scientific and technological projects (No. 2021DJ2205、2021DJ0403、2021DJ0406). Author contributions Yutan Dou. Fei Li. and Yonggang Wang. wrote the main manuscript text and Mengbo Zhang. Guanghong Du. Feng Liu. prepared figures 3-4. 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Research on joint inversion method of seismic compressional and shear waves from ocean-bottom nodes. Marine Geophysical Research 42 , doi:10.1007/s11001-021-09435-z (2021). Li, K.-R. & He, B.-S. Extraction of P- and S-wave angle-domain common-image gathers based on first-order velocity-dilatation-rotation equations. Applied Geophysics 17 , 92-102, doi:10.1007/s11770-019-0799-5 (2020). Dou, Y. A method to remove depositional background data based on the Modified Kernel Hebbian Algorithm. Acta Geophysica 68 , 701-710, doi:10.1007/s11600-020-00415-2 (2020). Dou, Y. et al. PP and PS wave seismic fluid detection techniques in SX area of Ordos Basin. Natural Gas Geoscience 25 , 1637-1643, doi:10.11764/j.issn.1672-1926.2014.10.1637 (2014). Dariu, H., Garotta, R. & Granger, P. Y. in SEG Technical Program Expanded Abstracts SEG Technical Program Expanded Abstracts 120-123 (Society of Exploration Geophysicists, 2003). Sayers, C. M., Woodward, M. J. & Bartman, R. C. Predrill pore-pressure prediction using 4-C seismic data. The Leading Edge 20 , 1056-1059, doi:10.1190/1.1487313 (2001). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-5250630","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":371126810,"identity":"708fc47f-cbe6-4d2e-b839-9958b56187e4","order_by":0,"name":"Yutan Dou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIiWNgGAWjYBACewhlA6EYGyQIazFsAJEJaQwMbMRqMTgA1nIYpoUIhxkc7zFg5v1xPo9fvvfhg587LPL4G5gfPrrBYJeHU8uZMwbMPAm3iyXb2I0Ne89IFEscYDM2zmFILsap5UYOWEvihmNsbNKMbRKJDQd42KRzGA4k4nIkVMu5xP0wLfOJ1HIgcQMbVMsGQloMe44VMM5JSy6WOJbGbNgL1LLxMMgvBsk4tdizN29geGNjl8fffIzxwc+2usR5x5sfPs6psMOpBQjYf/EAYwbBZwY7GLd6EGD8gaJlFIyCUTAKRgEaAACzElJWhJ7PXAAAAABJRU5ErkJggg==","orcid":"","institution":"Research institute of petroleum exploration \u0026 development-northwest, Petrochina","correspondingAuthor":true,"prefix":"","firstName":"Yutan","middleName":"","lastName":"Dou","suffix":""},{"id":371126811,"identity":"d4b189d8-3406-447f-afd6-21a625ab705b","order_by":1,"name":"Fei Li","email":"","orcid":"","institution":"Petrochina changqing oilfield company","correspondingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"Li","suffix":""},{"id":371126812,"identity":"6001f07d-17dc-454d-a077-2261afac3342","order_by":2,"name":"Yonggang Wang","email":"","orcid":"","institution":"Petrochina changqing oilfield company","correspondingAuthor":false,"prefix":"","firstName":"Yonggang","middleName":"","lastName":"Wang","suffix":""},{"id":371126813,"identity":"a1c888e5-2f71-4d43-b2ba-2bfdc7f0886e","order_by":3,"name":"Mengbo Zhang","email":"","orcid":"","institution":"Petrochina changqing oilfield company","correspondingAuthor":false,"prefix":"","firstName":"Mengbo","middleName":"","lastName":"Zhang","suffix":""},{"id":371126816,"identity":"a0dd602d-90f5-4c24-b8ff-d497cbd6630a","order_by":4,"name":"Guanghong Du","email":"","orcid":"","institution":"Petrochina changqing oilfield company","correspondingAuthor":false,"prefix":"","firstName":"Guanghong","middleName":"","lastName":"Du","suffix":""},{"id":371126818,"identity":"a3cd45c7-dfd4-4b5b-8ca8-a0e7a7a44e7e","order_by":5,"name":"Feng Liu","email":"","orcid":"","institution":"Petrochina changqing oilfield company","correspondingAuthor":false,"prefix":"","firstName":"Feng","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-10-12 09:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5250630/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5250630/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67857427,"identity":"ce8cd7f4-12d4-45f6-a84a-3f05e33a39fe","added_by":"auto","created_at":"2024-10-30 11:51:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":175459,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eWorkflow of pore pressure prediction based on prestack multiwave parameters\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/c7dc900f5a2f45c333b21a76.png"},{"id":67858564,"identity":"8632f47d-98a0-45f8-9aa8-a32e408141dd","added_by":"auto","created_at":"2024-10-30 11:59:40","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":470807,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePP-wave gather profile of (a, b) and PS-wave gather profile of (c, d)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/85a2866f416c86ee05a49e88.png"},{"id":67857428,"identity":"1db52353-8144-479a-8730-1cb5678e8347","added_by":"auto","created_at":"2024-10-30 11:51:40","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":266295,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePP-PS aligned stacked profiles (PP domain)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/66d92765c59db582c85d2189.png"},{"id":67857425,"identity":"04aba34e-1f04-4057-951e-a28149ceed91","added_by":"auto","created_at":"2024-10-30 11:51:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":396323,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eP-wave prestack inversion(a) and multiwave joint inversion(b) for the Poisson's ratio profiles of Line S10\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/16a97f47e7b4092b4285ee83.png"},{"id":67857422,"identity":"b280dedd-abe4-42dc-b3f0-712940521813","added_by":"auto","created_at":"2024-10-30 11:51:40","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":352101,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe P- and S-wave impedance and density of Line L1, derived from the PP+PS prestack simultaneous joint inversion (time domain)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/8114b4b8a3e63c93b707c79d.png"},{"id":67858563,"identity":"e9d4b8f4-0976-4fb3-a7eb-79c5d4c83c7c","added_by":"auto","created_at":"2024-10-30 11:59:40","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":317205,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe P- and S-wave impedance, and density of Line L1, derived from the PP+PS prestack simultaneous joint inversion (depth domain)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/77ccf2b3531bf2ed1188e3c9.png"},{"id":67858565,"identity":"41d39139-f91f-4293-8679-d359fd9eb1d3","added_by":"auto","created_at":"2024-10-30 11:59:40","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":278952,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePore pressure/pressure coefficient maps predicted by different methods\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/11b19f606801c0e0611e7b6f.png"},{"id":70533927,"identity":"18bfa733-3675-4f8f-a887-626309a07fd7","added_by":"auto","created_at":"2024-12-04 06:24:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2834377,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5250630/v1/636c56db-267c-435b-a28c-2f3c0e0f998c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Pore pressure prediction based on elastic parameters derived from seismic prestack multiwave inversion","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePore pressure is important for the successful exploration and production of hydrocarbons, and accordingly, its prediction is a major geological task. During the drilling process, accurate pore pressure prediction plays a vital role in improving drilling safety and efficiency and reducing costs. To develop oil and gas reservoirs safely, efficiently, and reasonably, it is necessary to develop a reasonable calculation method for pore pressure prediction\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn the 1960s, scholars began to study pore pressure prediction using seismic velocity\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Due to the limited level of research at that time, there were significant errors in the test results, and it was not until many years later that substantial progress was made. In recent years, with the continuous innovation of testing technology, new drilling, logging, and seismic technologies have rapidly improved the accuracy of pore pressure prediction.\u003c/p\u003e \u003cp\u003eThe gradual development of pore pressure prediction can be divided into three stages. The first stage was from 1968 to 2003, during which most seismic techniques were based on P-wave velocity data. Eaton\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e developed equations to predict geopressure magnitudes from well log and drilling parameter data. The present study relies on normal compaction trend lines. Through comprehensive research on logging, drilling, seismic and other data in the Gulf of Mexico and other regions, Fillippone\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e proposed two sets of simple and practical pore pressure calculation formulas that do not rely on normal compaction trend lines. Good results have been achieved in practical applications in areas such as the Gulf of Mexico. However, the accuracy of this method depends on the P-wave velocity data. Eberhart-Phillips\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e used multivariate analysis to investigate the influence of the effective pressure Pe, porosity phi, and clay content C on the compressional velocity Vp and shear velocity Vs of sandstones. However, these three parameters phi, C, and Pe are too simplified, which affects the prediction accuracy. Based on the work of many predecessors, Liu\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e more deeply studied the physical relation between the formation pressure and interval velocity and reasonably improved two models of pressure prediction. Then, the distribution of abnormal formation pressures in the Paleogene in the northern sag of the Liaoxi Depression was determined by excellent inversion of the seismic data. Liu's method has made significant improvements compared to Fillippone's method. After a large number of on-site case studies, Bowers\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e proposed that the porosity of formation rocks generally does not change with changes in effective rock stress due to the influence of different pressurization methods and stress evolution on formation rocks. In a sense, the proposal of this research theory has improved the pressure prediction method of the unloading curve to a certain extent.\u003c/p\u003e \u003cp\u003eSince 2003, a large number of scholars have introduced Poisson's ratio into the process of pore pressure prediction. Xia\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e analyzed the actual situation of using directional wells extensively in offshore drilling. In addition, how to use offshore directional well logging data to predict formation pressure in drilling areas is discussed in detail. In the process of calculating the seismic pressure, he approximated the effective stress as an exponent of Poisson's ratio. By introducing the S-wave velocity, Wang\u0026rsquo;s method\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e reduced the multiplicity of the pressure forecast and improved the accuracy. Based on the analysis of the formation pressure anomaly in the Wufeng-Longmaxi Formation, the abnormal formation pressure was attributed to horizontal and vertical forces, and the Poisson\u0026rsquo;s ratio formation pressure prediction method was developed based on the Poisson\u0026rsquo;s ratio calculation using seismic parameters. It has been proven that this prediction method is suitable for predicting the shale gas formation pressure in the Wufeng-Longmaxi Formations\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe third stage began after the rise of neural networks. The basic steps of predicting pore pressure in this context are to use various logging curves for pressure prediction, to use multiple regression measurements to predict pressure curves, or to use neural networks of different depths to fit pressure curves\u003csup\u003e\u003cspan additionalcitationids=\"CR16 CR17\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. However, due to the black box nature of neural networks, the physical meaning of this pressure prediction method is not very clear.\u003c/p\u003e \u003cp\u003eFor methods that rely on normal compaction trend lines, the prediction accuracy depends on plotting an accurate normal compaction trend, especially for deeply buried formations. However, the normal compaction trend in these theories can only be identified empirically, which leads to the intrinsic subjective uncertainty of such methods, and their applicability is limited to cases in which enough information is available to identify the normal compaction trend.\u003c/p\u003e \u003cp\u003eThe methods, which are independent of the normal compaction trend, predict pore pressure via seismic pore pressure modeling. Such methods are much more feasible and, in particular, applicable to areas that are subjected to preliminary exploration. The most representative methods are Liu's method and Fillippone's method.\u003c/p\u003e \u003cp\u003eLiu's method is responsible fora greater amount of progress compared to Fillippone's method due to the introduction of Poisson's ratio, but the disadvantage is that it is assumed to be a constant. In general, the current seismic pore pressure models are all ultimately based on correlations with the P-wave velocity and ignore the S-wave velocity and density\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. Therefore, such modeling methods fail to offer sufficient prediction accuracy and high resolution. This research focuses on the predrilling pore pressure prediction of tight gas reservoirs. The seismic pore pressure prediction model developed by Liu's method is modified. Then, reliable high-resolution elastic parameters (including the P- and S-wave impedance and density data) are obtained via prestack multiwave joint inversion of prestack multiwave multicomponent seismic data (PP and PS wave data). Finally, an accurate predrilling seismic pore prediction method based on prestack multiwave parameters was developed for tight gas reservoirs.\u003c/p\u003e"},{"header":"2 Method","content":"\u003cp\u003eThe workflow for pore pressure prediction based on prestack multiwave parameters (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) is described below.\u003c/p\u003e \u003cp\u003eStep 1: Obtain \u003cem\u003en\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;3) limited-offset stacks of PP and PS (converted wave) after amplitude-preserving processing, and align them; subsequently, perform the prestack PP-PS simultaneous joint inversion to obtain the elastic parameter data of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P_{{imp}}^{T}\\)\u003c/span\u003e\u003c/span\u003e (P-wave impedance), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S_{{imp}}^{T}\\)\u003c/span\u003e\u003c/span\u003e (S-wave impedance), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho ^{\\text{T}}}\\)\u003c/span\u003e\u003c/span\u003e(density) in the time domain.\u003c/p\u003e \u003cp\u003eStep 2: Correct the velocity model based on the velocity spectrum according to the calibrated well-logging velocity model. Then, convert the elastic parameter data obtained above into the burial depth domain using the corrected velocity model with the ground surface as the datum. Therefore, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P_{{imp}}^{D}\\)\u003c/span\u003e\u003c/span\u003e (P-wave impedance), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S_{{imp}}^{D}\\)\u003c/span\u003e\u003c/span\u003e (S-wave impedance), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho ^{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e (density) in the measured depth domain are obtained.\u003c/p\u003e \u003cp\u003eThe time‒depth conversion presented above is different from that of conventional methods. Specifically, the datum of the conventional time‒depth conversion is the sea level, and thus, the obtained depth is the altitude. In contrast, the datum of the presented time‒depth conversion is the ground surface, and the depth here refers to the measured depth. Accordingly, the converted data are in the measured depth domain. This step lays the foundation for estimating the overburden pressure.\u003c/p\u003e \u003cp\u003eStep 3: Calculate the overburden pressure \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_{ov}}\\)\u003c/span\u003e\u003c/span\u003e using the obtained density data.\u003c/p\u003e \u003cp\u003eSpecifically, integrate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho ^{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003ein the depth domain along the burial depth to obtain the overburden pressure:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${P_{ov}}=\\int_{0}^{{{H_0}}} {{\\rho ^{\\text{D}}}\\left( H \\right)} gdh$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H_0}\\)\u003c/span\u003e\u003c/span\u003e is the depth of the observation point from the ground surface; \u003cem\u003eg\u003c/em\u003e is the gravitational acceleration; and \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the burial depth.\u003c/p\u003e \u003cp\u003eStep 4: Calculate the effective stress of the rock framework \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_e}\\)\u003c/span\u003e\u003c/span\u003e according to the P- and S- wave impedance and density.\u003c/p\u003e \u003cp\u003eIn the seismic formation pressure Model I (SFPM-I) proposed by Liu\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, the effective stress of the rock framework is expressed as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${P_e}=\\frac{{1{\\text{+}}\\sigma }}{{3{\\text{-}}3\\sigma }} \\cdot \\rho \\cdot {V_p}^{2} \\cdot {{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e is Poisson's ratio; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V_p}\\)\u003c/span\u003e\u003c/span\u003eis the P-wave velocity; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho\\)\u003c/span\u003e\u003c/span\u003eis the density; and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003eis the compaction deformation per unit thickness.\u003c/p\u003e \u003cp\u003eLiu defines \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e in Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e as a constant (equal to 0.12), which makes Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e a univariate quadratic function of the P-wave velocity\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V_p}\\)\u003c/span\u003e\u003c/span\u003e. However, in this research \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e is kept a variable and Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e is rewritten as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${P_e}={{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} {{\\rho ^{\\text{D}}}}}} \\right. \\kern-0pt} {{\\rho ^{\\text{D}}}}} \\cdot {{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThen, the effective stress of the rock framework \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_e}\\)\u003c/span\u003e\u003c/span\u003e is calculated using Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eStep 5: Calculate the pore pressure \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_p}\\)\u003c/span\u003e\u003c/span\u003e by subtracting the rock framework effective stress from the overburden pressure:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${P_p}={P_{ov}} - {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} {{\\rho ^{\\text{D}}}}}} \\right. \\kern-0pt} {{\\rho ^{\\text{D}}}}} \\cdot {{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003e is a variable dependent on various factors, such as depth, lithology, and sedimentary burial history, which are, in most cases, difficult to calculate directly. The solution of this research is as follows. First, based on the measured pressure of multiple wells with available acoustic full-waveform well logging data, calculate the overburden pressure profiles of these wells; then, substitute the computed \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_{ov}}\\)\u003c/span\u003e\u003c/span\u003e, and measured \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_p}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P_{{imp}}^{{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S_{{imp}}^{{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho ^{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e into Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e to determine \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003e at these wells; finally, perform the second-order polynomial fitting between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003eand \u003cem\u003eH\u003c/em\u003e via the least square method based on the measured formation pressure data and the calculated \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003e of the wells:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}=a{H^2}+bH+c$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ea\u003c/em\u003e, \u003cem\u003eb\u003c/em\u003e and \u003cem\u003ec\u003c/em\u003e are the fitting coefficients.\u003c/p\u003e \u003cp\u003eBased on the built second-order polynomial relationship, the P- and S-wave impedances, and the density, the effective stress of the rock framework is calculated using Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe modified pore pressure presented in this research is:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${P_p}={P_{ov}} - {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} {{\\rho ^{\\text{D}}}}}} \\right. \\kern-0pt} {{\\rho ^{\\text{D}}}}} \\cdot \\left( {a{H^2}+bH+c} \\right)+D$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eD\u003c/em\u003e is an empirical constant specific to the area of interest.\u003c/p\u003e \u003cp\u003eThe corresponding pore pressure coefficient formula \u003cem\u003ek\u003c/em\u003e can be written as:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$k={{\\left( {{P_{ov}} - {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} {{\\rho ^{\\text{D}}}}}} \\right. \\kern-0pt} {{\\rho ^{\\text{D}}}}} \\cdot \\left( {a{H^2}+bH+c} \\right)+D} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {{P_{ov}} - {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} \\mathord{\\left/ {\\vphantom {{\\left( {P{{_{{imp}}^{{\\text{D}}}}^2} - \\frac{4}{3}S{{_{{imp}}^{{\\text{D}}}}^2}} \\right)} {{\\rho ^{\\text{D}}}}}} \\right. \\kern-0pt} {{\\rho ^{\\text{D}}}}} \\cdot \\left( {a{H^2}+bH+c} \\right)+D} \\right)} {{P_w}}}} \\right. \\kern-0pt} {{P_w}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_w}\\)\u003c/span\u003e\u003c/span\u003e is the hydrostatic pressure.\u003c/p\u003e \u003cp\u003eUltimately, the calculated pore pressure can be corrected according to the pressure measurements obtained from drilling, after which the pore pressure (coefficient) can be mapped.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3 Applications","content":"\u003cp\u003eThe Sulige area of the Ordos Basin is located at the border of Shaanxi, Gansu and Inner Mongolia provinces in China, with desert, grassland, and hilly areas on the surface. The terrain is relatively flat, with an altitude of 1200\u0026ndash;1500 meters. The sedimentary strata mainly include the Ordovician in the lower Paleozoic, the Permian in the upper Paleozoic, and the Carboniferous; the Cretaceous, Jurassic, Triassic, and the Tertiary and Quaternary strata of the Mesozoic. In 2000, the discovery of the Sulige gas field in the Upper Paleozoic Permian H8 and S1 formations of the Sulige region revealed abundant natural gas resources in the area. H8 is currently the main reservoir series developed by Sulige, with quartz sandstone as the main reservoir and locally developed lithic quartz sandstone. The porosity of the reservoir is low, the permeability is low, and the physical properties are relatively poor. The continuity of the sand layer is poor, and the gas storage enrichment area is affected by the tight lithological zone. The pore pressure coefficient of the Paleozoic formations in this area is generally 0.76\u0026ndash;0.95 (abnormal underpressure)\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. The method presented above is applied to this area for validation.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Multiwave resolution analysis\u003c/h2\u003e \u003cp\u003eAVO analysis technology is a technique that studies gas bearing properties based on the variation in amplitude with offset. The application of PP-wave AVO technology is quite extensive, and the amplitude of PP-wave reflection at the top of gas-bearing sandstone in the Sulige area increases with increasing offset, mostly belonging to the third type of AVO. PS-wave AVO is more complex, but its ability to identify gas-bearing layers in the local area is better than that of PP-waves. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the PP-wave gather profile of (a, b) and the PS-wave gather profile of (c, d). On the PP-wave gather profile, the H8 reflection of well S44 shows an increasing trend, while the H8 reflection of well S51 remains basically unchanged. On the PS-wave gather profile, the H8 reflections of wells S44 and S51 are initially enhanced and then weakened, but the gradient change in well S44 is greater. The gas test results are S44\u0026thinsp;\u0026gt;\u0026thinsp;S51. In summary, if the reflection amplitude at the top of the reservoir on the PP-wave gather profile increases significantly with increasing offset and the reflection amplitude gradient on the PS-wave gather profile changes greatly, the stacked profile shows a \"bright spot\" feature, then the thickness of the reservoir sand body is large, and the gas content is good; this proves that the resolution of PS-waves in gas-bearing reservoirs is greater than that of PP-waves. For tight sandstone, multiwave data can improve the resolution ability for favorable reservoirs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Prestack PP\u0026thinsp;+\u0026thinsp;PS simultaneous joint inversion\u003c/h2\u003e \u003cp\u003eIt is difficult to directly clarify the distribution of effective reservoirs using conventional reservoir prediction techniques and guide later exploration and development work. In theory, multicomponent seismic exploration technology has unique advantages in solving complex structures, complex lithology oil and gas reservoirs, and anisotropic research. Therefore, this topic has received increasing research, and many oil companies have begun to conduct experiments on this technology. Currently, this technology is mostly used for offshore hydrocarbon exploration worldwide and has achieved good results. The Colorado School of Mines in the United States and the University of Calgary in Canada have accumulated certain achievements in this research\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. However, there is relatively little research on onshore oil and gas exploration, and some good application effects have not yet been reported\u003csup\u003e\u003cspan additionalcitationids=\"CR24 CR25 CR26\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Multiwave data are used in this work to study tight and thin sand bodies in local areas.\u003c/p\u003e \u003cp\u003e \u003cb\u003e(1) PP-PS wave data alignment\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe processes of Pre-stack PP\u0026thinsp;+\u0026thinsp;PS simultaneous joint inversion and PP-wave pre-stack simultaneous inversion are basically the same; the difference is that the input data include not only PP-wave offset stacking data but also PS-wave offset stacking data in the PP domain. The primary issue in inversion is to align the PP-wave with the PS-wave data, which compresses the PS-wave from the PS domain to the PP domain.\u003c/p\u003e \u003cp\u003eAn accurate Vp/Vs ratio is derived from the PP prestack inversion, which is then used to transform the PS-wave offset stacking data to the PP domain. Subsequently, according to the reflection marker horizon, horizon compression is performed for the PS-wave data to obtain the optimal matched PP and PS wave profiles.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the PP-PS-aligned stacked profiles (PP domain). The PP-wave seismic profile and the PS-wave seismic profile are similar in terms of large wave group characteristics, but there are differences in many internal details. In fact, this is exactly the AVO feature that we are striving to find, and the addition of PS-wave data has increased the recognition ability of favorable reservoirs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e(2) Prestack PP\u0026thinsp;+\u0026thinsp;PS simultaneous joint inversion\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe multiwave survey line L1 is selected to perform the prestack PP\u0026thinsp;+\u0026thinsp;PS simultaneous joint inversion using seven selected limited-offset stacks of PP and PS stacks. Perform PP-PS wave data alignment. Furthermore, the PP and PS limited-offset stacks and corresponding angle wavelets are input to generate the vertical variation trends of various parameters (P-wave impedance, density, and Vp/Vs) and the lateral constraint ranges. An optimal group of parameters is identified via quality control. The simultaneous joint inversion of PP and PS wave data is performed based on the Knott-Zoeppritz equation. Simultaneous joint inversion can obtain the P- and S-wave impedance and density, which are more robust and have high resolution \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows P-wave prestack inversion (a) and multiwave joint inversion (b) for the Poisson's ratio profiles of Line S10. The consistency between the Poisson's ratio profile obtained from the multiwave joint inversion and the gas testing results is much greater than that obtained from the P-wave prestack inversion. Multiwave joint inversion overcomes the problem of multiple solutions for single P-wave detection of sand bodies and fluids and improves the accuracy of seismic reservoir prediction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the P- and S-wave impedances and density of Line L1 derived from PP\u0026thinsp;+\u0026thinsp;PS pre-stack simultaneous joint inversion. At CDP 7488 of Well SuX1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the P-wave impedance of the H8 reservoir is low (11182 g/cc*m/s), the S-wave impedance is high (6145.6 g/cc*m/s), and the density is low (2.46 g/cc).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Conversion from the time domain to the burial depth domain\u003c/h2\u003e \u003cp\u003eFine well-seismic calibration is carried out for wells SuX1, SuX2, and SuX3, which are crossed by Line L1, to generate the velocity model. Afterward, the developed velocity model is adopted to calibrate the velocity model originating from the velocity spectrum. Finally, the P- and S-wave impedances and density are converted to the measured burial depth domain (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), with the ground surface set as the depth datum.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Second-order polynomial fitting between \u003cem\u003e△H/H\u003c/em\u003e and \u003cem\u003eH\u003c/em\u003e using data from multiple wells\u003c/h2\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e \u003c/span\u003e is a complex variable influenced by multiple factors, such as \u003cem\u003eH\u003c/em\u003e, lithology, and sedimentary burial history. Establishing the relationship between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003eand \u003cem\u003eH\u003c/em\u003e is a complex process, and in general, fitting methods are used to establish empirical relationships to connect the relationships between these variables.\u003c/p\u003e \u003cp\u003eBased on the pore pressure measurements and measured or calculated elastic parameters (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_p}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P_{{imp}}^{{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S_{{imp}}^{{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho ^{\\text{D}}}\\)\u003c/span\u003e\u003c/span\u003e, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_{ov}}\\)\u003c/span\u003e\u003c/span\u003e) of the target interval, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003e values are obtained for the H8 reservoirs of wells SuX1, SuX2, SuX3, SuX4, SuX5, SuX6, and SuX7, which possess acoustic full-waveform logging data. Next, a second-order polynomial correlation between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003eand \u003cem\u003eH\u003c/em\u003e is derived for the study area via least-square-method fitting based on the measured pore pressure data and computed \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}\\)\u003c/span\u003e\u003c/span\u003e values of the wells and correction of the calculated pore pressure according to the measured pressure:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${{\\Delta H} \\mathord{\\left/ {\\vphantom {{\\Delta H} H}} \\right. \\kern-0pt} H}={\\text{-8}}{\\text{.957745}} \\times {\\text{1}}{{\\text{0}}^{ - 14}}{H^2}+{\\text{5}}{\\text{.7128389325}} \\times {\\text{1}}{{\\text{0}}^{ - 10}}H{\\text{-1}}{\\text{.1755738181174 }} \\times {\\text{1}}{{\\text{0}}^{ - 7}}{\\text{ }}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Pore pressure (coefficient) mapping\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows pore pressure/pressure coefficient maps predicted by different methods. Using Eqs.\u0026nbsp;\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, \u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, and \u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the pore pressure (coefficient) can be mapped across the study area, in which D is empirically set to -27 MPa. The maps are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) and 7(b). The pore pressure and pressure coefficients are 29.77 MPa and 0.92, respectively, at CDP 7488, which is also the location of Well SuX1. Moreover, the measured pore pressure and pressure coefficient are 29.52 MPa and 0.91, respectively. Hence, the prediction is in good agreement with the measurement and thus satisfactory. The resulting 2-D profiles have high resolution, which suggests improved pore pressure prediction performance for thin reservoirs. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(c) shows the pore pressure predicted by Liu\u0026rsquo;s methods. The resolution of the pressure profile is significantly lower than that of the method proposed in this paper. Due to the addition of multiwave data and the improvement of pressure prediction methods, the pore pressure prediction method presented in this research is particularly suitable for thin tight gas reservoirs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe conventional pore pressure prediction method is not suitable for low-porosity and low-permeability formations because although the acoustic time difference has a certain indicative effect on abnormally high pressure, the response is weak, and the magnitude of abnormally high pressure does not show a direct relationship with the deviation degree of the acoustic time difference. However, abnormally high pressure in low-porosity and low-permeability formations is difficult to accurately reflect during drilling, resulting in inaccurate reference data from conventional prediction methods and further leading to distorted prediction results.\u003c/p\u003e \u003cp\u003eThe seismic velocity is the key to accurately calculating the seismic pressure. When conditions permit, incorporating multiwave data as much as possible can help accurately predict the seismic pore pressure; this is particularly crucial for tight gas reservoirs.\u003c/p\u003e \u003cp\u003eThe pore pressure calculation model should introduce the shear wave velocity as much as possible to improve the prediction accuracy. The additional information provided by the S-wave velocity may help to reduce the ambiguity between variations in pore pressure and variations in lithology and fluid content\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"5 Conclusions","content":"\u003cp\u003ePore pressure prediction based on seismic wave velocities has become the main methodology for predrilling pore pressure prediction. The calculation of elastic parameters, conversion to the burial depth domain, and selection of prediction models are key to obtaining pore pressure prediction results.\u003c/p\u003e \u003cp\u003e(1) The elastic parameter datasets of the P- and S-wave impedance and density derived from PP\u0026thinsp;+\u0026thinsp;PS prestack simultaneous joint inversion are robust and have high resolution, which favors subsequent seismic pore pressure prediction.\u003c/p\u003e \u003cp\u003e(2) The pore pressure model proposed by Liu\u0026rsquo;s method is modified by incorporating the S-wave velocity and density terms, which improves the prediction accuracy and resolution.\u003c/p\u003e \u003cp\u003e(3) Predrilling seismic pore pressure modeling (prediction), based on prestack multiwave elastic parameters, can generate highly accurate estimates and is particularly suitable for tight gas fields.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThis paper is based on work supported by China National Petroleum Corporation \u0026quot;14th Five-Year Plan\u0026quot; forward-looking basic major scientific and technological projects (No. 2021DJ2205、2021DJ0403、2021DJ0406).\u003c/p\u003e\n\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eYutan Dou. Fei Li. and Yonggang Wang. wrote the main manuscript text and Mengbo Zhang. Guanghong Du. Feng Liu. prepared figures 3-4. All authors reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003eCompeting interests\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eAdditional information\u003c/p\u003e\n\u003cp\u003eThe datasets generated and/or analysed during the current study are not publicly available due to safety concerns in oilfield production, but are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eRashid, M.\u003cem\u003e et al.\u003c/em\u003e Reservoir quality prediction of gas-bearing carbonate sediments in the Qadirpur field: insights from advanced machine learning approaches of SOM and cluster analysis. \u003cem\u003eMinerals\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 29, doi:10.3390/min13010029 (2023).\u003c/li\u003e\n\u003cli\u003eMakarian, E.\u003cem\u003e et al.\u003c/em\u003e An efficient and comprehensive poroelastic analysis of hydrocarbon systems using multiple data sets through laboratory tests and geophysical logs: a case study in an iranian hydrocarbon reservoir. \u003cem\u003eCarbonates and Evaporites\u003c/em\u003e \u003cstrong\u003e38\u003c/strong\u003e, 37, doi:10.1007/s13146-023-00861-1 (2023).\u003c/li\u003e\n\u003cli\u003eSayers, C. 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Predrill pore-pressure prediction using 4-C seismic data. \u003cem\u003eThe Leading Edge\u003c/em\u003e \u003cstrong\u003e20\u003c/strong\u003e, 1056-1059, doi:10.1190/1.1487313 (2001).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"pore pressure, multiwave, pressure prediction, prestack multiwave joint inversion, elastic parameter, tight gas field","lastPublishedDoi":"10.21203/rs.3.rs-5250630/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5250630/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePore pressure prediction is one of the major geological tasks related to oil and gas exploration and development. In this research, highly accurate elastic parameters, such as P- and S-wave impedance and density from seismic prestack multiwave joint inversion, are obtained and then innovatively converted to the burial depth domain. Moreover, based on the formation pressure measurements of wells with acoustic full-waveform logging data, a second-order polynomial is applied for △H/H and H via the least-square method. Finally, the pore pressure is calculated using the modified Liu\u0026rsquo;s pore pressure model. The pore pressure prediction method, which incorporates accurately calculated elastic parameters, S-wave impedance, and density, is found to have a higher prediction accuracy than methods based solely on P-wave impedance; it also provides enhanced resolution for pore pressure prediction in thin reservoirs. The presented method is particularly suitable for tight gas fields.\u003c/p\u003e","manuscriptTitle":"Pore pressure prediction based on elastic parameters derived from seismic prestack multiwave inversion","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-30 11:51:35","doi":"10.21203/rs.3.rs-5250630/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bc11cd04-da08-4f5e-8da1-3acf567110e2","owner":[],"postedDate":"October 30th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-04T06:24:07+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-30 11:51:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5250630","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5250630","identity":"rs-5250630","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}