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Gravity data inversion necessitates solving large-dimensional numerical ill-posed inverse problems. The nature of these problems being ill-posed requires the implementation of a regularization scheme or any approach that integrates previous knowledge of the solution. Typically, Tikhonov-like or Laplacian-based regularizing schemes are employed to mitigate the ill-posedness. Since these types of regularization strategies promote smoothness in the quantities of interest, their approximating solutions have limitations in interpreting the sharp boundaries of source bodies. As a result, the boundaries of the retrieved source bodies appear blurred. This study proposes focusing on the representation of the source as a regularization technique. With that objective in mind, we suggest a low-dimensional representation, constructed using the alpha shape algorithm, to allow the use of non-smooth three-dimensional bodies as inversion instruments. Subsequently, the inverse problem is formulated within a Bayesian framework, and a Markov Chain Monte Carlo approach is developed for simulating from the posterior distribution associated with the proposed representation. This methodology enables the retrieval of the position, shape, and density of 3D source bodies while establishing clear geometrical boundaries and obtaining estimates of uncertainty quantification. The results are evaluated in three challenging synthetic test cases.

Greece is a country structured by land, several islands and sea. A regional gravity model of such a country demands the involvement of several types of gravity data in order to cover all its territory. In this paper, we present the development of a regional combined gravity model of Greece and its surrounding area, by integrating terrestrial, marine (shipborne and altimetry-derived gravity data) and satellite data (GOCE and GRACE data). These kinds of data, especially the terrestrial and marine ones, have passed quality and validation control since they were collected from different organizations, which means that they probably have been acquired and processed with different parameters and formulas. Following that, their integration was accomplished with the application of the least-squares collocation (LSC). Therefore, a newly combined regional gravity model of Greece and its surrounding areas has been developed. This gravity model can be valuable for regional geological and geophysical studies of Greece, since it provides homogeneously the distribution of Complete Bouguer anomaly (CBA) all over Greece, with updated gravity data and in good agreement with the initial gravity datasets that have been used.

The crustal architecture of northern Egypt, characterized by its tectonic complexity, remains poorly understood due to insufficient seismic data, limited coverage, and inaccuracies in prior gravity models. Recent advancements in satellite gravity methods, however, provide new opportunities to resolve crustal thickness variations with greater precision. In this study, we integrate GOCE gravity data, topography, sediment distributions, and seismic receiver functions to construct a high-resolution Moho depth model for the region. Using inverse and forward modeling techniques, we invert Bouguer anomalies from the GOCO06 gravity field and incorporate data from 50 seismic stations to constrain the model. Our results reveal significant variations in Moho depth, ranging from 23 to 38 km, with thinning to 23–29 km along the coastal zone and thickening to 35–38 km eastward toward the Sinai Peninsula and Red Sea. Forward modeling of three 2.5D crustal cross-sections further elucidates key tectonic features, including [specific features, e.g., fault zones, crustal thinning], which provide new constraints on the region’s tectonic evolution. This integrated approach, combining gravity modeling with seismic and geological constraints, offers a robust crustal thickness model that advances our understanding of northern Egypt’s tectonic history and structure. The findings have important implications for seismic hazard assessment and provide a foundation for future seismic data collection in the region.

The drift rate of relative gravimeters differs from time to time and from meter to meter. Furthermore, it is inefficient to estimate the drift rate by returning them frequently to the base station or stations with known gravity values during gravity survey campaigns for a large region. Unlike the conventional gravity adjustment procedure, which employs a linear drift model, we assumed that the variation of drift rate is a smooth function of lapsed time. Using this assumption, we proposed a new gravity data adjustment method by means of objective Bayesian statistical inference. Some hyper-parameters were used as trade-offs to balance the fitted residuals of gravity differences between station pairs and the smoothness of the temporal variation of the drift rate. We employed Akaike’s Bayesian information criterion (ABIC) to estimate these hyper-parameters. A comparison between results from applying the classical and the Bayesian adjustment methods to some simulated datasets showed that the new method is more robust and adaptive for solving problems caused by irregular nonlinear meter drift. The new adjustment method is capable of determining the time-varying drift rate function of any specific gravimeter and optimizing the weight constraints for every gravimeter used in a gravity survey. We also carried out an error analysis for the inverted gravity value at each station based on the marginal distribution. Finally, we used this approach to process actual gravity survey campaign data from an observation network in North China.

The paper presents 3D numerical modelling of the altimetry-derived marine gravity data with the high horizontal resolution 1 × 1 arc min. The finite volume method (FVM) as a numerical method is used to solve the altimetry–gravimetry boundary-value problem. Large-scale parallel computations result in the disturbing potential in every finite volume of the discretized 3D computational domain between an ellipsoidal approximation of the Earth’s surface and an upper boundary chosen at altitude of 200 km. Afterwards, the first, second or higher derivatives of the disturbing potential in different directions can be numerically derived using the finite differences. A crucial impact on achieved accuracy has the process of preparing the Dirichlet boundary conditions over oceans/seas. It is based on nonlinear filtering of the geopotential generated on a mean sea surface (MSS) from a GRACE/GOCE-based satellite-only global geopotential model. The paper presents different types of the altimetry-derived marine gravity data obtained on the DTU21_MSS as well as at higher altitudes of the 3D computational domain. The altimetry-derived gravity disturbances on the DTU21_MSS are compared with those from recent datasets like DTU21_GRAV or SS_v31.1. Standard deviations of the residuals are about 2.7 and 2.9 mGal, respectively. The obtained altimetry-derived gravity disturbances at higher altitudes are compared with airborne gravity data from the GRAV-D campaign in US showing accuracy about 3 mGal. In addition, the gravity disturbing gradients as the second derivatives or the third derivatives are provided with the same high resolution on the DTU21_MSS as well as at different altitudes.

We present results of repeated absolute gravity and GPS measurements, carried out at Mt. Etna volcano between 2009 and 2018. Absolute gravity measurements are rarely performed along arrays of stations on active volcanoes and, through our unprecedented dataset, we highlight the possibilities of this method to track underground mass changes over long time-scales. Analysis of the residual absolute gravity data and ground deformation reveals a cycle of gravity increase and uplift during 2009 to 2011, followed by gravity decrease and subsidence during 2011 to 2014. Data inversion points to a common mass and pressure source, lying beneath the summit area of the volcano, at depth of ~ 5 km b.s.l. The bulk volume change inferred by the inversion of the deformation data can account for only a small portion of the mass change needed to explain the correspondent gravity variations. We propose that the observed relationship between gravity and vertical deformation was mostly due to the compressibility of the magma in the inferred reservoir, which, in turn, was enhanced by the presence of exsolved gas. Overall, the gravity and deformation data we present reveal a cycle of magma recharge (2009–2011) and discharge (2011–2014) to/from the inferred storage zone. During the recharge phase only degassing occurred from the summit craters of Mt. Etna. During the following phase of discharge, the magma lost from the reservoir at ~ 5 km b.s.l. fed the exceptional phase of volcanic activity during 2011–2014, when tens of lava fountaining episodes took place.

This study presents the digitization and integration of Kazakhstan’s legacy gravimetric maps at a scale of 1:200,000 into a modern geospatial database using ArcGIS. The primary objective was to convert analog gravity data into a structured, queryable, and spatially analyzable digital format to support contemporary geoscientific applications, including geoid modeling and regional geophysical analysis. The project addresses critical gaps in national gravity coverage, particularly in underrepresented regions such as the Caspian Sea basin and the northeastern frontier, thereby enhancing the accessibility and utility of gravity data for multidisciplinary research. The methodology involved a systematic workflow: assessment and selection of gravimetric maps, raster image enhancement, georeferencing, and digitization of observation points and anomaly values. Elevation data and terrain corrections were incorporated where available, and metadata fields were populated with information on the methods and accuracy of elevation determination. Gravity anomalies were recalculated, including Bouguer anomalies (with densities of 2.67 g/cm3 and 2.30 g/cm3), normal gravity, and free-air anomalies. A unified ArcGIS geodatabase was developed, containing spatial and attribute data for all digitized surveys. The final deliverables include a 1:1,000,000-scale gravimetric map of free-air gravity anomalies for the entire territory of Kazakhstan, a comprehensive technical report, and supporting cartographic products. The project adhered to national and international geophysical mapping standards and utilized validated interpolation and error estimation techniques to ensure data quality. The validation process by the modern gravimetric surveys also confirmed the validity and reliability of the digitized historical data. This digitization effort significantly modernizes Kazakhstan’s gravimetric infrastructure, providing a robust foundation for geoid modeling, tectonic studies, and resource exploration.

Natural hydrogen is regarded as a potential resource for the global energy transition, and its accumulation is closely linked to water–rock reactions involving Fe2+ bearing minerals and effective sealing conditions. The Liaohe Basin, located on the northeastern margin of the North China Craton within a key metallogenic belt, is surrounded by sedimentary-metamorphic iron deposits and is a potential area for natural hydrogen accumulation. In this study, aeromagnetic and satellite gravity data were integrated to estimate basement depth through gravity interface inversion, followed by three-dimensional magnetic susceptibility and density inversion and structural–mineralization correlation analysis. The results reveal strong basement heterogeneity. Iron-rich anomalous bodies show clustered and belt-like to dome-like distributions, mainly along the transitional zone between deep depressions and basement uplifts. Combined density–magnetic zonation suggests that high-density, high-magnetic units may correspond to iron-rich bodies, whereas high-magnetic, low-density units likely indicate fractured and altered fluid pathways. Based on the measured results of surface hydrogen concentration, it is inferred that the high magnetic anomaly in the uplift transition zone at the edge of the depression might be the coupling area of iron-rich rock bodies and channel zones, which is the priority response area of natural hydrogen in the Liaohe Basin, China.

We present depth estimates and structural information, using aeromagnetic and gravity data, relating to the basement near the southwestern margin of the lower Benue trough between, and including, the Anambra basin and Afikpo syncline. The basement depth is calculated on the basis of the scaling spectral method, Euler deconvolution, and source parameter imaging (SPI) applied to gridded aeromagnetic data and 2D gravity modeling across the three main tectonic features (i.e., Anambra basin, Abakaliki anticlinorium, and Afikpo basin/syncline). We interpreted basement depths between 8.4 and 9.1 km within the Anambra basin, 3.1 and 9.8 km within the Abakaliki anticlinorium, and 3.8–8.5 km within the Afikpo basin/syncline. The magnetic basement depths estimated from the three methods applied on the aeromagnetic data are in good agreement with each other and that provided by the 2D gravity model which produced a reliable picture of the basement relief in the region. We also mapped and interpreted magnetic lineaments/faults in the region. Three well-defined magnetic lineaments/faults (NE–SW, ENE–WSW, and WNW–ESE) correlate very closely with the trends of geological structures of the Pan-African plate which predated the compressional folds and faults within the Cretaceous sediments and strike-slip movements during the separation of Africa and South America.

Compilation of gravity maps from Romania and Bulgaria provided geophysical data with very good regional coverage, making possible enhanced data processing and cross-border geological interpretation of gravity data on the Moesian Platform. By merging the available gravity data into a unique dataset, a Bouguer gravity anomaly map of the Moesian Platform in Romania and Bulgaria was produced. When applying filtering techniques, the residual gravity anomaly map of the Moesian Platform provided valuable information on the Intramoesian Fault segments in both Romania and Bulgaria. Large and deep geological structures of the Moesian Platform were interpreted on gravity anomalies at crustal depths based on density contrasts as compared with the neighbouring background. Aeromagnetic data processing using different filtering methods in Oasis montaj software, resulted in a series of other magnetic maps and offered new possibilities of interpreting the available data.