Regional Gravity Field Research Articles

A convolutional neural network to optimize multi-mission satellite altimeter fusion for improving the marine gravity field

Satellite altimetry is the main tool for constructing global or regional marine gravity fields. To improve the accuracy and spatial resolution, it is necessary to fuse multi-mission altimeters. How to determine the weights of multi-mission altimeters is a crucial issue, making the conventional calculation process very complex. In addition, traditional satellite inversion methods are often independent of shipborne gravity, which is used only as validation data, thus not take full advantages of high accuracy and resolution of shipborne gravity. In this study, we introduce a convolutional neural network (CNN) to merge the vertical deflections (DOVs) obtained from multi-altimeter missions to construct a marine gravity model in the South China Sea. High-accuracy shipborne gravity and a dataset comprising DOVs and geo-locations are employed as input data for neural network training. For the validation of CNN method, the gravity model is also computed by conventional Inverse Vening Meinesz (IVM) method. Independent shipborne gravity measurements and SIO V32.1, DTU17 models are used as validation data. The evaluation results show that the CNN-derived model achieves a higher level of accuracy, yielding a standard deviation (STD) of 3.21 mGal, with an improvement of 36.56% compared to IVM-derived model. More than 92% of the differences between the CNN-derived model and shipborne gravity are less than 5 mGal. In addition, spectral analysis results further show that the CNN-derived model has stronger energy at short wavelengths (less than 25 km) compared to other models. These findings reveal that CNN method is feasible for marine gravity recovery and the CNN-derived model can achieve higher accuracy. The CNN method can improve the accuracy and spectral characteristics of the constructed gravity model by taking advantage of the high accuracy and high resolution of shipborne gravity.Graphical

Gravity and magnetic study of the Xitle volcanic field, Basin of Mexico – Inferences on the pre-eruptive topography

Results of a gravity and magnetic study over a lava field in the southern Basin of Mexico are used to investigate on lava emplacement and pre-eruptive topography. The characteristics of lava flows depend on multiple factors, including the lava composition, effusion rate, rheology, fluid content and underlying terrain. The ∼2000 years old volcanic field, formed by seven flow units emplaced by the Xitle eruption, covers an extensive area >80 km2 characterized by topographic relief on the Ajusco volcano flank and surrounding plain. The study is conducted on the northern end of the volcanic field. The gravity and magnetic study is based on regional-residual separation, vertical and horizontal derivatives, reduced to the pole, analytical signal, spectral analysis and forward modeling. The regional gravity field shows two anomaly lows in the central sector, with the residual field showing trends of gravity highs. The residual magnetic anomaly is characterized by trends of magnetic highs associated to the lava field. Depths estimated from spectral analysis of gravity and magnetic anomalies show shallow sources at ∼22 m and ∼46 m, and deep sources at ∼469 m and ∼268 m, respectively. The underground sequence is modeled as a volcanoclastic succession of varying thickness. The first vertical derivatives, gradients and analytical signal enhance the anomalies associated to lava thickness variations. Joint gravity and magnetic analysis constraints the deep/shallow anomaly sources in the volcanic field and relations to pre-eruptive structure.

Tectonics of Cauvery basin (India) in onshore and offshore portions

Morphometric studies coupled with geophysical investigations from petroliferous basins provide valuable information about tectonics of the regions. We deduce six morphologic parameters from the River Cauvery's designated (sub)watersheds and perform dendrogram clustering analysis. The main channels of the (sub)watersheds showcase steeper gradient and meandering nature with less concavity. On the other hand, the distributaries portray lesser gradient and straight nature with greater concavity. From the offshore region of the Cauvery basin, we perform gravity modeling. The results show variations in gravity values from low to high, -150 to 50 mGal probably because of the basement ridge-depression features. This anomaly orientation indicates the extension of the sub-basin in the region. A strong NE-SW gravity trend possibly suggests a high-density plug at mid-crust. The low gravity values near the Vedaranyam region indicate low-density rocks within the basement. Places of high gravity anomaly show a decrease in bathymetry depth and vice versa. This indicates isostatic compensation of the Moho geometry, possibly due to crustal thinning in the offshore areas. Isostatic regional gravity fields are manifested by Moho relief and can have implications on the lithospheric mechanical strengths. Bathymetric studies indicate multi-directional slopes. Relatively flat areas can indicate depocenters. E-W trending lineaments mapped on the Precambrian basement from a portion of the study area is presumably a manifestation of Cauvery Shear zone, which also persists in the offshore region.

Строение центральной части палеопротерозойского Лосевского террейна по данным плотностного моделирования

The results of detailed three-dimensional density modeling of the upper crust of the central part of the Losevsky terrane located in the northern part of the Voronezh crystal massif are considered. The distribution of absolute crustal density values of to a depth of 16 km was obtained as a result of the inversion of local anomalies of the gravitational field in the Bouguer reduction. The solution of the inverse problem of gravimetry was implemented within the framework of the initial model, which was formed using digital geological and geophysical data from the study area: the regional density model of the East European Platform lithosphere and its corresponding regional gravity field; the field of local gravity anomalies, representing the difference between the observed and regional fields of the lithosphere model; generalized information on the density of sedimentary cover rocks and the crystal basement; the thickness scheme of the «gravity-active» layer, obtained on the basis of statistical analysis of the anomalous field; geological and topographic information. Quantitative interpretation of the gravimetry data allowed us to obtain fundamentally new information about the geological structure of the upper crust of the study area. The reliability of the obtained results is confirmed by the consistency of a priori data and the correspondence of the total model (local plus regional) and observed gravitational fields.

A New Combination Approach for Gibbs Phenomenon Suppression in Regional Validation of Global Gravity Field Model: A Case Study in North China

A global gravity field model (GGM) is essential to be validated with ground-based or airborne observational data for the accurate application of the GGM at a regional scale. Furthermore, accurately understanding the commission errors between the GGM and observational data are crucial for improving regional gravity fields. Taking the North China region as an example, to circumvent the omission errors, it is necessary to unify the spatial resolutions of the EIGEN-6C4 model and terrestrial gravity observational data to 110 km (determined by the distribution of gravity stations) by employing the spherical harmonic function for the EIGEN-6C4 model and the Slepian basis function for the gravity data, respectively. However, the application of spherical harmonic function expansions in the gravity model results in the Gibbs phenomenon, which may be a primary factor contributing to commission errors and impedes the accurate validation of the EIGEN-6C4 model with terrestrial gravity data. To effectively mitigate this issue, this study proposes a combination approach of window function filtering and regional eigenvalue constraint (based on the Slepian basis). Utilizing the EIGEN-6C4 gravity model to derive the gravity disturbance field at a resolution of 110 km (with spherical harmonic expansion up to the 180th degree and order), the combination approach effectively suppresses over 90% of high-degree (above the 120th degree) Gibbs phenomena. This approach also reduces signal leakage outside the region, thus enhancing the spatial accuracy of the regional gravity disturbance field. A subsequent comparison of the regional gravity disturbance field derived from the true model and terrestrial gravity data in North China indicates excellent consistency, with a root mean squared error (RMSE) of 0.80 mGal. This validation confirms that the combined approach of window function filtering and regional eigenvalue constraints effectively mitigates the Gibbs phenomenon and yields precise regional gravity fields. This approach is anticipated to significantly benefit scientific applications such as improving the accuracy of regional elevation benchmarks and accurately inverting the Earth’s internal structure.

Benefit of classical leveling for geoid-based vertical reference frames

Classically, vertical reference frames were realized as national or continent-wide networks of geopotential differences derived from geodetic leveling, i.e., from the combination of spirit leveling and gravimetry. Those networks are affected by systematic errors in leveling, leading to tilts in the order of decimeter to meter in larger networks. Today, there opens the possibility to establish a worldwide unified vertical reference frame based on a conventional (quasi)geoid model. Such a frame would be accessible through GNSS measurements, i.e., physical heights would be derived by the method of GNSS-leveling. The question arises, whether existing geodetic leveling data are abolished completely for the realization of vertical reference frames, are used for validation purposes only, or whether existing or future geodetic leveling data can still be of use for the realization of vertical reference frames. The question is mainly driven by the high quality of leveled potential differences over short distances. In the following we investigate two approaches for the combination of geopotential numbers from GNSS-leveling and potential differences from geodetic leveling. In the first approach, both data sets are combined in a common network adjustment leading to potential values at the benchmarks of the leveling network. In the second approach, potential differences from geodetic leveling are used as observable for regional gravity field modeling. This leads to a grid of geoid heights based on classical observables like gravity anomalies and now also on leveled potential differences. Based on synthetic data and a realistic stochastic model, we show that incorporating leveled potential differences improves the quality of a continent-wide network of GNSS-heights (approach 1) by about 40% and that formal and empirical errors of a regional geoid model (approach 2) are reduced by about 20% at leveling benchmarks. While these numbers strongly depend on the chosen stochastic model, the results show the benefit of using leveled potential differences for the realization of a modern geoid-based reference frame. Independent of the specific numbers of the improvement, an additional benefit is the consistency (within the error bounds of each observation type) of leveling data with vertical coordinates from GNSS and a conventional geoid model. Even though we focus on geodetic leveling, the methods proposed are independent of the specific technique used to observe potential (or equivalently height) differences and can thus be applied also to other techniques like chronometric or hydrodynamic leveling.

Connecting the Brazilian Vertical System to the International Height Reference Frame by estimating the vertical datum parameters

One of the challenges in the unification of the global vertical datum is to determine the vertical offset between the local vertical datum and the global vertical datum. Since 2015, the scientific community has been working on the unification of the global vertical datum, following the publication of the resolution for the definition and realization of an International Height Reference System. This paper aims to estimate the vertical offset in Brazil (Imbituba and Santana Data) by combining a regional gravity field model, using the Geodetic Boundary Value Problem approach applying the Remove-Compute-Restore procedure, and GNSS/leveling data. In the Imbituba vertical datum 1271 stations were used and 66 stations were connected to the Santana tide gauge. The results showed that the geopotential value of Imbituba was 62,636,849.87 ± 0.224 m2s-2, and the vertical offset concerning the reference surface (W0) was 0.358 ± 0.023 m. In Santana, the geopotential value was 62,636,836.88 ± 4.108 m2s-2, and the vertical offset was 1.689 ± 0.420 m. The offset between Imbituba and Santana was computed once the physical connection between Brazil's two local vertical data is a challenge. The estimated value was 1.331 ± 0.421 m. This means the Santana vertical datum is 1.331 m higher than the Imbituba vertical datum.

A data-adaptive network design for the regional gravity field modelling using spherical radial basis functions

A high-precision regional gravity field model is significant in various geodesy applications. In the field of modelling regional gravity fields, the spherical radial basis functions (SRBFs) approach has recently gained widespread attention, while the modelling precision is primarily influenced by the base function network. In this study, we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm, and the performance of the algorithm is verified by the observed gravity data in the Auvergne area. Furthermore, the turning point method is used to optimize the bandwidth of the basis function spectrum, which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously. Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model. Compared to the existing methods, the number of SRBFs used for modelling has been reduced by 15.8%, and the time cost to determine the centre positions of SRBFs has been saved by 12.5%. Hence, the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.

High-resolution regional gravity field modeling in data-challenging regions for the realization of geopotential-based height systems

Modern height systems are based on the combination of satellite positioning and gravity field models of high resolution. However, in many regions, especially developing or newly industrializing countries, there is no (reliable) regional gravity model at all, due to challenges such as limited data availability, unknown/low data quality, and missing metadata. This paper addresses this issue in a case study of Colombia, where eight decades of historical terrestrial and airborne gravity measurements are available but widely contain systematic errors, outliers, and biases. Correspondingly, processing strategies and structures are proposed and applied to validate and improve the quality of old gravity datasets. A novel method is developed based on spherical radial basis functions (SRBFs) for estimating biases, which are found in different airborne surveys with values exceeding 40 mGal. The validity of this bias estimation method is demonstrated both by a simulation test and by the evaluation of the airborne data in comparison to the SATOP (SAtellite-TOPography) model, which merges the satellite-only global gravity model GOCO06s with the Earth2014 topography model. The terrestrial and airborne data are then combined with a global gravity model (GGM), ultra-high-resolution topography models, as well as altimetry-derived gravity anomalies from DTU21GRA for the offshore areas. The results are presented in terms of height anomalies (QGeoidCOL2023), and they are thoroughly validated using GPS/leveling data both in the absolute and relative manner. The standard deviation in comparison to the GPS/leveling data after applying a correction surface to account for the datum inconsistencies amounts to 15.76 cm, which is 27% smaller compared to the mean standard deviation value given by five recent high-resolution GGMs, and 36% smaller than the one delivered by the latest South American quasi-geoid model QGEOID2021. The relative validation results show that QGeoidCOL2023 performs better, i.e., delivers lower RMS errors than the GGMs and QGEOID2021 in all the baseline length groups. These results indicate the validity and benefits of the developed methods and procedures, which can be used for other data-challenging areas to facilitate the realization of geopotential-based height systems.Graphical

Influence of thick lithomargic soil cover on Bouguer gravity low: Imprints from passive continental margin of southwestern India

The Periyar Plateau in central Kerala is characterized by a strong negative Bouguer gravity field around three major islands of a strongly negative field of the value of -150 mGal. Detailed gravity studies reveal that these islands of strong negative field are of a shallow nature and are not traceable in the 1/4° average gravity grids. Spectral analysis of Bouguer anomaly map and 2D gravity modelling of Periyar Plateau region reveal the average depth of the shallow source layer is as shallow as 700-1000 m, which is correlatable with the layer of lateritic/lithomargic soil cover and the underlying weathered country rock having a density of 2.2 g/cc. Such a strong influence on the regional gravity field is due to the wide contrast in the densities of the lateritic cover and the primary rocks of the basement. These results underline the need to recognize the strong influence of such alteration zones on the regional gravity fields, especially the tropics, a factor not always considered.

Application of Sparse Regularization in Spherical Radial Basis Functions-Based Regional Geoid Modeling in Colorado

Spherical radial basis function (SRBF) is an effective method for calculating regional gravity field models. Calculating gravity field models with high accuracy and resolution requires dense basis functions, resulting in complex models. This study investigated the application of sparse regularization in SRBFs-based regional gravity field modeling. L1-norm regularization, also known as the least absolute shrinkage selection operator (LASSO), was employed in the parameter estimation procedure. LASSO differs from L2-norm regularization in that the solution obtained by LASSO is sparse, specifically with a portion of the parameters being zero. A sparse model would be advantageous for improving the numerical efficiency by reducing the number of SRBFs. The optimization problem of the LASSO was solved using the fast iterative shrinkage threshold algorithm, which is known for its high efficiency. The regularization parameter was selected using the Akaike information criterion. It was specifically tailored to the L1-norm regularization problem. An approximate covariance matrix of the estimated parameters in the sparse solution was analytically constructed from a Bayesian viewpoint. Based on the remove–compute–restore technique, a regional geoid model of Colorado (USA) was calculated. The numerical results suggest that the LASSO adopted in this study provided competitive results compared to Tikhonov regularization; however, the number of basis functions in the final model was less than 25% of the Tikhonov regularization. Without significantly reducing model accuracy, the LASSO solution provides a very simple model. This is the first study to apply the LASSO to SRBFs-based modeling of the regional gravity field in real gravity observation data.

Regional Gravity Field Modeling Using Band-Limited SRBFs: A Case Study in Colorado

The use of spherical radial basis functions (SRBFs) in regional gravity field modeling has become popular in recent years. However, to our knowledge, their potential for combining gravity data from multiple sources, particularly for data with different spectrum information in the frequency domain, has not been extensively explored. Therefore, band-limited SRBFs, which have good localization characteristics in the frequency domain, were taken as the main tool in this study. To determine the optimal expansion degree of SRBFs for gravity data, a residual and a priori accuracy comparative analysis method was proposed. Using this methodology, the expansion degrees of terrestrial and airborne data were determined to be 5200 and 1840, respectively, and then a high-resolution geoid model called ColSRBF2023 was constructed for use in Colorado. The results indicated that ColSRBF2023 had a standard deviation (STD) of 2.3 cm with respect to the GSVS17 validation data. This value was 2–6 mm lower than models obtained using different expansion degrees for gravity data and models from other institutions considered in this study. Furthermore, when comparing it with the validation geoid model on a 1′ × 1′ grid, ColSRBF2023 exhibited an STD value of 2.4 cm, which was also the best among the examined models. These findings highlight the importance of determining the optimal expansion degree of gravity data, particularly for constructing high-resolution gravity field models in rugged mountainous areas.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system. Compared to the satellite gravity measurement, the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface. However, the suitable and unified method for gravity model estimation is a key problem for further applications. In this study, we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region (99–104°E, 23–29°N) in the four epochs from 2015 to 2017. Compared to the experimental results based on Slepian or spherical harmonics frequency domain method, this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data, by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal. The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Antarctic Time-Variable Regional Gravity Field Model Derived from Satellite Line-of-Sight Gravity Differences and Spherical Cap Harmonic Analysis

This study focuses on the development of a time-variable regional geo-potential model for Antarctica using the spherical cap harmonic analysis (SCHA) basis functions. The model is derived from line-of-sight gravity difference (LGD) measurements obtained from the GRACE-Follow-On (GFO) mission. The solution of a Laplace equation for the boundary values over a spherical cap is used to expand the geo-potential coefficients in terms of Legendre functions with a real degree and integer order suitable for regional modelling, which is used to constrain the geo-potential coefficients using LGD measurements. To validate the performance of the SCHA, it is first utilized with LGD data derived from a L2 JPL (Level 2 product of the Jet Propulsion Laboratory). The obtained LGD data are used to compute the local geo-potential model up to Kmax = 20, corresponding to the SH degree and order up to 60. The comparison of the radial gravity on the Earth’s surface map across Antarctica with the corresponding radial gravity components of the L2 JPL is carried out using local geo-potential coefficients. The results of this comparison provide evidence that these basis functions for Kmax = 20 are valid across the entirety of Antarctica. Subsequently, the analysis proceeds using LGD data obtained from the Level 1B product of GFO by transforming these LGD data into the SCHA coordinate system and applying them to constrain the SCHA harmonic coefficients up to Kmax = 20. In this case, several independent LGD profiles along the trajectories of the satellites are devised to verify the accuracy of the local model. These LGD profiles are not employed in the inverse problem of determining harmonic coefficients. The results indicate that using regional harmonic basis functions, specifically spherical cap harmonic analysis (SCHA) functions, leads to a close estimation of LGD compared to the L2 JPL. The regional harmonic basis function exhibits a root mean square error (RMSE) of 3.71 × 10−4 mGal. This represents a substantial improvement over the RMSE of the L2 JPL, which is 6.36 × 10−4 mGal. Thus, it can be concluded that the use of local geo-potential coefficients obtained from SCHA is a reliable method for extracting nearly the full gravitational signal within a spherical cap region, after validation of this method. The SCHA model provides significant realistic information as it addresses the mass gain and loss across various regions in Antarctica.

Relationship between gravity change and Yangbi MS6.4 earthquake

Based on the relative and absolute gravity measurements in the southern South-North Seismic Belt since 2015, we analyzed the dynamic change of the regional gravity field and its relationship with the Yangbi MS6.4 earthquake that occurred on May 21, 2021. The results show that: 1) The regional gravity field changes are closely related to the Weixi-Qiaohou fault, which reflects the surface gravity field changes caused by the fault activity from 2015 to 2021; 2) The gravity field change related to the preparation of Yangbi earthquake has experienced the evolution process of " steady state - regional gravity anomaly - local gravity anomaly - four-quadrant distribution - large area positive anomaly - earthquake occurring in the reverse change process "; 3) The cumulative and differential change images of the gravity field show that there were significant gravity changes in the two years preceding the Yangbi earthquake, and the earthquake occurred in the high-gradient belt of gravity variation, the center of the four-quadrant, and close to the zero contour turn; 4) The dynamic evolution image of the gravity field can well reflect the precursory phenomena during the preparation for the Yangbi MS6.4 earthquake. Based on the anomaly change of mobile gravity, a certain degree of medium-term prediction was made before the Yangbi MS6.4 earthquake, especially the determination of strong earthquake location.

A new data-adaptive network design methodology based on the k-means clustering and modified ISODATA algorithm for regional gravity field modeling via spherical radial basis functions

A new data-adaptive network design methodology based on the k-means clustering and modified ISODATA algorithm for regional gravity field modeling via spherical radial basis functions

Geophysical insights on the crustal structure of Greenland's northern continental margin towards the Morris Jesup Spur

During expedition PS115/1, the German research vessel Polarstern acquired seismic refraction data along a 102-km-long profile crossing Greenland's northern continental margin and extending up to the southwestern limit of the Morris Jesup Spur. A P–wave velocity model is obtained and validated by gravity modelling. A nearby seismic reflection line provides insights on the structures within the sedimentary cover. Beneath a 2-km-thick sedimentary cover with velocities of 1.8 km/s to 3.4 km/s, an up to 1.5-km-thick layer is characterized by velocities of 4.2 km/s and is interpreted to consist of volcanic rocks. This is consistent with proposed volcanic activity on the Morris Jesup Spur and exposed volcano-sedimentary rocks of the nearby Kap Washington Group. Below the volcanic rocks, an up to 7 km-thick unit with velocities of 4.4 to 5.8 km/s is interpreted to consist of metasedimentary rocks still belonging to the deformed units of the Franklinian Basin. The seismic reflection data image a tectonic overprint of the acoustic basement and the lowermost sedimentary layers. Tectonic faults indicating the tectonic overprint do not reach to the uppermost sedimentary layers. This hints at an older fracture zone that is also observed in the velocity model and aligns well with observed anomalies in the regional gravity and magnetic fields. The seismic velocity model reveals a highly extended continental crust that shows a magmatic overprint at all crustal levels. The upper crust is 5 km thick with a velocity of 6.0 km/s. However, in three distinct zones its thickness is up to 8 km and the velocity increases to 6.3 km/s. These zones are interpreted as magmatic intrusions into the upper crust. The lower crust represents a 9-km-thick high-velocity layer (7.2 km/s) that is interpreted as magmatic underplating or lower crustal sill intrusions. Such a high-velocity lower crust is not present in models of adjacent Arctic margins.PACS: 0000, 11112000 MSC: 0000, 1111

Combination of different observation types through a multi-resolution representation of the regional gravity field using the pyramid algorithm and parameter estimation

The optimal combination of different types of gravity observations is the key to obtaining a high-resolution and high-precision regional gravity model. Current studies based on spherical radial basis functions (SRBFs) majorly consider a single-level approach for data combination. Despite the promising results reported in numerous publications, it has been suspected that the single-level model might be biased towards high-resolution measurements. Instead, a multi-resolution representation (MRR) can be applied to further take into consideration the varying spectral sensitivities of different observation techniques. In this study, we develop a new MRR scheme based on the pyramid algorithm and sequential parameter estimation. We propose strategies to solve the challenges in the practical application of the pyramid algorithm, and this study represents its first successful realization in regional gravity field modeling. The modeling results based on both simulated and real gravity data show that either the single-level approach or the MRR without pyramid algorithm is able to capture gravity information from lower resolution measurements as sufficient as our newly developed MRR algorithm. In the simulated case, the RMS error w.r.t. the validation data obtained by the MRR based on the pyramid algorithm decreases by 50% and 35%, in comparison to that of the single-level model and the MRR without pyramid algorithm, respectively. In the real case, the improvement achieved by the MRR based on the pyramid algorithm is 35% and 23% in the onshore area, and it reaches 63% and 57% in the offshore area, compared to the single-level approach and the MRR without pyramid algorithm, respectively.

A review of different mascon approaches for regional gravity field modelling since 1968

Abstract. The geodetic and geophysical literature shows an abundance of mascon approaches for modelling the gravity field of the Moon or Earth on global or regional scales. This article illustrates the differences and similarities between the methods, which are labelled as mascon approaches by their authors. Point mass mascons and planar disc mascons were developed for modelling the lunar gravity field from Doppler tracking data. These early models had to consider restrictions in observation geometry, computational resources or geographical pre-knowledge, which influenced the implementation. Mascon approaches were later adapted and applied for the analysis of GRACE observations of the Earth's gravity field, with the most recent methods based on the simple layer potential. Differences among the methods relate to the geometry of the mascon patches and to the implementation of the gradient and potential for field analysis and synthesis. Most mascon approaches provide a direct link between observation and mascon parameters – usually the surface density or the mass of an element – while some methods serve as a post-processing tool of spherical harmonic solutions. This article provides a historical overview of the different mascon approaches and sketches their properties from a theoretical perspective.

Optimization of CO2 geological storage sites based on regional stability evaluation—A case study on geological storage in tianjin, china

Carbon dioxide geological storage is one of the important means to mitigate the greenhouse effect and curb global warming. The key to carbon dioxide (CO2) geological storage is to select a suitable storage site. Using the geological analysis method and analytic hierarchy process (AHP)–fuzzy comprehensive evaluation method, combining the qualitative analysis of geological conditions with the quantitative calculation of site parameters, this study determines a site target area suitable for CO2 geological storage in Tianjin. First, the regional crustal stability of Tianjin is discussed, and the characteristics of regional gravity field anomaly, regional crustal thickness, and regional aeromagnetic characteristics are comprehensively analyzed. The site is focused on Banqiao sag, a class ⅳ tectonic unit in Bohai Bay Basin. Second, aiming at the storability, safety, and economy of the site, the expert investigation method is used to construct the target area evaluation index system, including four primary indexes and ten secondary indexes. The weight of each index is determined using the analytic hierarchy process. A two-level fuzzy comprehensive evaluation mathematical model is constructed. The suitability of CO2 geological storage in three sites (site A, site B, and site C) in Banqiao sag is evaluated. The results are as follows: the comprehensive membership of site A, site B, and site C is 0.8629, 0.3926 and 0.1750, respectively. The comprehensive membership of site A is the largest. The evaluation results show that the preferred target area of Tianjin local carbon dioxide geological storage site is located in ‘site A’ near Dazhangtuo fault in Banqiao sag, Huanghua depression, Bohai Bay Basin (with an area of about 5 km2). In this study, a suitable target area is delineated for the local CO2 geological storage site in Tianjin, which can be used as an advantageous location for CO2 geological storage. The conclusion has a positive response to the problem of CO2 emission reduction in Tianjin.