Assessment of Gravity Filtration Techniques for Shipborne Marine Gravity Observations Over the Mediterranean Sea

Assessment of Gravity Filtration Techniques for Shipborne Marine Gravity Observations Over the Mediterranean Sea | 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 Assessment of Gravity Filtration Techniques for Shipborne Marine Gravity Observations Over the Mediterranean Sea Mahmoud Hamdy, Mohamed El Tokhey, Mohamed Ramadan, Tarek Hassan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6722175/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 Marine gravity provides vital geodetic and geophysical information for several applications, such as regional geology, tectonic structures, and oceanographic processes. Filtering these data represents a crucial pre-processing step to eliminate any erroneous signals and improve the data quality for better analysis and interpretation. This study investigates five gravity filtration techniques to improve the quality of shipborne marine gravity data collected over the Mediterranean Sea. The assessed techniques include Least Squares Collocation (LSC), Interquartile Range (IQR), three-sigma limit, Inverse Distance Weighted (IDW) interpolation, and refinement using Geopotential Earth Models (GEMs). The study employs 66229 shipborne gravity anomaly data points acquired from the International Gravimetric Bureau (BGI). The results indicate that the IDW interpolation and LSC techniques are the most effective. IDW interpolation can provide a balance between error detection and computational time, while LSC requires a significantly longer processing time. It is also shown that using any recent GEM yields almost the same performance. Moreover, a cross-check between the assessed techniques shows that they all accepted about 67% of the data as not erroneous. These findings can be exploited to significantly improve the accuracy of marine gravity datasets for different geodetic and geophysical studies. Shipborne Gravity Anomaly Mediterranean Sea Geopotential Earth Model Interquartile Range Gross Error Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Gravity data are essential for various applications, especially in geodesy and geophysics. These data can be collected from terrestrial, aerial, and satellite measurements. (Andersen, 2013 ). Marine gravity data plays a vital role in numerous applications such as interpreting the regional geology and structural features of offshore sedimentary basins. Also, they are critical for investigating deep crustal structures, particularly in the context of marine oil and gas exploration (Li et al., 2022 ; Pavlis et al., 2012 ; Sandwell et al., 2014 ). Shipborne gravity anomaly data are essential for building several products (i.e., gravity models, geoid models, or geopotential Earth models). These data are usually recorded with an average accuracy of around 5 mgal (Drewes et al., 2016 ). This limited accuracy is caused by navigational errors (e.g., positioning uncertainties and the Eötvös effect), instrumental errors (e.g., gravimeter drift and cross-coupling), and other error sources such as datum inconsistencies, inaccuracies in ties, and sea condition variations (Wessel & Watts, 1988 ). Therefore, enhancement and filtration of these data are essential for producing reliable products. Several studies highlighted this filtration issue to eliminate any existing outliers in the raw data. For instance, the study in(Pa’Suya et al., 2023 ) filtered the data in a sequential process over two steps. In the first step, all shipborne gravity anomaly data were filtered using a 95% confidence level rule, while in the second step, the remaining data were filtered using cross-validation employing neighboring data points. In a similar work, the study in(Zaki et al., 2022 ) performed data filtration using cross-validation after independently assessing each ship survey data using different Geopotential Earth Models (GEMs) and altimetry-derived gravity models. Moreover, a leave-one-out cross-validation method was used in (Gautier et al., 2022 ), considering gravity data points with residuals greater than twice the standard deviation as outliers. In another approach, Least Squares Collocation (LSC) was used to discover gross errors in altimetry data in the Baltic Sea(Tscherning, 1991 ) and in the Egyptian gravity network (Abd-Elmotaal & El-Tokhey, 1997 ). Also, in (Vergos et al., 2005 ), the blunders in the gravity data in the eastern part of the Mediterranean Sea were detected by comparing with a GEM. Then, the LSC method was used to detect the remaining blunders. The study in(Xavier & Rolim, 2012 ) adopted a different approach for examining gravity data by setting a rejection threshold based on the calculated residuals using the digital elevation models of the Shuttle Radar Topography Mission (SRTM) (Farr et al., 2007 ), the Gravity Recovery and Climate Experiment (GRACE), and the interpolated observations of gravity observations (i.e., Bouguer anomaly). As several filtration techniques exist, it remains a challenge to choose the most suitable technique for each gravity anomaly dataset. This study evaluates different gravity filtration techniques for shipborne marine gravity observations in the Mediterranean Sea, which is known for its complex marine environment with significant geophysical and oceanographic interest (Tziavos, 2020 ). The study employs 66229 shipborne gravity anomaly data points in the Mediterranean Sea, acquired from the International Gravimetric Bureau (BGI). The evaluated techniques include LSC, Interquartile Range (IQR), three-sigma limit, Inverse Distance Weighted (IDW) interpolation, and refinement using GEMs. The evaluation process focuses on their performance, accuracy, and applicability. The following parts of this paper are organized as follows. Section 2 presents the datasets used in this research. Section 3 describes the utilized filtration techniques and the processing strategy. Then, Section 4 presents and discusses the results of each filtration technique. Finally, the conclusions of this research are given in Section 5. 2. Gravity Datasets In geodetic applications, free-air gravity anomaly plays a crucial role in calculating geoid models, which are essential for understanding the Earth's gravitational field. This calculation is performed using Stokes’ formula (Heiskanen & Moritz, 1967 ): $$\:\text{N}=\frac{\text{R}}{4{\pi\:}{\gamma\:}}{\iint\:}_{{\sigma\:}}^{}\varDelta\:\text{g}\:\text{S}\left({\psi\:}\right)\text{d}{\sigma\:}$$ 1 where \(\:N\) is the geoid undulation and \(\:\text{R}\) is the radius of the Earth’s sphere. \(\:\gamma\:\) denotes the normal gravity, \(\:\varDelta\:\text{g}\) refers to the gravity anomaly, while \(\:{\sigma\:}\) represents the unit sphere. \(\:\text{S}\left({\psi\:}\right)\) is the Stokes kernel function, where \(\:{\psi\:}\) denotes the geocentric angle. In our study, 66229 shipborne gravity anomaly points were acquired from BGI ( https://bgi.obs-mip.fr/data-products/gravity-databases/marine-gravity-data-prod/#/data/sea ). The acquired data cover four study regions in the Mediterranean Sea, each with different dimensions, observation intensity, and topology. The size, location, and data distribution of each zone are shown in Fig. 1 . These data points were collected during different ship tracks over almost 50 years. Also, it should be noted that there is no metadata describing the accuracy of the acquired raw data. The tested data points included 5560 duplicate observation data. Therefore, the average of each duplicate pair is taken as the observed value at this point. This process reduced the total number of observations to 63449. The general properties of these observations in each zone are shown in Table 1 . This includes data coverage, gravity anomaly range, and its standard deviation (STD). Table 1 The general properties of the acquired shipborne data in each zone ZONE Count Latitude Coverage Longitude Coverage \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\) (mgal) \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) STD (mgal) ZONE 1 22006 35.1901°: 38.3950° -4.9994°:0.0000 ° -787.80 86.57 38.63 ZONE 2 11466 38.0005°: 42.9997° 5.0000°: 9.9996° -92.00 114.70 25.27 ZONE 3 21261 33.3129°: 37.9995° 16.0002°: 21.0000° -142.50 146.90 29.51 ZONE 4 8716 32.0003°: 36.7600° 30.0000°: 34.9995° -189.50 140.00 56.33 For assessment purposes, some of the most recent GEMs are needed in this study. The employed models encompass different degrees and are constructed using diverse data sources. Table 2 summarizes the main characteristics of the used GEMs. Table 2 The employed GEMs in this study Model Year Degree Data* Reference Tongji-GMMG2021S 2022 300 S (GOCE, GRACE) Chen, J. et al. ( 2022 ) SGG-UGM-2 2020 2190 A, EGM2008, S(GOCE, GRACE) Liang et al. ( 2020 ) XGM2019e_2159 2019 2190 A, G, S(GOCO06s), T Zingerle, et al. ( 2019a ) GO_CONS_GCF_2_TIM_R6e 2019 300 G, S(GOCE) Zingerle, et al. ( 2019b ) GOCO06s 2019 300 S (GOCE, GRACE, CHAMP, Swarm A + B + C, TerraSAR-X, TanDEM-X, LAGEOS, LAGEOS 2, Starlette, Stella, AJISAI, LARES, LARETS, Etalon 1/2 and BLITS) Kvas et al. ( 2021 ) SGG-UGM-1 2018 2159 EGM2008, S(GOCE) Xu et al. ( 2017 ) Liang et al. ( 2018 ) EGM2008 2008 2190 A, G, S(GRACE) Pavlis et al. ( 2012 ) * S: Satellite Data, G: Ground Data, A: Altimetric Data, GOCE: Gravity field and steady-state Ocean Circulation Explorer, GRACE: Gravity and Climate Recovery Experiment, CHAMP: Challenging Mini-Satellite Payload, LAGEOS: Laser Geodynamic Satellite, LARES: Laser Relativity Satellite, BLITS: Ball Lens In The Space 3. Gravity Filtration Techniques In this study, different gravity filtration techniques are applied to the acquired data. A brief description of each technique is provided in this section. In addition, the processing strategy to make the assessment process unbiased is presented at the end of the section. 3.1 Least Squares Collocation (LSC) LSC is the most commonly used prediction technique in practice. It is a very straightforward algorithm. However, it requires a large storage requirement and significant computational time (especially when used for large gravity networks) (Ruffhead, 1987 ). Based on this technique, the gravity anomaly at any point can be predicted using the gravity anomalies of other points as well as the covariance between these points. The expression of the least-squares prediction is given by (Moritz, 1980 ): $$\:\varDelta\:{g}_{P}=\left[C\left(p,{p}_{1}\right)\:\:\:C\left(p,{p}_{2}\right)\dots\:\dots\:C(p,{p}_{n})\right]{\left[\begin{array}{ccc}\begin{array}{c}C\left({p}_{1},{p}_{1}\right)\\\:C\left({p}_{2},{p}_{1}\right)\\\:\begin{array}{c}⋮\\\:C\left({p}_{n},{p}_{1}\right)\end{array}\end{array}&\:\begin{array}{c}C\left({p}_{1},{p}_{2}\right)\\\:C\left({p}_{2},{p}_{2}\right)\\\:\begin{array}{c}⋮\\\:C\left({p}_{n},{p}_{2}\right)\end{array}\end{array}&\:\begin{array}{cc}\begin{array}{c}\cdots\:\\\:\cdots\:\\\:\begin{array}{c}\ddots\:\\\:\dots\:\end{array}\end{array}&\:\begin{array}{c}C\left({p}_{1},{p}_{n}\right)\\\:C\left(2,{p}_{n}\right)\\\:\begin{array}{c}⋮\\\:C\left({p}_{n},{p}_{n}\right)\end{array}\end{array}\end{array}\end{array}\right]}^{-1}\left[\begin{array}{c}\varDelta\:{g}_{{p}_{1}}\\\:\varDelta\:{g}_{{p}_{2}}\\\:\begin{array}{c}⋮\\\:\varDelta\:{g}_{n}\end{array}\end{array}\right]$$ 2 where \(\:n\) in the number of observed points. \(\:\varDelta\:{g}_{P}\) and \(\:\varDelta\:{g}_{{p}_{n}}\) are the gravity anomalies of the required point ( \(\:p\) ) and the observed point ( \(\:{p}_{n}\) ), respectively. \(\:C(p,{p}_{n})\) refers to the covariance between \(\:p\) and \(\:{p}_{n}\) , while \(\:C\left({p}_{1},{p}_{1}\right)\) to \(\:C\left({p}_{n},{p}_{n}\right)\) denote the covariance between the observed points. Here, the used covariance function is a second-order Gauss-Markov function (Götzelmann et al., 2006 ) that can be expressed as follows: $$\:C\left(s\right)={C}_{0}(1+\frac{s}{\alpha\:}){e}^{\left(\raisebox{1ex}{$-s$}\!\left/\:\!\raisebox{-1ex}{$\alpha\:$}\right.\right)}$$ 3 where \(\:s\) is the distance between points, \(\:{C}_{0}\) is the signal variance, and \(\:\alpha\:\) is the correlation length. The open-source code of the GravSoft program(Forsberg & Tscherning, 2008 ) was utilized to calculate the predicted gravity anomalies in this study. This includes estimating the empirical covariance function parameters, computing the gravity anomalies, and finding the difference between the predicted and the observed values. If this difference exceeds three times the standard deviation, the concerned point is considered a blunder. 3.2 Interquartile Range (IQR) In this method, observations are arranged in ascending order and divided into four quarters. The IQR quantifies the variability within a dataset by measuring the spread of the middle 50% of the data points (Lock et al., 2021 ). As it represents the range in which the central half of the observations fall, it can be calculated as: $$\:IQR={Q}_{3}-\:{Q}_{1}$$ 4 where \(\:{Q}_{1}\) and \(\:{Q}_{3}\) are the upper limits of the 25th and 75th percentiles, respectively. Then, the observations falling outside the range defined by the lower boundary (Eq. (5)) and upper boundary (Eq. (6)) are considered outliers (Lock et al., 2021 ). Lower boundary \(\:={Q}_{1}-\:1.5\times\:IQR\) (5) Upper boundary \(\:={Q}_{3}+\:1.5\times\:IQR\) (6) 3.3 Three-Sigma Limit This simple method is based on the basic statistical principle of standard deviations, which quantify the extent to which data points differ from the mean. Under the assumption that the data is normally distributed, the three-sigma limit defines a range that is expected to include 99.7% of data points. Any data points lying outside this range are considered outliers (Lehmann, 2013 ). 3.4 Inverse Distance Weighted (IDW) Interpolation This interpolation technique is considered a special case of the LSC method (Hofmann-Wellenhof & Moritz, 2006 ). The gravity anomaly of any point can be predicted, assuming that this anomaly is inversely proportional to the distance between the required point and the observed point. For each point, the gravity anomaly is interpolated using the nearest observed gravity anomalies (Achilleos, 2011 ) such that: $$\:\varDelta\:{g}_{p}=\frac{\sum\:_{i=1}^{n}(\varDelta\:{g}_{{p}_{i}}/{d}_{i})}{\sum\:_{i=1}^{n}(1/{d}_{i})}$$ 7 where \(\:\varDelta\:{g}_{p}\) is the predicted gravity anomaly of the examined point, while \(\:\varDelta\:{g}_{{p}_{i}}\) is the observed gravity anomaly of point \(\:{p}_{i}\) near the examined point. \(\:{d}_{i}\) refers to the distance from point \(\:{p}_{i}\) to the examined point, and \(\:n\) is the number of points included in a 10 km search radius around the examined point. Finally, the rule of three-sigma is applied to the differences between the interpolated and the actual gravity anomalies to detect any blunders in the raw data. 3.5 Refinement Using GEMs GEMs are widely used for modeling anomalies as a part of a well-known remove-restore technique (Barzaghi, 2016 ). These models play an important role in smoothing the gravity field by removing the effect of the long gravitational wavelength. Additionally, they have a role in filtering gravity data to enhance data accuracy and consistency. In this technique, the GEMs, presented in Section 2, are employed to refine shipborne gravity observations. The predicted value of the gravity anomaly can be computed as follows (Barthelmes, 2013 ): $$\:{\varDelta\:g}_{P}\left(r,\lambda\:,\phi\:\right)=\frac{GM}{{r}^{2}}\sum\:_{l=0}^{{l}_{max}}{\left(\frac{R}{r}\right)}^{l}(l-1)\sum\:_{m=0}^{l}{P}_{lm}\left(sin\phi\:\right)({C}_{lm}\text{cos}m\lambda\:+{S}_{lm}\text{sin}m\lambda\:)$$ 8 where \(\:\left(r,\lambda\:,\phi\:\right)\) are the spherical geocentric coordinates of the point (radius, longitude, latitude), \(\:R\) is the reference radius, and \(\:GM\) is the product of the gravitational constant and the mass of Earth. \(\:l\) and \(\:m\) refer to degree and order of spherical harmonic, \(\:{P}_{lm}\) represents fully normalized Legendre functions, while \(\:{C}_{lm}\) and \(\:{S}_{lm}\) denote Stokes’ coefficients. Then, the difference between the gravity anomaly observation and the corresponding predicted value is calculated, and the three-sigma rule is applied to detect the outliers in the raw data. 3.6 Processing Strategy For applying the described techniques to the acquired shipborne data, a unified processing criterion is selected to make the assessment process unbiased. The dataset of each zone is divided into two sets (Set A and Set B). Consequently, data points are sorted according to their spatial location. Then, they are divided so that Set A contains the points with odd arrangement and Set B contains the points with even arrangement. This procedure governs the similarity of data distribution. After data splitting, the general properties of the observations of each subset are given in Table 3 . Table 3 The general properties of the observations of each data subset after data splitting ZONE Count Latitude Coverage Longitude Coverage \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\) (mgal) \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) STD (mgal) ZONE 1_A 11003 35.1901°: 38.3380° -4.9994°: -0.0001° -787.80 86.57 38.40 ZONE 1_B 11003 35.1903°: 38.3950° -4.9992°: 0.0000° -121.40 83.50 38.85 ZONE 2_A 5733 38.0005°: 42.9995° 5.0000°: 9.9976° -92.00 110.70 25.19 ZONE 2_B 5733 38.0033°: 42.9997° 5.0003°: 9.9996° -91.50 114.70 25.35 ZONE 3_A 10631 33.3200°: 37.9985° 16.0002°: 21.0000° -136.35 146.70 29.52 ZONE 3_B 10630 33.3129°: 37.9995° 16.0004°: 21.0000° -142.50 146.90 29.49 ZONE 4_A 4358 32.0013°: 36.6741° 30.0000°: 34.9993° -189.50 116.30 56.17 ZONE4_B 4358 32.0003°: 36.7600° 30.0000°: 34.9995° -186.10 140.00 56.49 Table 3 shows that each pair of subsets in the same zone has almost the same characteristics, except zone 1, in which a significant difference between the minimum gravity anomalies is realized. This can be caused if large outliers exist in one of the two subsets, which will be investigated in the following parts of this study. By utilizing two datasets, each set is used to predict the gravity anomalies of the required points in the other set. Each predicted anomaly is then compared to the corresponding observed anomaly to identify if there is an outlier. This processing strategy works iteratively to avoid contaminating the predicted values by biased points. In each step of the iterative process, the possible outliers in the previous step are omitted from the prediction process. The iteration process stops when the percentage of detected errors becomes less than 1% of the corresponding set for Set A and Set B. Figure 2 summarizes this shipborne data processing strategy. 4. Results and Discussion This section presents the results obtained after applying the processing techniques described to the acquired shipborne data. This includes a comprehensive analysis for each zone and each data subset. It is worth noting that after applying the refinement using GEMs method, it was deduced that the different GEMs had a similar attitude in detecting the gross errors in the data. Consequently, the most recent higher degree GEM (XGM2019e_2159) is chosen to be involved in the following analysis and comparison stages in this section. Table 4 shows the statistics of the filtration process and the results achieved after erroneous data removal for all techniques. Table 4 The statistics of the filtered data after using the filtration techniques Technique Parameter ZONE 1_A ZONE 1_B ZONE 2_A ZONE 2_B ZONE 3_A ZONE 3_B ZONE 4_A ZONE 4_B LSC %Errors 27.73% 25.57% 24.61% 25.55% 4.81% 12.99% 38.18% 39.17% \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\) (mgal) -119.80 -121.40 -92.00 -91.50 -80.80 -85.60 -180.10 -183.10 \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) 86.57 83.50 94.90 96.60 63.70 90.20 115.00 115.55 STD (mgal) 37.42 38.53 21.29 21.23 24.02 24.42 55.63 56.01 IQR %Errors 2.91% 2.43% 2.77% 2.70% 4.72% 4.74% 2.18% 2.27% \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\) (mgal) -121.30 -121.33 -78.10 -90.80 -136.35 -142.50 -187.25 -186.10 \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) 86.57 83.50 110.70 114.70 146.70 146.90 116.30 140.00 STD (mgal) 37.79 38.96 25.03 25.26 29.57 29.57 56.27 56.63 Three-Sigma %Errors 0.58% 0.32% 0.47% 0.51% 1.64% 1.68% 0.11% 0.09% \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\) (mgal) -787.80 -121.40 -92.00 -91.50 -136.35 -142.50 -189.50 -186.10 \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) 86.57 83.50 110.70 114.70 146.70 146.90 116.30 140.00 STD (mgal) 38.44 38.87 25.14 25.33 29.58 29.52 56.18 56.51 IDW Interpolation %Errors 9.13% 8.74% 13.62% 12.87% 13.91% 13.47% 24.51% 23.52% \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\:\) (mgal) -121.30 -121.40 -78.10 -77.00 -134.30 -127.80 -178.50 -176.40 \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) 79.62 80.17 94.90 96.60 132.80 128.70 114.70 140.00 STD (mgal) 37.27 38.39 23.70 23.67 27.33 27.23 48.66 49.17 XGM2019e_2159 %Errors 3.77% 5.71% 2.93% 2.69% 6.75% 6.41% 1.03% 1.28% \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\:\) (mgal) -121.30 -121.40 -92.00 -91.50 -134.30 -142.50 -187.25 -186.10 \(\:{\varDelta\:\mathbf{g}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\) (mgal) 86.57 83.50 94.90 96.60 125.90 115.50 116.30 121.90 STD (mgal) 36.06 37.20 23.08 23.30 26.50 26.32 55.37 55.23 It is clear from Table 4 that each filtration technique worked uniformly in almost the same manner for each pair of data subsets. In the case of using LSC filtration, the percentages of detected errors are almost the same for each pair, except in Zone 3. The reason behind the recorded difference (i.e., 4.81% and 12.99%) may be due to the inconvenience of the covariance function. In addition, the percentages of detected errors in Zone 4 are relatively larger, and this behavior was expected due to the sparsity of the data in this zone. Moreover, the results showed a reduction in the gravity anomaly standard deviations after error removal. It was recorded that each trial took a noticeably longer processing time compared to the other methods. In addition, it was clear that this method requires a lot of trials until the stop condition is met. Using the IQR filtration technique provided promising homogeneous results. The percentages of detected blunders were much less than those detected using the LSC method. Also, the gravity anomaly standard deviations were slightly reduced. It can also be concluded from Table 4 that using the three-sigma method failed to detect errors, showing a very low detection capability in all zones. As a result, the gravity anomaly standard deviations are almost the same before and after removing the detected errors. Regarding the IDW interpolation technique, it provided a reasonable error detection rate. The results indicate that the detected error percentages are not excessively large, preventing the misclassification of valid data as errors, nor too low, ensuring that the method remains capable of detecting a significant portion of actual errors. In addition, the results’ homogeneity, particularly in Zone 4, emphasizes that this technique can deal with all zones in the same manner without being affected by data density. Also, the reduction in the gravity anomaly standard deviations indicates the efficiency of this method. The results in Table 4 also, show that the percentages of errors detected after refinement using GEMs aree relatively similar to the IQR method. However, it was apparent that this method detected a higher percentage of outliers in Zone 3 than in the other zones. This may be due to the lack of short-wavelength components in this zone, in the satellite-derived gravity field (Sandwell & Smith, 1997 ). To summarize the results in Tables 4 and compare the different techniques, Fig. 3 and Fig. 4 depict the percentage of detected errors and the gravity anomaly standard deviation of the remaining data points of all techniques in each zone. It can be inferred from Fig. 3 that the LSC and IDW interpolation methods had the highest percentage of detected errors. In addition, Fig. 4 shows that the resulting gravity anomaly standard deviations did not have significant differences from one technique to another over the four zones. For comparison purposes, the average gravity anomaly gradient ( \(\:{G}_{a}\) ), which indicates the smoothness of the gravity field, is calculated for each technique after removing the outliers as follows: $$\:{G}_{a}=\frac{\sum\:_{i=1}^{m}\sum\:_{j=1}^{m}\frac{\varDelta\:{g}_{ij}}{{D}_{ij}}}{m}$$ 9 where \(\:\varDelta\:{g}_{ij}\) is the difference in the gravity anomaly between points \(\:i\) and \(\:j\) . \(\:{D}_{ij}\) denotes the distance between points \(\:i\) and \(\:j\) . \(\:m\) represents the total number of remaining data points. Table 5 shows the average gravity anomaly gradient at each zone before and after the filtration process using each technique. Table 5 Average gravity gradient (mgal/m) at each zone before and after filtration for all techniques Technique Zone 1 Zone 2 Zone 3 Zone 4 Before filtration 0.0107 0.0058 0.0068 0.0127 LSC 0.0074 0.0042 0.0058 0.0106 Three Sigma 0.0104 0.0055 0.0063 0.0126 IQR 0.0099 0.0047 0.0058 0.0126 IDW Interpolation 0.0081 0.0040 0.0051 0.0101 XGM2019e_2159 0.0098 0.0058 0.0062 0.0127 It is clear that the gravity anomaly gradient was significantly improved in all zones using the LSC, IQR, and IDW interpolation methods. On the other hand, the three-sigma method and XGM2019e_2159 did not perform similarly, as the average gravity gradient is approximately equal to that before filtration. This gives other techniques a superiority in smoothing the gravity field. Figure 5 shows the calculated average gradient of the remaining data points using all techniques over the four zones. It is clear from Fig. 5 that the IDW interpolation technique could provide the smoothest gravity field in Zones 2, 3, and 4, while the LSC technique provided the smoothest gravity field in Zone 1. This emphasizes the efficiency of the IDW interpolation technique, particularly with a lower percentage of errors detected than the LSC method. In addition, the results of employing GEMs did not show significant differences. In order to choose the most effective filtration technique, a score is proposed to each filtration technique based on its gravity gradient, remaining data points, and the decrease in the standard deviation values. The criterion is chosen so that the efficiency score increases with a smoother gravity field (i.e., a lower gravity gradient), a higher percentage of remaining points, and a larger decrease in the standard deviation value. This can be expressed mathematically as follows: $$\:score=\left|\frac{{G}_{i}-\:{G}_{a}}{{G}_{i}}\right|\times\:{W}_{1}+\left|1-\frac{\%E}{100}\right|\times\:{W}_{2}+\left|\frac{{STD}_{i}-\:STD}{{STD}_{i}}\right|\times\:{W}_{3}$$ 10 where \(\:{G}_{i}\) and \(\:{G}_{a}\) are the average gravity gradients before and after filtration, respectively. \(\:\%E\) denotes the percentage of detected errors. \(\:{STD}_{i}\) and \(\:STD\) are the gravity anomaly standard deviations before and after filtration, respectively. \(\:{W}_{1}\) , \(\:{W}_{2}\) , and \(\:{W}_{3}\) refer to the weights allocated for gravity gradient change, percentage of remaining data points, and standard deviation change, respectively. In our study, \(\:{W}_{1}\) , \(\:{W}_{2}\) , and \(\:{W}_{3}\) are assumed as 1, 0.75, and 0.5, respectively. These weights were chosen based on repeated trials to represent the differences between the tested techniques in the best way while maintaining the priority of the three factors. Figure 6 shows the calculated efficiency scores of the tested filtration techniques. It is clear from Fig. 6 that the IDW interpolation method achieved the best scores in the four zones, which emphasizes its high efficiency. In addition, the LSC technique came in the second order in all zones except Zone 4 due to the sparsity of the data in this zone, as discussed earlier. In addition, the low-degree GEMs achieved almost the same scores, which is also true for the high-degree GEMs. To test the level of agreement between the used methods, a cross-check is conducted to determine the methods that agreed on their outlier detection. This is performed for each observed point. Therefore, we can evaluate the confidence in the validity of each observation based on the consensus among the filtration techniques. For this purpose, the point rejection agreement among the used filtration techniques is depicted in Fig. 7 . Figure 7 indicates that less than 1% of the data was detected by at least 4 methods as gross errors. In addition, the results provided a good confidence level in the different filtration techniques, as all methods agreed on approving about 67% of the data as non-erroneous. 5. Conclusion In this research, several filtration techniques were applied to detect outliers in gravity anomaly shipborne data. The acquired data includes 66229 shipborne gravity anomaly points covering four regions in the Mediterranean Sea, each with different dimensions, observation intensity, and topology. A comparative study was performed to assess the performance that can be achieved using each applied technique. This includes LSC, IQR, three-sigma limit, IDW interpolation, and refinement using GEMs. The comparison criterion is chosen so that efficiency increases with a smoother gravity field (i.e., a lower gravity gradient), a higher percentage of remaining points, and a larger decrease in the standard deviation value. The results showed that the most effective technique is the IDW interpolation, followed by the LSC technique. The IDW interpolation detected outliers with percentages ranging between 8.94% (Zone 1) and 24.02% (Zone 4) of the total data points, while the percentages in the case of using LSC ranged from 8.90% (Zone 3) to 38.68% (Zone 4). Moreover, the IDW interpolation technique could provide the smoothest gravity field in Zones 2, 3, and 4, while the LSC technique provided the smoothest gravity field in Zone 1. Despite the promising results provided by the LSC technique, it required a significantly long processing time. On the other hand, the IDW interpolation method could provide reliable results with a short processing time. Regarding the correlation between every two techniques, the results showed that each method has its unique strategy for outlier detection, with weak to moderate correlations between them. After investigating the agreement level between the used methods, it was deduced that all methods agreed on approving about 67% of the data as non-erroneous. Declarations Acknowledgements The authors thank the Bureau Gravimetrique International (BGI) for providing shipborne gravity data over the study area. The International Center for Global Gravity Field Models (ICGEM) is appreciated for making global Geopotential Earth Models (GEM) available free of charge on its web page. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. CRediT Author Contribution Mahmoud Hamdy: conceptualization, literature review, methodology, software, formal analysis, resources, data curation, original draft preparation, and writing. Mohamed El Tokhey: methodology, software, validation, investigation, resources, review, and editing. Mohamed Ramadan: methodology, validation, investigation, resources, review, and editing. Tarek Hassan: methodology, software, formal analysis, resources, review, and editing. Yasser Mogahed: conceptualization, data curation, original draft preparation, review, and editing. Statements and Declarations 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. Data Availability Some data used in the study are publicly accessible through the following links: BGI: https://bgi.obs-mip.fr/data-products/gravity-databases/marine-gravity-datas/. ICGEM: https://icgem.gfz-potsdam.de/home Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. Use of Generative AI and AI-Assisted Technologies No generative AI or AI-assisted technologies were employed in the preparation of this manuscript. References Abd-Elmotaal H, El-Tokhey M (1997) Detection of Gross Errors in the Gravity Net in Egypt. Surv Rev 34(266):223–228. https://doi.org/10.1179/003962697791484546 Achilleos GA (2011) The Inverse Distance Weighted interpolation method and error propagation mechanism - creating a DEM from an analogue topographical map. J Spat Sci 56(2):283–304. https://doi.org/10.1080/14498596.2011.623348 Andersen OB (2013) Marine Gravity and Geoid from Satellite Altimetry. In M. G. Sansò Fernando and Sideris (Ed.), Geoid Determination: Theory and Methods (pp. 401–451). 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J Sustain Sci Manage 18(12):111–122. https://doi.org/10.46754/jssm.2023.12.010 Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Research: Solid Earth 117(B4). https://doi.org/https://doi.org/10.1029/2011JB008916 Ruffhead A (1987) An Introduction to Least-Squares Collocation. Surv Rev 29(224):85–94. https://doi.org/10.1179/003962687791512662 Sandwell DT, Müller RD, Smith WHF, Garcia E, Francis R (2014) New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure. Science 346(6205):65–67. https://doi.org/10.1126/science.1258213 Sandwell DT, Smith WHF (1997) Marine Gravity Anomaly from Geosat and ERS 1 Satellite Altimetry. J Geophys Res B: Solid Earth 102(B5):10039–10054. https://doi.org/10.1029/96JB03223 Tscherning CC (1991) A Strategy for Gross-Error Detection in Satellite Altimeter Data Applied in the Baltic-Sea Area for Enhanced Geoid and Gravity Determination. In F. Rapp Richard H. and Sansò (Ed.), Determination of the Geoid (pp. 95–107). Springer New York. https://doi.org/https://doi.org/10.1007/978-1-4612-3104-2_12 Tziavos IN (2020) Gravity and geoid in the Mediterranean Sea: the GEOMED project. Rend Lincei 31:83–97. https://doi.org/10.1007/s12210-020-00880-3 Vergos G, Tziavos I, Andritsanos V (2005) Gravity Data Base Generation and Geoid Model Estimation Using Heterogeneous Data. In: Jekeli C, Bastos L, Fernandes J (eds) Gravity, Geoid and Space Missions. International Association of Geodesy Symposia, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26932-0_27 Wessel P, Watts AB (1988) On the accuracy of marine gravity measurements. J Geophys Research: Solid Earth 93(B1):393–413. https://doi.org/10.1029/JB093IB01P00393 Xavier MB, Rolim SBA (2012) Detection of gross errors in the gravimetric database of the Rio Grande do Sul State. Revista Brasileira de Geofis 30(3):277–285. https://doi.org/10.22564/rbgf.v30i3.185 Xu X, Zhao Y, Reubelt T, Tenzer R (2017) A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models. Geodesy Geodyn 8(4):260–272. https://doi.org/10.1016/J.GEOG.2017.03.013 Zaki A, Magdy M, Rabah M, Saber A (2022) Establishing a Marine Gravity Database around Egypt from Satellite Altimetry-Derived and Shipborne Gravity Data. Mar Geodesy 45(2):101–120. https://doi.org/10.1080/01490419.2021.2020185 Zingerle P, Pail R, Gruber T, Oikonomidou X (2019a) The Experimental Gravity Field Model XGM2019e. GFZ Data Services. https://doi.org/10.5880/ICGEM.2019.007 Zingerle P, Brockmann JM, Pail R, Gruber T, Willberg M (2019b) The Polar Extended Gravity Field Model TIM_R6e . GFZ Data Services. https://doi.org/10.5880/ICGEM.2019.005 Additional Declarations No competing interests reported. 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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-6722175","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":462848313,"identity":"99577c39-c980-4bca-8ee2-1f5facea7ac2","order_by":0,"name":"Mahmoud Hamdy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABL0lEQVRIiWNgGAWjYFACHhDBzGAAJCUYKhDijA3EaTlDshbGNiK06LafPbrhY5s1gzn76cTbvPNs8uQdmB9/5mGwkd1wgPnwCyxazM7kpd2c2ZbOYNmTu9mad1taseEBNjNpHoY04w0H2NIssGk5kGN2m7ftMIPBgdxt0rzbDidubGAwY+ZhOJy44QCPmQE2LeffQLWcfwvUMuc/UAv7Z6DD/gO18H/DquUGzJYbIFsaDiTOZ+AxADrsAMgW5gdYtbwxuznjXDqPwY23my3nHEtO3MDMUyY5xyDZeOZhNjNsIWZ2PsfsxocyazmD87kbb7ypsUuc396++cObCjvZvuPNjz/gCGgQAMcOE4g0OAxigjzBzMAmgUcLGDD+ABLyDQgBZny2jIJRMApGwYgBABcCa09wydofAAAAAElFTkSuQmCC","orcid":"","institution":"Ain Shams University","correspondingAuthor":true,"prefix":"","firstName":"Mahmoud","middleName":"","lastName":"Hamdy","suffix":""},{"id":462848314,"identity":"c62cc5ed-a0a5-41de-94b2-ad4467373a0b","order_by":1,"name":"Mohamed El Tokhey","email":"","orcid":"","institution":"Ain Shams 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07:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6722175/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6722175/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83616083,"identity":"39165c93-f308-4f4a-8e48-fe52b6a1f361","added_by":"auto","created_at":"2025-05-29 13:49:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":3809602,"visible":true,"origin":"","legend":"\u003cp\u003eThe study area and the data distribution over the chosen zones\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/79474e215ad7c20250766acc.png"},{"id":83616869,"identity":"2c2ae4df-d7bf-4164-a1c0-e0b34b5544c0","added_by":"auto","created_at":"2025-05-29 13:57:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":167016,"visible":true,"origin":"","legend":"\u003cp\u003eThe processing strategy used for data filtration\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/650ef8dcf54f69806655a4a3.png"},{"id":83616871,"identity":"871590e4-a4b0-49e0-b6ce-9f19b304ba8e","added_by":"auto","created_at":"2025-05-29 13:57:59","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":28375,"visible":true,"origin":"","legend":"\u003cp\u003eThe percentage of detected errors in each zone using all filtration techniques\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/4bf6cf67409f82974ea741e2.jpg"},{"id":83616077,"identity":"64d4a939-d507-48e8-bef1-060ca74707c8","added_by":"auto","created_at":"2025-05-29 13:49:59","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":104296,"visible":true,"origin":"","legend":"\u003cp\u003eThe gravity anomaly standard deviations of the remaining data points in each zone using all filtration techniques\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/bbed5cb2c900d6758e20d68e.jpg"},{"id":83616080,"identity":"7ab98c72-d0d3-4350-86ee-77c461d53a40","added_by":"auto","created_at":"2025-05-29 13:49:59","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":33860,"visible":true,"origin":"","legend":"\u003cp\u003eThe average gravity gradient of the remaining data points (mgal/m) at each zone using all techniques\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/0888dba46802e847f8ca3b55.jpg"},{"id":83616870,"identity":"2bb89071-3aad-4341-b7c4-0fc31f9ed1ac","added_by":"auto","created_at":"2025-05-29 13:57:59","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":39102,"visible":true,"origin":"","legend":"\u003cp\u003eThe calculated efficiency scores of the tested filtration techniques in the four zones\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/289b324144d69c9fdce1fd97.jpg"},{"id":83616085,"identity":"b7427983-1fb9-49e7-8968-186779ea22f0","added_by":"auto","created_at":"2025-05-29 13:49:59","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":18127,"visible":true,"origin":"","legend":"\u003cp\u003eThe point rejection agreement among the filtration techniques\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/078459c7ce966963a1ef000b.jpg"},{"id":86094094,"identity":"5f4d37ee-53ef-4eb9-a0cd-a404b55e5a0d","added_by":"auto","created_at":"2025-07-06 09:31:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5085345,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6722175/v1/cde38284-129e-48d7-abfb-ebd02a25b3c1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eAssessment of Gravity Filtration Techniques for Shipborne Marine Gravity Observations Over the Mediterranean Sea\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eGravity data are essential for various applications, especially in geodesy and geophysics. These data can be collected from terrestrial, aerial, and satellite measurements. (Andersen, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Marine gravity data plays a vital role in numerous applications such as interpreting the regional geology and structural features of offshore sedimentary basins. Also, they are critical for investigating deep crustal structures, particularly in the context of marine oil and gas exploration (Li et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Pavlis et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Sandwell et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eShipborne gravity anomaly data are essential for building several products (i.e., gravity models, geoid models, or geopotential Earth models). These data are usually recorded with an average accuracy of around 5 mgal (Drewes et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). This limited accuracy is caused by navigational errors (e.g., positioning uncertainties and the E\u0026ouml;tv\u0026ouml;s effect), instrumental errors (e.g., gravimeter drift and cross-coupling), and other error sources such as datum inconsistencies, inaccuracies in ties, and sea condition variations (Wessel \u0026amp; Watts, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). Therefore, enhancement and filtration of these data are essential for producing reliable products.\u003c/p\u003e \u003cp\u003eSeveral studies highlighted this filtration issue to eliminate any existing outliers in the raw data. For instance, the study in(Pa\u0026rsquo;Suya et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) filtered the data in a sequential process over two steps. In the first step, all shipborne gravity anomaly data were filtered using a 95% confidence level rule, while in the second step, the remaining data were filtered using cross-validation employing neighboring data points. In a similar work, the study in(Zaki et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) performed data filtration using cross-validation after independently assessing each ship survey data using different Geopotential Earth Models (GEMs) and altimetry-derived gravity models. Moreover, a leave-one-out cross-validation method was used in (Gautier et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), considering gravity data points with residuals greater than twice the standard deviation as outliers. In another approach, Least Squares Collocation (LSC) was used to discover gross errors in altimetry data in the Baltic Sea(Tscherning, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) and in the Egyptian gravity network (Abd-Elmotaal \u0026amp; El-Tokhey, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). Also, in (Vergos et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), the blunders in the gravity data in the eastern part of the Mediterranean Sea were detected by comparing with a GEM. Then, the LSC method was used to detect the remaining blunders. The study in(Xavier \u0026amp; Rolim, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) adopted a different approach for examining gravity data by setting a rejection threshold based on the calculated residuals using the digital elevation models of the Shuttle Radar Topography Mission (SRTM) (Farr et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), the Gravity Recovery and Climate Experiment (GRACE), and the interpolated observations of gravity observations (i.e., Bouguer anomaly).\u003c/p\u003e \u003cp\u003eAs several filtration techniques exist, it remains a challenge to choose the most suitable technique for each gravity anomaly dataset. This study evaluates different gravity filtration techniques for shipborne marine gravity observations in the Mediterranean Sea, which is known for its complex marine environment with significant geophysical and oceanographic interest (Tziavos, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The study employs 66229 shipborne gravity anomaly data points in the Mediterranean Sea, acquired from the International Gravimetric Bureau (BGI). The evaluated techniques include LSC, Interquartile Range (IQR), three-sigma limit, Inverse Distance Weighted (IDW) interpolation, and refinement using GEMs. The evaluation process focuses on their performance, accuracy, and applicability.\u003c/p\u003e \u003cp\u003eThe following parts of this paper are organized as follows. Section 2 presents the datasets used in this research. Section 3 describes the utilized filtration techniques and the processing strategy. Then, Section 4 presents and discusses the results of each filtration technique. Finally, the conclusions of this research are given in Section 5.\u003c/p\u003e"},{"header":"2. Gravity Datasets","content":"\u003cp\u003eIn geodetic applications, free-air gravity anomaly plays a crucial role in calculating geoid models, which are essential for understanding the Earth's gravitational field. This calculation is performed using Stokes\u0026rsquo; formula (Heiskanen \u0026amp; Moritz, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1967\u003c/span\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\text{N}=\\frac{\\text{R}}{4{\\pi\\:}{\\gamma\\:}}{\\iint\\:}_{{\\sigma\\:}}^{}\\varDelta\\:\\text{g}\\:\\text{S}\\left({\\psi\\:}\\right)\\text{d}{\\sigma\\:}$$\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\\(\\:N\\)\u003c/span\u003e\u003c/span\u003e is the geoid undulation and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{R}\\)\u003c/span\u003e\u003c/span\u003e is the radius of the Earth\u0026rsquo;s sphere. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\gamma\\:\\)\u003c/span\u003e\u003c/span\u003e denotes the normal gravity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{g}\\)\u003c/span\u003e\u003c/span\u003e refers to the gravity anomaly, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}\\)\u003c/span\u003e\u003c/span\u003e represents the unit sphere. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{S}\\left({\\psi\\:}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the Stokes kernel function, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}\\)\u003c/span\u003e\u003c/span\u003e denotes the geocentric angle.\u003c/p\u003e \u003cp\u003eIn our study, 66229 shipborne gravity anomaly points were acquired from BGI (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://bgi.obs-mip.fr/data-products/gravity-databases/marine-gravity-data-prod/#/data/sea\u003c/span\u003e\u003cspan address=\"https://bgi.obs-mip.fr/data-products/gravity-databases/marine-gravity-data-prod/#/data/sea\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The acquired data cover four study regions in the Mediterranean Sea, each with different dimensions, observation intensity, and topology. The size, location, and data distribution of each zone are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These data points were collected during different ship tracks over almost 50 years. Also, it should be noted that there is no metadata describing the accuracy of the acquired raw data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe tested data points included 5560 duplicate observation data. Therefore, the average of each duplicate pair is taken as the observed value at this point. This process reduced the total number of observations to 63449. The general properties of these observations in each zone are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This includes data coverage, gravity anomaly range, and its standard deviation (STD).\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\u003eThe general properties of the acquired shipborne data in each zone\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCount\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLatitude Coverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLongitude Coverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSTD\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35.1901\u0026deg;: 38.3950\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-4.9994\u0026deg;:0.0000\u0026nbsp;\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-787.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e38.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11466\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e38.0005\u0026deg;: 42.9997\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.0000\u0026deg;: 9.9996\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-92.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e114.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e25.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21261\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e33.3129\u0026deg;: 37.9995\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.0002\u0026deg;: 21.0000\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-142.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e146.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e29.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8716\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e32.0003\u0026deg;: 36.7600\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30.0000\u0026deg;: 34.9995\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-189.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e140.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e56.33\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 assessment purposes, some of the most recent GEMs are needed in this study. The employed models encompass different degrees and are constructed using diverse data sources. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes the main characteristics of the used GEMs.\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\u003eThe employed GEMs in this study\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDegree\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eData*\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTongji-GMMG2021S\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS (GOCE, GRACE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eChen, J. et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSGG-UGM-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eA, EGM2008,\u003c/p\u003e \u003cp\u003eS(GOCE, GRACE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLiang et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGM2019e_2159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eA, G, S(GOCO06s), T\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eZingerle, et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2019a\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGO_CONS_GCF_2_TIM_R6e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eG, S(GOCE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eZingerle, et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2019b\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGOCO06s\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS (GOCE, GRACE, CHAMP, Swarm A\u0026thinsp;+\u0026thinsp;B\u0026thinsp;+\u0026thinsp;C, TerraSAR-X, TanDEM-X, LAGEOS, LAGEOS 2, Starlette, Stella, AJISAI, LARES, LARETS, Etalon 1/2 and BLITS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eKvas et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSGG-UGM-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEGM2008, S(GOCE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXu et al. (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e)\u003c/p\u003e \u003cp\u003eLiang et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEGM2008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eA, G, S(GRACE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePavlis et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2012\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003e* S: Satellite Data, G: Ground Data, A: Altimetric Data, GOCE: Gravity field and steady-state Ocean Circulation Explorer, GRACE: Gravity and Climate Recovery Experiment, CHAMP: Challenging Mini-Satellite Payload, LAGEOS: Laser Geodynamic Satellite, LARES: Laser Relativity Satellite, BLITS: Ball Lens In The Space\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"3. Gravity Filtration Techniques","content":"\u003cp\u003eIn this study, different gravity filtration techniques are applied to the acquired data. A brief description of each technique is provided in this section. In addition, the processing strategy to make the assessment process unbiased is presented at the end of the section.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Least Squares Collocation (LSC)\u003c/h2\u003e \u003cp\u003eLSC is the most commonly used prediction technique in practice. It is a very straightforward algorithm. However, it requires a large storage requirement and significant computational time (especially when used for large gravity networks) (Ruffhead, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Based on this technique, the gravity anomaly at any point can be predicted using the gravity anomalies of other points as well as the covariance between these points. The expression of the least-squares prediction is given by (Moritz, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1980\u003c/span\u003e):\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:{g}_{P}=\\left[C\\left(p,{p}_{1}\\right)\\:\\:\\:C\\left(p,{p}_{2}\\right)\\dots\\:\\dots\\:C(p,{p}_{n})\\right]{\\left[\\begin{array}{ccc}\\begin{array}{c}C\\left({p}_{1},{p}_{1}\\right)\\\\\\:C\\left({p}_{2},{p}_{1}\\right)\\\\\\:\\begin{array}{c}⋮\\\\\\:C\\left({p}_{n},{p}_{1}\\right)\\end{array}\\end{array}\u0026amp;\\:\\begin{array}{c}C\\left({p}_{1},{p}_{2}\\right)\\\\\\:C\\left({p}_{2},{p}_{2}\\right)\\\\\\:\\begin{array}{c}⋮\\\\\\:C\\left({p}_{n},{p}_{2}\\right)\\end{array}\\end{array}\u0026amp;\\:\\begin{array}{cc}\\begin{array}{c}\\cdots\\:\\\\\\:\\cdots\\:\\\\\\:\\begin{array}{c}\\ddots\\:\\\\\\:\\dots\\:\\end{array}\\end{array}\u0026amp;\\:\\begin{array}{c}C\\left({p}_{1},{p}_{n}\\right)\\\\\\:C\\left(2,{p}_{n}\\right)\\\\\\:\\begin{array}{c}⋮\\\\\\:C\\left({p}_{n},{p}_{n}\\right)\\end{array}\\end{array}\\end{array}\\end{array}\\right]}^{-1}\\left[\\begin{array}{c}\\varDelta\\:{g}_{{p}_{1}}\\\\\\:\\varDelta\\:{g}_{{p}_{2}}\\\\\\:\\begin{array}{c}⋮\\\\\\:\\varDelta\\:{g}_{n}\\end{array}\\end{array}\\right]$$\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\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e in the number of observed points. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{g}_{P}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{g}_{{p}_{n}}\\)\u003c/span\u003e\u003c/span\u003e are the gravity anomalies of the required point (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\)\u003c/span\u003e\u003c/span\u003e) and the observed point (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{n}\\)\u003c/span\u003e\u003c/span\u003e), respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C(p,{p}_{n})\\)\u003c/span\u003e\u003c/span\u003e refers to the covariance between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{n}\\)\u003c/span\u003e\u003c/span\u003e, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left({p}_{1},{p}_{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left({p}_{n},{p}_{n}\\right)\\)\u003c/span\u003e\u003c/span\u003e denote the covariance between the observed points. Here, the used covariance function is a second-order Gauss-Markov function (G\u0026ouml;tzelmann et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) that can be expressed as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:C\\left(s\\right)={C}_{0}(1+\\frac{s}{\\alpha\\:}){e}^{\\left(\\raisebox{1ex}{$-s$}\\!\\left/\\:\\!\\raisebox{-1ex}{$\\alpha\\:$}\\right.\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\)\u003c/span\u003e\u003c/span\u003e is the distance between points, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the signal variance, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e is the correlation length.\u003c/p\u003e \u003cp\u003eThe open-source code of the GravSoft program(Forsberg \u0026amp; Tscherning, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) was utilized to calculate the predicted gravity anomalies in this study. This includes estimating the empirical covariance function parameters, computing the gravity anomalies, and finding the difference between the predicted and the observed values. If this difference exceeds three times the standard deviation, the concerned point is considered a blunder.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Interquartile Range (IQR)\u003c/h2\u003e \u003cp\u003eIn this method, observations are arranged in ascending order and divided into four quarters. The IQR quantifies the variability within a dataset by measuring the spread of the middle 50% of the data points (Lock et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As it represents the range in which the central half of the observations fall, it can be calculated as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:IQR={Q}_{3}-\\:{Q}_{1}$$\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\\(\\:{Q}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{3}\\)\u003c/span\u003e\u003c/span\u003e are the upper limits of the 25th and 75th percentiles, respectively. Then, the observations falling outside the range defined by the lower boundary (Eq.\u0026nbsp;(5)) and upper boundary (Eq.\u0026nbsp;(6)) are considered outliers (Lock et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLower boundary\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:={Q}_{1}-\\:1.5\\times\\:IQR\\)\u003c/span\u003e\u003c/span\u003e\u003cb\u003e(5)\u003c/b\u003e\u003c/p\u003e \u003cp\u003eUpper boundary\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:={Q}_{3}+\\:1.5\\times\\:IQR\\)\u003c/span\u003e\u003c/span\u003e\u003cb\u003e(6)\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Three-Sigma Limit\u003c/h2\u003e \u003cp\u003eThis simple method is based on the basic statistical principle of standard deviations, which quantify the extent to which data points differ from the mean. Under the assumption that the data is normally distributed, the three-sigma limit defines a range that is expected to include 99.7% of data points. Any data points lying outside this range are considered outliers (Lehmann, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Inverse Distance Weighted (IDW) Interpolation\u003c/h2\u003e \u003cp\u003eThis interpolation technique is considered a special case of the LSC method (Hofmann-Wellenhof \u0026amp; Moritz, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). The gravity anomaly of any point can be predicted, assuming that this anomaly is inversely proportional to the distance between the required point and the observed point. For each point, the gravity anomaly is interpolated using the nearest observed gravity anomalies (Achilleos, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) such that:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:{g}_{p}=\\frac{\\sum\\:_{i=1}^{n}(\\varDelta\\:{g}_{{p}_{i}}/{d}_{i})}{\\sum\\:_{i=1}^{n}(1/{d}_{i})}$$\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\\(\\:\\varDelta\\:{g}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the predicted gravity anomaly of the examined point, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{g}_{{p}_{i}}\\)\u003c/span\u003e\u003c/span\u003e is the observed gravity anomaly of point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e near the examined point. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{i}\\)\u003c/span\u003e\u003c/span\u003e refers to the distance from point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e to the examined point, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the number of points included in a 10 km search radius around the examined point. Finally, the rule of three-sigma is applied to the differences between the interpolated and the actual gravity anomalies to detect any blunders in the raw data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Refinement Using GEMs\u003c/h2\u003e \u003cp\u003eGEMs are widely used for modeling anomalies as a part of a well-known remove-restore technique (Barzaghi, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). These models play an important role in smoothing the gravity field by removing the effect of the long gravitational wavelength. Additionally, they have a role in filtering gravity data to enhance data accuracy and consistency.\u003c/p\u003e \u003cp\u003eIn this technique, the GEMs, presented in Section 2, are employed to refine shipborne gravity observations. The predicted value of the gravity anomaly can be computed as follows (Barthelmes, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2013\u003c/span\u003e):\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\varDelta\\:g}_{P}\\left(r,\\lambda\\:,\\phi\\:\\right)=\\frac{GM}{{r}^{2}}\\sum\\:_{l=0}^{{l}_{max}}{\\left(\\frac{R}{r}\\right)}^{l}(l-1)\\sum\\:_{m=0}^{l}{P}_{lm}\\left(sin\\phi\\:\\right)({C}_{lm}\\text{cos}m\\lambda\\:+{S}_{lm}\\text{sin}m\\lambda\\:)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(r,\\lambda\\:,\\phi\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e are the spherical geocentric coordinates of the point (radius, longitude, latitude), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e is the reference radius, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:GM\\)\u003c/span\u003e\u003c/span\u003e is the product of the gravitational constant and the mass of Earth. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:l\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e refer to degree and order of spherical harmonic, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{lm}\\)\u003c/span\u003e\u003c/span\u003e represents fully normalized Legendre functions, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{lm}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{lm}\\)\u003c/span\u003e\u003c/span\u003e denote Stokes\u0026rsquo; coefficients. Then, the difference between the gravity anomaly observation and the corresponding predicted value is calculated, and the three-sigma rule is applied to detect the outliers in the raw data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Processing Strategy\u003c/h2\u003e \u003cp\u003eFor applying the described techniques to the acquired shipborne data, a unified processing criterion is selected to make the assessment process unbiased. The dataset of each zone is divided into two sets (Set A and Set B). Consequently, data points are sorted according to their spatial location. Then, they are divided so that Set A contains the points with odd arrangement and Set B contains the points with even arrangement. This procedure governs the similarity of data distribution. After data splitting, the general properties of the observations of each subset are given in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\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\u003eThe general properties of the observations of each data subset after data splitting\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCount\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLatitude Coverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLongitude Coverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSTD\u003c/p\u003e \u003cp\u003e(mgal)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 1_A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35.1901\u0026deg;: 38.3380\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.9994\u0026deg;: -0.0001\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-787.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 1_B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35.1903\u0026deg;: 38.3950\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.9992\u0026deg;: 0.0000\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-121.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e83.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 2_A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5733\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38.0005\u0026deg;: 42.9995\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.0000\u0026deg;: 9.9976\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-92.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e110.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 2_B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5733\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38.0033\u0026deg;: 42.9997\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.0003\u0026deg;: 9.9996\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-91.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e114.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 3_A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10631\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e33.3200\u0026deg;: 37.9985\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e16.0002\u0026deg;: 21.0000\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-136.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e146.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 3_B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10630\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e33.3129\u0026deg;: 37.9995\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e16.0004\u0026deg;: 21.0000\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-142.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e146.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE 4_A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32.0013\u0026deg;: 36.6741\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.0000\u0026deg;: 34.9993\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-189.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e116.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e56.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZONE4_B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32.0003\u0026deg;: 36.7600\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.0000\u0026deg;: 34.9995\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-186.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e140.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e56.49\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\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that each pair of subsets in the same zone has almost the same characteristics, except zone 1, in which a significant difference between the minimum gravity anomalies is realized. This can be caused if large outliers exist in one of the two subsets, which will be investigated in the following parts of this study.\u003c/p\u003e \u003cp\u003eBy utilizing two datasets, each set is used to predict the gravity anomalies of the required points in the other set. Each predicted anomaly is then compared to the corresponding observed anomaly to identify if there is an outlier. This processing strategy works iteratively to avoid contaminating the predicted values by biased points. In each step of the iterative process, the possible outliers in the previous step are omitted from the prediction process. The iteration process stops when the percentage of detected errors becomes less than 1% of the corresponding set for Set A and Set B. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes this shipborne data processing strategy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results and Discussion","content":"\u003cp\u003eThis section presents the results obtained after applying the processing techniques described to the acquired shipborne data. This includes a comprehensive analysis for each zone and each data subset. It is worth noting that after applying the refinement using GEMs method, it was deduced that the different GEMs had a similar attitude in detecting the gross errors in the data. Consequently, the most recent higher degree GEM (XGM2019e_2159) is chosen to be involved in the following analysis and comparison stages in this section. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the statistics of the filtration process and the results achieved after erroneous data removal for all techniques.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe statistics of the filtered data after using the filtration techniques\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTechnique\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZONE 1_A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZONE 1_B\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eZONE 2_A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eZONE 2_B\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eZONE 3_A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eZONE 3_B\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eZONE 4_A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eZONE 4_B\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLSC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e%Errors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e27.73%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.57%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24.61%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25.55%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.81%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e12.99%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e38.18%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e39.17%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-119.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-121.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-92.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-91.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-80.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-85.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-180.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-183.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e83.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e94.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e96.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e63.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e90.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e115.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e115.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eSTD\u003c/b\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e21.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e21.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e24.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e24.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e55.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e56.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eIQR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e%Errors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.91%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.43%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.77%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.72%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4.74%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.18%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.27%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-121.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-121.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-78.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-90.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-136.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-142.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-187.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-186.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e83.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e110.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e114.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e146.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e146.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e116.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e140.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eSTD\u003c/b\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e29.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e56.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e56.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eThree-Sigma\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e%Errors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.58%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.32%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.47%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.51%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.64%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.68%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.11%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.09%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-787.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-121.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-92.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-91.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-136.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-142.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-189.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-186.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e83.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e110.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e114.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e146.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e146.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e116.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e140.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eSTD\u003c/b\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e29.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e56.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e56.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eIDW Interpolation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e%Errors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.13%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.74%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e13.62%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e12.87%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e13.91%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e13.47%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e24.51%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e23.52%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\:\\)\u003c/span\u003e\u003c/span\u003e(mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-121.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-121.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-78.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-77.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-134.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-127.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-178.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-176.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e79.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e94.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e96.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e132.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e128.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e114.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e140.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eSTD\u003c/b\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e23.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e27.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e27.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e48.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e49.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eXGM2019e_2159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e%Errors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.77%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.71%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.93%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.69%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.75%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.41%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.03%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.28%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{i}\\mathbf{n}}\\:\\)\u003c/span\u003e\u003c/span\u003e(mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-121.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-121.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-92.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-91.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-134.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-142.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-187.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-186.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\mathbf{g}}_{\\mathbf{m}\\mathbf{a}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e86.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e83.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e94.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e96.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e125.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e115.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e116.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e121.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eSTD\u003c/b\u003e (mgal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e36.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e37.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e23.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e26.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e26.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e55.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e55.23\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\u003eIt is clear from Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e that each filtration technique worked uniformly in almost the same manner for each pair of data subsets. In the case of using LSC filtration, the percentages of detected errors are almost the same for each pair, except in Zone 3. The reason behind the recorded difference (i.e., 4.81% and 12.99%) may be due to the inconvenience of the covariance function. In addition, the percentages of detected errors in Zone 4 are relatively larger, and this behavior was expected due to the sparsity of the data in this zone. Moreover, the results showed a reduction in the gravity anomaly standard deviations after error removal. It was recorded that each trial took a noticeably longer processing time compared to the other methods. In addition, it was clear that this method requires a lot of trials until the stop condition is met.\u003c/p\u003e \u003cp\u003eUsing the IQR filtration technique provided promising homogeneous results. The percentages of detected blunders were much less than those detected using the LSC method. Also, the gravity anomaly standard deviations were slightly reduced. It can also be concluded from Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e that using the three-sigma method failed to detect errors, showing a very low detection capability in all zones. As a result, the gravity anomaly standard deviations are almost the same before and after removing the detected errors.\u003c/p\u003e \u003cp\u003eRegarding the IDW interpolation technique, it provided a reasonable error detection rate. The results indicate that the detected error percentages are not excessively large, preventing the misclassification of valid data as errors, nor too low, ensuring that the method remains capable of detecting a significant portion of actual errors. In addition, the results\u0026rsquo; homogeneity, particularly in Zone 4, emphasizes that this technique can deal with all zones in the same manner without being affected by data density. Also, the reduction in the gravity anomaly standard deviations indicates the efficiency of this method.\u003c/p\u003e \u003cp\u003eThe results in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e also, show that the percentages of errors detected after refinement using GEMs aree relatively similar to the IQR method. However, it was apparent that this method detected a higher percentage of outliers in Zone 3 than in the other zones. This may be due to the lack of short-wavelength components in this zone, in the satellite-derived gravity field (Sandwell \u0026amp; Smith, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). To summarize the results in Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and compare the different techniques, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e depict the percentage of detected errors and the gravity anomaly standard deviation of the remaining data points of all techniques in each zone.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can be inferred from Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e that the LSC and IDW interpolation methods had the highest percentage of detected errors. In addition, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows that the resulting gravity anomaly standard deviations did not have significant differences from one technique to another over the four zones.\u003c/p\u003e \u003cp\u003eFor comparison purposes, the average gravity anomaly gradient (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{a}\\)\u003c/span\u003e\u003c/span\u003e), which indicates the smoothness of the gravity field, is calculated for each technique after removing the outliers as follows:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{G}_{a}=\\frac{\\sum\\:_{i=1}^{m}\\sum\\:_{j=1}^{m}\\frac{\\varDelta\\:{g}_{ij}}{{D}_{ij}}}{m}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{g}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the difference in the gravity anomaly between points \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{ij}\\)\u003c/span\u003e\u003c/span\u003e denotes the distance between points \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e represents the total number of remaining data points. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the average gravity anomaly gradient at each zone before and after the filtration process using each technique.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage gravity gradient (mgal/m) at each zone before and after filtration for all techniques\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTechnique\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBefore filtration\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0127\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLSC\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0074\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0106\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThree Sigma\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0104\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIQR\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIDW Interpolation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0101\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eXGM2019e_2159\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0127\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\u003eIt is clear that the gravity anomaly gradient was significantly improved in all zones using the LSC, IQR, and IDW interpolation methods. On the other hand, the three-sigma method and XGM2019e_2159 did not perform similarly, as the average gravity gradient is approximately equal to that before filtration. This gives other techniques a superiority in smoothing the gravity field. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the calculated average gradient of the remaining data points using all techniques over the four zones.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is clear from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that the IDW interpolation technique could provide the smoothest gravity field in Zones 2, 3, and 4, while the LSC technique provided the smoothest gravity field in Zone 1. This emphasizes the efficiency of the IDW interpolation technique, particularly with a lower percentage of errors detected than the LSC method. In addition, the results of employing GEMs did not show significant differences.\u003c/p\u003e \u003cp\u003eIn order to choose the most effective filtration technique, a score is proposed to each filtration technique based on its gravity gradient, remaining data points, and the decrease in the standard deviation values. The criterion is chosen so that the efficiency score increases with a smoother gravity field (i.e., a lower gravity gradient), a higher percentage of remaining points, and a larger decrease in the standard deviation value. This can be expressed mathematically as follows:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:score=\\left|\\frac{{G}_{i}-\\:{G}_{a}}{{G}_{i}}\\right|\\times\\:{W}_{1}+\\left|1-\\frac{\\%E}{100}\\right|\\times\\:{W}_{2}+\\left|\\frac{{STD}_{i}-\\:STD}{{STD}_{i}}\\right|\\times\\:{W}_{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{a}\\)\u003c/span\u003e\u003c/span\u003e are the average gravity gradients before and after filtration, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\%E\\)\u003c/span\u003e\u003c/span\u003e denotes the percentage of detected errors. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{STD}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:STD\\)\u003c/span\u003e\u003c/span\u003e are the gravity anomaly standard deviations before and after filtration, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{2}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{3}\\)\u003c/span\u003e\u003c/span\u003e refer to the weights allocated for gravity gradient change, percentage of remaining data points, and standard deviation change, respectively. In our study, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{2}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{3}\\)\u003c/span\u003e\u003c/span\u003e are assumed as 1, 0.75, and 0.5, respectively. These weights were chosen based on repeated trials to represent the differences between the tested techniques in the best way while maintaining the priority of the three factors. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the calculated efficiency scores of the tested filtration techniques.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is clear from Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e that the IDW interpolation method achieved the best scores in the four zones, which emphasizes its high efficiency. In addition, the LSC technique came in the second order in all zones except Zone 4 due to the sparsity of the data in this zone, as discussed earlier. In addition, the low-degree GEMs achieved almost the same scores, which is also true for the high-degree GEMs.\u003c/p\u003e \u003cp\u003eTo test the level of agreement between the used methods, a cross-check is conducted to determine the methods that agreed on their outlier detection. This is performed for each observed point. Therefore, we can evaluate the confidence in the validity of each observation based on the consensus among the filtration techniques. For this purpose, the point rejection agreement among the used filtration techniques is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e indicates that less than 1% of the data was detected by at least 4 methods as gross errors. In addition, the results provided a good confidence level in the different filtration techniques, as all methods agreed on approving about 67% of the data as non-erroneous.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this research, several filtration techniques were applied to detect outliers in gravity anomaly shipborne data. The acquired data includes 66229 shipborne gravity anomaly points covering four regions in the Mediterranean Sea, each with different dimensions, observation intensity, and topology. A comparative study was performed to assess the performance that can be achieved using each applied technique. This includes LSC, IQR, three-sigma limit, IDW interpolation, and refinement using GEMs. The comparison criterion is chosen so that efficiency increases with a smoother gravity field (i.e., a lower gravity gradient), a higher percentage of remaining points, and a larger decrease in the standard deviation value. The results showed that the most effective technique is the IDW interpolation, followed by the LSC technique. The IDW interpolation detected outliers with percentages ranging between 8.94% (Zone 1) and 24.02% (Zone 4) of the total data points, while the percentages in the case of using LSC ranged from 8.90% (Zone 3) to 38.68% (Zone 4). Moreover, the IDW interpolation technique could provide the smoothest gravity field in Zones 2, 3, and 4, while the LSC technique provided the smoothest gravity field in Zone 1. Despite the promising results provided by the LSC technique, it required a significantly long processing time. On the other hand, the IDW interpolation method could provide reliable results with a short processing time. Regarding the correlation between every two techniques, the results showed that each method has its unique strategy for outlier detection, with weak to moderate correlations between them. After investigating the agreement level between the used methods, it was deduced that all methods agreed on approving about 67% of the data as non-erroneous.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThe authors thank the Bureau Gravimetrique International (BGI) for providing shipborne gravity data over the study area. The International Center for Global Gravity Field Models (ICGEM) is appreciated for making global Geopotential Earth Models (GEM) available free of charge on its web page.\u003c/p\u003e\n\u003ch2\u003eFunding\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCRediT Author Contribution\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eMahmoud Hamdy: conceptualization, literature review, methodology, software, formal analysis, resources, data curation, original draft preparation, and writing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMohamed El Tokhey: methodology, software, validation, investigation, resources, review, and editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMohamed Ramadan: methodology, validation, investigation, resources, review, and editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTarek Hassan: methodology, software, formal analysis, resources, review, and editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eYasser Mogahed: conceptualization, data curation, original draft preparation, review, and editing.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eStatements and Declarations\u003c/h2\u003e\n\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\n\u003ch2\u003eData Availability\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eSome data used in the study are publicly accessible through the following links:\u003c/p\u003e\n\u003cp\u003eBGI: \u0026nbsp;https://bgi.obs-mip.fr/data-products/gravity-databases/marine-gravity-datas/.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eICGEM: https://icgem.gfz-potsdam.de/home\u003c/p\u003e\n\u003cp\u003eSome or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eUse of Generative AI and AI-Assisted Technologies\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eNo generative AI or AI-assisted technologies were employed in the preparation of this manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbd-Elmotaal H, El-Tokhey M (1997) Detection of Gross Errors in the Gravity Net in Egypt. 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GFZ Data Services. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5880/ICGEM.2019.005\u003c/span\u003e\u003cspan address=\"10.5880/ICGEM.2019.005\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\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":"Shipborne Gravity Anomaly, Mediterranean Sea, Geopotential Earth Model, Interquartile Range, Gross Error","lastPublishedDoi":"10.21203/rs.3.rs-6722175/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6722175/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMarine gravity provides vital geodetic and geophysical information for several applications, such as regional geology, tectonic structures, and oceanographic processes. Filtering these data represents a crucial pre-processing step to eliminate any erroneous signals and improve the data quality for better analysis and interpretation. This study investigates five gravity filtration techniques to improve the quality of shipborne marine gravity data collected over the Mediterranean Sea. The assessed techniques include Least Squares Collocation (LSC), Interquartile Range (IQR), three-sigma limit, Inverse Distance Weighted (IDW) interpolation, and refinement using Geopotential Earth Models (GEMs). The study employs 66229 shipborne gravity anomaly data points acquired from the International Gravimetric Bureau (BGI). The results indicate that the IDW interpolation and LSC techniques are the most effective. IDW interpolation can provide a balance between error detection and computational time, while LSC requires a significantly longer processing time. It is also shown that using any recent GEM yields almost the same performance. Moreover, a cross-check between the assessed techniques shows that they all accepted about 67% of the data as not erroneous. These findings can be exploited to significantly improve the accuracy of marine gravity datasets for different geodetic and geophysical studies.\u003c/p\u003e","manuscriptTitle":"Assessment of Gravity Filtration Techniques for Shipborne Marine Gravity Observations Over the Mediterranean Sea","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-29 13:49:54","doi":"10.21203/rs.3.rs-6722175/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":"cb275f0e-e4a7-4d60-be41-27dbd7bc8943","owner":[],"postedDate":"May 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-06T09:23:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-29 13:49:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6722175","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6722175","identity":"rs-6722175","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}