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SUMMARY Volgo–Uralia is the easternmost segment of the East European Craton. It accommodates the Volga–Ural petroleum province where the maturity of source rocks is tightly related to the temperature distribution in the crust. Numerous heat flow and temperature measurements have been reported for this region. However, no consistent geothermal model was presented for the Volgo–Uralian crustal block so far. In this study, we present a novel model of the Volgo–Uralian geothermal field where we aim to reconcile the reported heat flow and temperature data. The main goal of the study is to explore lateral variations of the unknown thermal parameters within Volgo–Uralia. For this purpose, we applied a Bayesian Markov Chain Monte Carlo approach where we used the known surface heat flow, surface temperature, lithosphere–asthenosphere boundary temperature and thicknesses of the Earth's lithospheric and crustal layers as input and investigated the possible lateral variations of crustal and lithospheric mantle thermal conductivities, crustal heat production and mantle heat flow. We implemented this methodology for a single-layer and multilayer crust and validated the obtained geothermal models with existing subsurface temperature measurements for the region. The results show that the Volgo–Uralian subcraton is characterized by significant lateral variations of crustal radiogenic heat production (RHP) and mantle heat flow. The variations of crustal and lithospheric mantle thermal conductivities are less pronounced. According to our model, the surface heat flow distribution is controlled mostly by crustal RHP which accounts for more than half of Volgo–Uralian surface heat flow. Validation of the models shows that single-layer and multilayer crustal models give roughly the same fit of measured and modelled temperatures. This implies that a single-layer crust with constant RHP can be considered a sufficient approximation for regional-scale geothermal modelling.

SUMMARY By combining gravity and magnetic data in a joint inversion approach, 3-D information on the crustal structure of Wilkes Land, East Antarctica, is obtained and possible geological features become evident. Both data sets are combined through a coupling method which decreases the variation of information (VI) so data misfit and model dissimilarity are minimized simultaneously. In this manner, statistically compatible inversion results are obtained. The suitability of the method is demonstrated through a synthetic example using magnetic data and pseudo-gravity. Subsequently, we apply the method to gravity residuals and magnetic data and identify matching features of high magnitude density and susceptibility. Prominent structures in NW–SE direction along the edge of the Mawson craton and at the presumed Australo-Antarctic and Indo-Antarctic terrane boundaries are enhanced. Given the structural similarity between inverted susceptibility and density, and a strong indication of a parameter relationship, we suggest a clustering approach in order to differentiate distinct groups with similar parameter properties. The spatial distribution of these clusters reveals possible geological structures that agree with previous 2-D studies and rock measurements from the Indian and Australian continents. This shows that the VI joint inversion is a convenient approach for remote regions like East Antarctica with sparse geological samples.

Antarctic subglacial properties impact geothermal heat, subglacial sedimentation, and glacial isostatic adjustment; critical parameters for predicting the ice sheet's response to warming oceans. However, the tectonic architecture of the Antarctic interior is unresolved, with results dependent on datasets or extrapolation used. Most existing deterministic suggestions are derived from qualitative observations and often presented as robust results; however, they hide possible alternative interpretations. Using information entropy as a measure of certainty, we present a robust tectonic segmentation model generated from similarity analysis of multiple geophysical and geological datasets. The use of information entropy provides us with an unbiased and transparent metric to communicate the ambiguities from the uncertainties of qualitative classifications. Information theory also allows us to test and optimise the methods and data to evaluate how choices impact the distribution of alternative output maps. We further discuss how this metric can quantify the predictive power of parameters as a function of regions with different tectonic settings.

We present the result of an integrated petrological and geophysical 3D modelling of the lithospheric mantle over the West and Central African rift system. For modelling, the integrated geophysical and petrological forward modelling software LitMod3D has been used. The initial geometry of the model is based on the Moho depth and base lithosphere of the global model WINTERC-G, and the sediment thickness from the global model Crust1.0 and the available seismic Moho depth have been used for validation. The model is fitted to satellite gravity gradients and the Bouguer anomaly calculated from the XGM2019e-2190 model. Different classes of mantle composition data have been considered and by iteratively trying to compute the best fitting between different modelled and observed signals, the final models of density, velocity and temperature distributions have been estimated. The model shows lateral transitions curved shape, extending horizontally for about 50km, between the West and Central African rift system, and the surrounding Congo craton and West African craton. More in detail, the results show the lateral and vertical variation of density, temperature and velocity in respect between the different lithospheric mantle domains. We notice the absence of a clear signature of the Saharan meta-craton, making this area more similar to the West and Central African rift system than the bordering cratons. Moreover, the modelled density profile shows a continuous depth dependent gradient under the rift system, but three steps in the depth profile under the cratons, suggest a layering of the lithospheric mantle with respect to its density gradient, which can be interpreted as metasomatism of the lower lithospheric mantle.

The Wilkes Subglacial Basin hosts potentially the largest unstable sector of the East Antarctica Ice Sheet due to the depth of the ice bed below sea level. Ice covering such basins poses a potentially high, but poorly constrained risk for future sea-level rise, as it is more vulnerable to melting by warming of the surrounding ocean. Such melting could potentially trigger mechanisms of unstable retreat. The neighbouring Transantarctic Mountains are the largest non-contractional mountain range on Earth. Traditionally, the Transantarctic Mountains are viewed as dividing the ancient East Antarctic craton from the younger West Antarctic Rift system. However, petrological samples and previous geophysical mapping suggest that the craton boundary is further west, following the western edge of the Wilkes Subglacial Basin. Subglacial geology influences geothermal heat flow and bed roughness, and therefore to better understand the past, present and possible future behaviour of the East Antarctic Ice Sheet improved understanding of the subglacial geology on which it flows, especially in the Wilkes Subglacial Basin and Transantarctic Mountains region, is important.We present a new 3D crustal model of the Wilkes Subglacial Basin and the Transantarctic Mountains based on joint inversion of airborne gravity and magnetic data using the mutual information inversion algorithm incorporated in the software JIF3D. Our model shows a large intrusive body located in the interior of the Wilkes Subglacial Basin and suggests a tectonically complex area west of the Basin, which could potentially indicate the transition zone at the margin of the Terre Adélie Craton. Geological units are inferred by clustering of inverted susceptibility and density distribution and are validated against sparse petrological samples from the Transantarctic Mountains region and along the George V Land and Terre Adélie coasts. Our inferred crustal properties model can provide crucial insight into the heterogeneity of subglacial geology in terms of thermal conductivity and crustal heat production, which could influence the geothermal heat flow in this area and therefore make the overlying ice sheet more vulnerable than commonly thought.

The Eastern Gulf of Guinea hosts several buried Cretaceous-aged oceanic fracture zones. 3D broadband seismic data acquired offshore São Tomé and Príncipe revealed a complex crustal architecture. Mapped oceanic fracture zones show low-angle reflectors that detach onto or eventually cross through the Moho boundary, overlain by strong reflectors that are interpreted as transform process related extrusive lava flows. Here, we use a high resolution shipborne free-air gravity and total field intensity magnetic data set to reassess whether previously defined seismic models of the crust are in conformity with potential field data. The study area is located offshore São Tomé with a size of c. 150x150 km. Using the software IGMAS+, we model the gravity and magnetic properties of the crust (i.e. density and susceptibility) in 3D. Long record length seismic sections plus mapped seismic horizons, which include bathymetry, sediments, upper and lower crust, are used as constraints. While the general trend of the free-air anomaly can be explained within a range of expected crustal densities, the magnetic field anomaly reflects high residuals that are predominantly oriented parallel to the transform faults. This indicates that gravity and magnetic data cannot be explained by the same simple source geometry. Therefore, we first perform sensitivity tests to isolate the source of the residual magnetic anomaly, followed by a structural analysis along the transform faults with special emphasis to the extrusive lava flows in the crustal domain. Our final model reconciles seismic horizons and potential field data and will stimulate a discussion on the architecture and evolution of transform faults and their signatures in different data sets.

We estimate the depth of the Curie isotherm and the associated heat flow for the Circum-Arctic Region using a Monte Carlo Markov Chain approach. In the first step, Curie depths are determined where heat flow measurements are available. For the depth estimates, different parameters and concepts are tested (e.g. pure conduction compared to half-space cooling) in order to assess the uncertainty underlying the depth estimates, but also of the observing point. Hereby, we rely on existing models of the Arctic lithosphere including ArcCRUST and LithoRef18. Half of the calculated Curie depth points show a low sensitivity to the choice of the parameters and models and hence can be regarded as stable, representing the thermal field of the lithosphere and not local effects. Hence, we can use these points as constraints for the second step, where we invert an aeromagnetic anomaly map for both the Curie depth and susceptibility for the Circum-Arctic Region. The new model shows that in areas where reliable constraints exist, the magnetic inversion is preferring to explain the magnetic anomalies with lateral susceptibility distribution, reflecting hereby the main geological features of the region.

Greenland’s tectonic history is complex, and the resulting lithospheric structure is, although extensively studied, not well constrained. Most models agree regarding the location of the North Atlantic Craton in South Greenland, and the most recent surface heat flow model also predicts a cold lithosphere for that area. However, the velocity anomaly from the regional tomography NAT2021 shows two additional cratonic blocks in North Greenland that are not included in geological maps and previous lithospheric models. To resolve these differences, we built a lithospheric model for Greenland that is compatible with multiple observables and focuses on data integration. In the first step, a background model is set up that uses petrological information of the mantle to model coherent seismic velocities, densities, and temperatures down to a depth of 400 km. The lithospheric model is then adjusted to reproduce the seismic velocities from NAT2021, the gravity field from satellite data and the isostatic elevation. In a second step, we jointly inverted the residual gravity field data from the lithospheric background model together with airborne magnetic data to estimate the crustal density and susceptibility structure. Both rock properties are coupled with a variation of information coupling constraint that establishes a distinct parameter relationship. To assess the compatibility of the thermal structure of our model with the most recent geothermal heat flow model for Greenland, we perform a grid search for the crustal radiogenic heat production, which would be necessary to reproduce this recent geothermal heat flow map. Finally, the results from the different steps are combined by cluster analysis and compared with petrophysical data from a newly established database of Greenland.The iterative workflow provides novel insights into the sub-ice geology of Greenland. We can model three cratonic blocks with LAB depths greater than 200 km and simultaneously fit the gravity, magnetic and elevation data in Greenland and the most recent geothermal heat flow model.

The Central Asian Orogenic Belt (CAOB) is a Paleozoic accretionary-collisional orogen located at the eastern Pangea in between the Siberian Craton to the north and the North China and Tarim cratons to the south. Several contradictory geodynamic models were proposed to explain the tectonic assemblage: oroclinal bending and strike-slip duplication of a giant intraoceanic arc or a progressive lateral accretion of linear continental and oceanic terranes towards the Siberian Craton. However, none is generally accepted. A multidisciplinary and multiscale approach integrating potential field analysis and modelling provides new insights into understanding the crustal structures beneath the CAOB.First, we present a synthesis of the previous geophysical studies, which constitute the constraints for the modelling. Second, based on global gravity and magnetic anomaly grids, the large-scale statistical analysis of their lineaments reveals the distribution of the contrasting tectonic zones. Then, the topography of the Moho is determined by 3D forward modelling of the GOCE gravity gradients, which is then integrated into 2D and 3D crustal scale models of southern and central Mongolia. A geodynamic model is derived from the resulting crustal architectures. Thus, the combination of these methods allows us to: (1) unravel the existence and distribution of suspect terranes in accretionary systems; (2) correlate the contrasting tectonic zones with the gravity and magnetic signals and the thickness of the crust, thereby revealing the inheritance of Paleozoic and Mesozoic orogenic history; and (3) determine the significance and possible origin of the major anomalies, which are related to tectonic processes such as lower crustal relamination, presence of deep-seated fault zones and sutures, or delimitation of main tectonomagmatic domains. Finally, with the case study of Central Mongolia, we demonstrate the real benefit and the significant progress, which can be achieved by using potential field analysis combined with seismic receiver function and geological analyses.

We present a novel approach for the combination of aeromagnetic and satellite data applying an equivalent dipole layer and spherical harmonic (SH) expansion of the dipoles. The method involves two steps: (1) inversion for the magnetic parameters of the equivalent dipole layer and (2) conversion of the magnetic parameters into SH coefficients. With this approach, SH analysis can be used for a regional study area, and, for example, the long-wavelength range of aeromagnetic data can be replaced with satellite data. We test our approach on the third, fourth, and fifth editions of the Magnetic Anomaly Map of Australia, which were releveled using independent aeromagnetic data sets for long-wavelength correction. The results indicate that the magnetic compilations leveled to long-haul control lines have a good agreement with the LCS-1 satellite model in the range of SH degree 40 to 110 (corresponding to half-wavelengths between 180 to 500 km), whereas the third edition of the Magnetic Anomaly Map of Australia demonstrates poor control over long- wavelengths in this spectral range. Our analysis suggests that even the carefully processed fifth edition would benefit from the replacement of long-wavelength data with satellite data.

SUMMARY Estimating the depth to magnetic bottom (DTB) from magnetic data is one of the most important and difficult potential field inversion problems. Since DTB can often be linked to the Curie isotherm depth of magnetite (∼580 °C), it could provide crucial constraints on heat flow, even in remote or inaccessible areas. Spectral methods are the most popular approach to estimate DTB, but their reliability has been challenged on many grounds. In contrast, space-domain methods have received relatively little attention, even though they might avoid some of the limitations of spectral methods. Furthermore, many DTB estimation methods are to some extent ad hoc, which makes uncertainty estimation and effective communication of the results difficult. In this work, we develop a Bayesian approach to estimate susceptibility and DTB from magnetic data. We describe the subsurface in terms of tesseroids and use a two-step inversion procedure that consists of a Monte Carlo Markov Chain hyperparameter optimization and a linearized inversion. This way, the uncertainties due to unknown hyperparameter are rigorously propagated to the final maps of susceptibility and DTB. Additionally, pointwise constraints based on heat flow measurements can be easily included into the inversion. Synthetic tests are used to determine the accuracy and reliability of the new algorithm. We find that heat flow constraints are necessary to achieve reliable results, although already a small number of points is sufficient. Finally, we apply the algorithm to the Australian continent and demonstrate applicability to real data.

The Transantarctic Mountains (TAM) separate the warmer lithosphere of the Cretaceous-Tertiary West Antarctic rift system and the colder and older provinces of East Antarctica. Low velocity zones beneath the TAM imaged in recent seismological studies have been interpreted as warm low-density mantle material, suggesting a strong contribution of thermal support to the uplift of the TAM. We present new Curie Point Depth (CPD) and geothermal heat flow (GHF) maps of the northern TAM and adjacent Wilkes Subglacial Basin (WSB) based exclusively on high resolution magnetic airborne measurements. We find shallow CPD and high GHF beneath the northern TAM, reinforcing the hypothesis of thermal support of the topography of the mountain range. Additionally, this study demonstrates, that limiting spectral analysis to areas with a high density of aeromagnetic measurements increases the resolution of CPD estimates revealing localized shallow CPD and associated high heat flow in the Central Basin of the WSB and the Rennick Graben. Across the study area the CPD ranges from 15 to 35 km and the GHF values range from 30 to 110 mW/m2. The recovered CPD range is compatible with recent Moho depth estimates, as the CPD predominantly lies within the crust, rather than in the magnetite-poor mantle. GHF estimates, based on the CPD estimates, show a good agreement to sparse in situ GHF measurements and the location of active volcanoes. Comparison to existing continent-wide GHF estimates shows strong differences from magnetically-derived heat flow estimates, while seismologically-derived heat flow estimates show the best agreement to our results.

Inverting LRI data from GRACE-FO (NASA/GFZ) is challenging from multiple points of view. To benefit from the laser instrument, that provides a higher precision compared with the KBR ranging, the global basis functions such as spherical harmonics may not provide the best service for exploiting data the full potential. Because the regional analyses use surface elements such as mascons, we present two alternatives in terms of the spherical triangles that may also be used as target elements for the inversion. Since the spherical trigonometry can be used, a relatively easy manipulation and remeshing is possible if appropriate indexing is used. Furthermore, such grids are also used in the solid-Earth models models like LITHO1.0 and WINTER-C, and, thus they may provide an easy link from satellite gravimetry to solid-Earth disciplines. We show the properties of both grids, how to properly index them and how to reduce SST data for the continental part of the signal with the monthly solutions.

The AlpArray Gravity Research Group (AAGRG), as part of the European AlpArray program, focuses on the compilation of a homogeneous surface-based gravity data set across the Alpine area. In 2017 10 European countries in the Alpine realm agreed to contribute with gravity data for a new compilation of the Alpine gravity field in an area spanning from 2 to 23∘ E and from 41 to 51∘ N. This compilation relies on existing national gravity databases and, for the Ligurian and the Adriatic seas, on shipborne data of the Service Hydrographique et Océanographique de la Marine and of the Bureau Gravimétrique International. Furthermore, for the Ivrea zone in the Western Alps, recently acquired data were added to the database. This first pan-Alpine gravity data map is homogeneous regarding input data sets, applied methods and all corrections, as well as reference frames. Here, the AAGRG presents the data set of the recalculated gravity fields on a 4 km × 4 km grid for public release and a 2 km × 2 km grid for special request. The final products also include calculated values for mass and bathymetry corrections of the measured gravity at each grid point, as well as height. This allows users to use later customized densities for their own calculations of mass corrections. Correction densities used are 2670 kg m−3 for landmasses, 1030 kg m−3 for water masses above the ellipsoid and −1640 kg m−3 for those below the ellipsoid and 1000 kg m−3 for lake water masses. The correction radius was set to the Hayford zone O2 (167 km). The new Bouguer anomaly is station completed (CBA) and compiled according to the most modern criteria and reference frames (both positioning and gravity), including atmospheric corrections. Special emphasis was put on the gravity effect of the numerous lakes in the study area, which can have an effect of up to 5 mGal for gravity stations located at shorelines with steep slopes, e.g., for the rather deep reservoirs in the Alps. The results of an error statistic based on cross validations and/or “interpolation residuals” are provided for the entire database. As an example, the interpolation residuals of the Austrian data set range between about −8 and +8 mGal and the cross-validation residuals between −14 and +10 mGal; standard deviations are well below 1 mGal. The accuracy of the newly compiled gravity database is close to ±5 mGal for most areas. A first interpretation of the new map shows that the resolution of the gravity anomalies is suited for applications ranging from intra-crustal- to crustal-scale modeling to interdisciplinary studies on the regional and continental scales, as well as applications as joint inversion with other data sets. The data are published with the DOI https://doi.org/10.5880/fidgeo.2020.045 (Zahorec et al., 2021) via GFZ Data Services., Earth System Science Data, 13 (5), ISSN:1866-3516, ISSN:1866-3508

This chapter describes the application and coverage of gravity and magnetic data for Antarctica with emphasis on airborne and satellite models. Low resolution satellite data help to fill gaps between high-resolution airborne data. Satellite gravity data are best used to study broad-scale lithospheric architecture while airborne data, especially magnetic data, provide finer detail. We review examples of gravity and magnetic analysis and describe the possibilities and pitfalls for estimating the properties of the lithosphere as it relates to the mantle. This is followed by a discussion on geothermal heat flow and possible ways to combine different geophysical and petrological models for a better understanding of the Antarctic mantle.

SUMMARY We present a novel approach for linearized gravity inversion to estimate the Moho depth, which allows the use of any gravitational component instead of the vertical gravity component only. The inverse problem is solved with the Gauss–Newton algorithm and the gravitational field of the undulating Moho depth is calculated with tesseroids. Hereby, the density contrast can be laterally variable by using information from seismological regionalization. Our approach is illustrated with a synthetic example, which we use to explore different regularization parameters. The vertical gravity gradient gzz provides the most reasonable results with appropriate parameters. As a case example, we invert for the Moho depth of the Amazonian Craton and its surroundings. The results are constrained by estimates from active seismic measurements. Our new Moho depth model correlates to tectonic domains and is in agreement with previous models. The estimated density contrasts of the tectonic domains agree well with the lithospheric architecture and show with 300–450 kg m–3 lower density contrasts for continental domains, whereas the oceans reveal a density contrast of 450–500 kg m–3. The wider range of estimated density contrast for the continent reflects uncertainties in Precambrian Fold Belts that arise from its small gravity signal. Our results demonstrate that a variable density contrast at the Moho depth is a valuable enhancement for gravity inversion.

Sub-ice-bathymetry is an important boundary condition when modelling the evolution of ice shelves and ice sheets. Radar sounding is a proven method to reveal the sub-ice-topography beneath grounded ice. However, it fails to image the bathymetry beneath the floating ice shelves due to the strong radar reflectivity of sea water. As an alternative, the inversion of gravity measurements has been used increasingly frequently in recent years. To overcome the ambiguity of inverse modelling, this method benefits from independent depth constraints derived from direct measurements distributed throughout the model area, such as by active seismic, hydroacoustic, and radar methods.Here, we present a novel geostatistical approach to gravity inversion and compare it to the classical and more commonly used FFT approach. Instead of only fitting individual points, we also include the spatial continuity of the sub-ice morphology. To do so, we calculate a variogram that fits the available depth measurements and derive a covariance matrix from it. The covariance matrix and an initial bathymetry model obtained by kriging together describe an a-priori probability density. For the inversion, the model bathymetry is related to the measured gravity using a quasi-Newton method, for which the derived probability density serves as the inversion’s regularization term. We successfully apply the algorithm to airborne gravity data across the Ekström ice shelf (Antarctica) and compare our results with those of previous studies based on the classical approach. The simplified addition of constraints both for the geometry and the density structure in our approach proves to be advantageous.

In this contribution, we present a global estimate of crustal thickness with emphasis to cratons. In an inverse scheme, satellite gravity gradient data are inverted for the Moho depth, exploiting laterally variable density contrasts based on seismic tomography. Our results are constrained by an active source seismic data base, as well as a tectonic regionalization map, derived from seismic tomography. For the global analysis, we implement a moving window approach to perform the gravity inversion, followed by interpolating the estimated density contrasts of common tectonic units with a flood-fill algorithm. The estimated Moho depth and density contrasts are especially interesting for the cratons of the Earth. Our results reveal a surprising variability of patterns with average Moho depth between 32-42 km, reflecting an individual tectonic history of each craton. Statistical patterns of Moho depth and density contrasts are discussed for the individual cratons and linked to their stabilization age. For example, Australia shows the lowest average Moho depth (32.7 km), indicating early stabilization in the Archean and removal of a dense lower protocrust. This observation matches well with receiver function studies. The globally inverted Moho depth is validated by gridded seismic Moho depth information, which shows that for many cratons the inverted Moho depth is within expected uncertainties of the seismic Moho depth. In addition, the formerly connected cratons of South America and Africa are analyzed and discussed in a Gondwana reconstruction. Here, the once-connected West African and Amazonian Cratons have a shallow Moho depth, indicating that only little tectonic activity occurred during the Phanerozoic. The tectonically-linked Congo and Sao Francisco Cratons have intermediate Moho depths, with the Congo Craton having a slightly shallower Moho depth. This could reflect dynamic support of the upper mantle on the African side.

We present results of cluster analysis and geophysical modelling of the West and Central African rift system, where we integrate seismological and satellite data. For a description of lithospheric domains, two different methods based on seismic tomography and satellite gravity data have been used. First, the terracing method using the shape index, has been applied to the gravity field in order to enhance the signal of the large-scale tectonic units. In addition, the K-means cluster method (which is an unsupervised machine learning algorithm) has been applied to a seismic tomography model over the area.Both models are compared and interpreted towards similarities and differences. The preliminary analysis based on K-means clustering of seismic tomography shows that the West and Central African rift system and its surroundings can be divided into at least three clearly distinct tectonic domains: The Northern part of the Congo craton, the Eastern part of the West African craton and an area in between. In addition, the preliminary analysis of the terracing of satellite gravity data, confirms the location of both the Congo and the West African craton, but also splits the area in between into two known tectonic units, the Southern part of the Saharan meta-craton and the West and Central African rift system in the center.The cluster analysis is also pointing to differences at crustal and upper mantle level and is the first step towards the evolution of a lithospheric scale model. In the model, we integrate our tectonic domain analysis with the existing seismic Moho depths estimate and other information.

Geothermal heat flux (GHF), coupled with subglacial topography and hydrology, influences the flow of the overlying Antarctic ice sheet. GHF is related to crustal and lithospheric structure and composition and tectonothermal evolution, and is also modulated by subglacial sedimentary basins and bedrock morphology. Despite its importance for both solid earth and cryosphere studies, our knowledge of Antarctic GHF heterogeneity remains limited compared to other continents- especially at regional scale. This is due to the paucity of direct measurements and the spatial gap wrt much larger scale geophysical proxies for GHF, based on continental-scale magnetic and seismological predictions that also differ considerably from each other in several regions. To reduce this major knowledge gap, the international community is increasingly active in analysing geophysical, geological and glaciological datasets to help constrain GHF (e.g. Burton-Johnson et al., SCAR-SERCE White Paper, 2020). Here we focus on 4D Antarctica- an ESA project that aims to help link bedrock, crust, lithosphere and GHF studies, by analysing recent airborne and satellite-derived potential field datasets. We present our recent aeromagnetic, aerogravity and satellite data compilations for 5 study regions, including the Amundsen Sea Embayment sector of the West Antarctic Ice Sheet (e.g. Dziadek et al., 2021- Communications Earth & Environment) and the Wilkes Subglacial Basin (WSB), the Recovery glacier catchment, the South Pole and Gamburtsev Subglacial Mountains and East Antarctic Rift region. We apply Curie Depth Point (CDP) estimation on existing aeromagnetic datasets and compilations in our study regions conformed with SWARM satellite magnetic data (Ebbing et al., 2021- Scientific Reports). We tested the application of different methods, including the centroid (e.g. Martos et al., 2017, GRL) and Bayesian inversion approaches of Curie depth and uncertainty (e.g. Mather and Fullea, 2019- Solid Earth) and defractal and geostatistical methods (e.g. Carrillo-de la Cruz et al., 2021- Geothermics). We then compare our CDP results with crust and lithosphere thickness and interpretations of crustal and lithospheric setting. Using our new aeromagnetic interpretations we define Precambrian and early Paleozoic subglacial basement in East Antarctica that is mostly concealed beneath Phanerozoic sedimentary basins and ice sheet cover. This enables us to discuss whether different basement provinces differ in terms of CDP estimates (as expected), or if these are either not or only partially resolved. A particularly informative case is the WSB. Here our magnetic assessments of GHF heterogeneity for the Terre Adelie Craton, Wilkes Terrane and Ross Orogen can be indirectly tested by exploiting independent geological and geophysical information derived from their Australians correlatives, namely the Gawler and Curnamona cratons and the Delamerian Orogen. Our Curie depth estimates yield geologically reasonable thermal boundary conditions required to initialise new thermal modelling efforts in several study areas. However, developing 3D models of crust and lithosphere thickness and intracrustal composition (as a proxy for the ranges of radiogenic heat production and thermal conductivity) with reasonably detailed crustal architecture, derived from both potential field and seismological datasets is a key next step to constrain Antarctic geothermal heat flux heterogeneity at higher-resolution ice stream scale.

Conjugate margins along mature oceans indicate two end-member types of rifted margins, distinguished by their crustal architecture, e.g. the Iberia-Newfoundland and Central South Atlantic. Numerical simulations and analogue models show that these types could be explained by rheology, state of stress (depth depended) and role of magmatism (magma assisted). The Red Sea is a young rift, offering the opportunity to study early break-up conditions and to relate them to the architecture and the type of passive margins. The morphology of the Red Sea indicates variability and dissimilarities between its southern and northern regions, nevertheless, the lithospheric structure of the rift remains elusive, mainly due to lack of high-resolution direct geophysical measurements, e.g. seismic profiles.In this study, we explore the deep architecture of the Red Sea rift using geophysical data, in particular gravity and magnetic data, and constraints from seismic interpretations, receiver functions and tomographic models. We present a 3D structural and density model for the Red Sea, including the African and Arabian shoulders down to 120 km depth. The model includes four main sections: sediments, crystalline crust (continental and oceanic), lithospheric mantle (including a thermal gradient) and a uniform asthenosphere. In order to test different scenarios, we evaluate combinations of (1) exhumed continental mantle lithosphere (Type I margin) versus wide/ultrawide continental crust (Type II margin), and, (2) limited versus extended distribution of oceanic crust. The 3D gravity model favors Type II architecture and limited oceanic crust in the southern-central parts of the Red Sea rift. In the northern parts, the model cannot distinguish between the pre and post break-up stages.

Volgo–Uralia is a Neoarchaean easternmost part of the East European craton. Recent seismic studies of the Volgo–Uralian region provided new insights into the crustal structure of this area. In this study, we combine satellite gravity and seismic data in a common workflow to perform a complex study of Volgo–Uralian crustal structure, which is useful for further basin analysis of the area. In this light, a new crustal model of the Volgo–Uralian subcraton is presented from a step-wise approach: (1) inverse gravity modelling followed by (2) 3D forward gravity modelling. First, inversion of the satellite gravity gradient data was applied to determine the Moho depth for the area. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region, and the model is constrained by the available active seismic data. The Moho discontinuity obtained from the gravity inversion was consequently modified and complemented in order to define a complete 3D crustal model by adding information on the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modelling, where both seismic and gravity constraints were respected. The obtained model shows crustal thickness variations from 32 to more than 55 km in certain areas. The thinnest crust with a thickness below 40 km is found beneath the Precaspian basin, which is covered by a thick sedimentary layer. The thickest crust is located underneath the Ural Mountains as well as in the centre of the Volgo–Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, initial forward gravity modelling has shown a gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and the forward calculated gravity field in the central area of the Volgo–Uralian subcraton. This misfit was interpreted and modelled as a high-density lower crust, which possibly represents underplated material. Our preferred crustal model of the Volgo–Uralian subcraton respects the gravity and seismic constraints and reflects the main geological features of the region with Moho thickening in the cratons and under the Ural Mountains and thinning along the Palaeoproterozoic rifts, Precaspian sedimentary basin, and Pre-Urals foredeep.

We compile and analyze all available geothermal heat flow measurements collected in and around Greenland into a new database of 419 sites and generate an accompanying spatial map. This database includes 290 sites previously reported by the International Heat Flow Commission (IHFC), for which we now standardize measurement and metadata quality. This database also includes 129 new sites, which have not been previously reported by the IHFC. These new sites consist of 88 offshore measurements and 41 onshore measurements, of which 24 are subglacial. We employ machine learning to synthesize these in situ measurements into a gridded geothermal heat flow model that is consistent across both continental and marine areas in and around Greenland. This model has a native horizontal resolution of 55 km. In comparison to five existing Greenland geothermal heat flow models, our model has the lowest mean geothermal heat flow for Greenland onshore areas. Our modeled heat flow in central North Greenland is highly sensitive to whether the NGRIP (North GReenland Ice core Project) elevated heat flow anomaly is included in the training dataset. Our model's most distinctive spatial feature is pronounced low geothermal heat flow (

Volgo-Uralia is a Neoarchean easternmost part of the East European craton. Recent seismic studies of the Volgo-Uralian region provided new insights into the crustal structure of this area. In this study, we combine satellite gravity and seismic data in a common workflow to perform a complex study of Volgo-Uralian crustal structure which is useful for further basin analysis of the area. In this light, a new crustal model of the Volgo-Uralian subcraton is presented from a step-wise approach: (1) inverse gravity modeling followed by (2) 3D forward gravity modeling. First, inversion of satellite gravity gradient data was applied to determine the Moho depth for the area. Density contrasts between crust and mantle were varied laterally according to the tectonic units present in the region, and the model is constrained by the available active seismic data. The Moho discontinuity obtained from the gravity inversion was consequently modified and complemented in order to define a complete 3D crustal model by adding information on the sedimentary cover, upper crust, lower crust, and lithospheric mantle layers in the process of forward gravity modeling where both seismic and gravity constraints were respected. The obtained model shows crustal thickness variations from 32 to more than 55 km in certain areas. The thinnest crust with a thickness below 40 km is found beneath the Pericaspian basin, which is covered by a thick sedimentary layer. The thickest crust is located underneath the Ural Mountains as well as in the center of the Volga-Uralian subcraton. In both areas the crustal thickness exceeds 50 km. At the same time, initial forward gravity modeling has shown a gravity misfit of ca. 95 mGal between the measured Bouguer gravity anomaly and the forward calculated gravity field in the central area of the Volga-Uralian subcraton. This misfit was interpreted and modeled as a high-density lower crust which possibly represents underplated material. Our preferred crustal model of the Volga-Uralian subcraton respects the gravity and seismic constraints and reflects the main geological features of the region with Moho thickening in the cratons and under the Ural Mountains and thinning along the Paleoproterozoic rifts, Pericaspian sedimentary basin, and Pre-Urals foredeep.

Airborne gravity gradiometry measures several gravity gradient components unlike conventional gravimetry taking only the vertical gravity component into account. However, processing of multicomponent airborne gravity gradient (AGG) data without corrupting their internal consistency is often challenging. Therefore, we have developed an equivalent source technique to tackle this challenge. With a combination of Gauss-fast Fourier transform and the Landweber iteration, we have developed an efficient way to compute equivalent sources for AGG data. This method can handle two components simultaneously. We first examined its viability by applying this approach to a synthetic example. Afterward, we applied our method to real AGG data collected in the area of Karasjok, Norway. Our result is almost the same as the results that meet the industry standard but with great efficiency.

A 3D crustal density model for Egypt was compiled. It is constrained by available deep seismic refraction, receiver functions analysis, borehole, and geological data. In Egypt, seismic data are sparsely and irregularly distributed. Consequently, we developed the crustal thickness model by integrating seismic and gravity data. Satellite gravity data was inverted to build an initial model, which was followed by a detailed 3D forward gravity modelling. The initial crustal thickness is determined by applying seismically constrained non-linear inversion, based on the modified Bott's method and Tikhonov regularization assuming spherical Earth approximation. Moreover, the gravity inversion-based Moho depth estimates are in good agreement with results of seismic studies and are exploited for the 3D forward modelling. Crustal thicknesses range from 25 to 30 km along the rifted margins of the Red Sea, which thin toward the Mediterranean Sea. Thicknesses in southern Egypt reach values between 35 and 40 km. A maximum crustal thickness of 45 km is found in the southwestern part of Egypt. Within the Sinai Peninsula, the thickness varies from the shallow southern edge (∼ 31 km) and increases toward the North (∼ 36 km). Our model revealed a thick lower crust beneath the southern part of Egypt, which can be associated with crustal modification that occurred during the collision of East Gondwana and the Saharan Metacraton along the Keraf suture zone during the final assembly of Gondwana in the Neoproterozoic. Finally, the isostatic implications of the differences between the seismic and gravity-derived Mohos are thoroughly discussed. In conclusion, the developed 3D crustal thickness model provides high-resolution Moho depth estimates that closely resembles the major geological and tectonic features. Also, the existing correlation between the topography, Bouguer anomalies, and Moho depths indicates that the investigated area is close to its isostatic equilibrium.

Introduction: The morphology of impact basins formed during the first 700 Ma after the Moon-forming event (e.g., [1-2]) is affected by the impactor's size and velocity, and the thermal state of the crust and upper mantle, which is related to the cooling history of the Moon (e.g., [3-5]). Due to alteration and erosion of structural surface features by subsequent impact flux, the size of given basins cannot be determined unequivocally. High resolution Bouguer gravity data from the Gravity Recovery and Interior Laboratory (GRAIL) mission [6-7] show a strong positive anomaly in the center, surrounded by a gravity low for impact basins located at the lunar farside. The relationship between the size of these gravity patterns and basin diameter may allow for estimating the impactor's size and thermal state of the Moon at the time of impact (e.g., [3, 5, 8]). Previous studies (e.g., [7, 9]) showed that basin formation processes are followed by isostatic adjustment and cooling processes. As a result, basin structures undergo relaxation processes, coupled with modifications in gravity signature. Therefore, the direct comparison of GRAIL data with gravity data from numerical models of basin formation may be questionable. We summarize results of our systematic numerical modeling study on the influence of the thermal state and impactor size on basin formation processes [5]. Using observed gravity data as constraints for our numerical basin formation models allows for estimating the thermal conditions and the size of the impactor at the time of impact for observable basin structures [5]. Based on this work we now aim at considering isostatic compensation processes and show preliminary results on how to investigate the problem. Methods: In our previous work, we account for different impactor sizes, crustal thicknesses, and thermal states of the Moon. Different depth-temperature profiles represent the lunar thermal evolution at 4.5 Ga ("warm"), 4.1 Ga ("intermediate") and 3.8 Ga ("cold"), which correspond to approximate basin ages. We correlate modeled Bouguer gravity from our models of basin formation with observed gravity signatures of 16 lunar farside basins. To evaluate the state of isostatic equilibrium in our best-fit models, we use as a first attempt the isostatic model assuming the Airy concept. Here, different topographic heights are accommodated by changes in crustal thickness. With this approach, we can estimate the location of the crust-mantle boundary for our best-fit models to evaluate the state of isostatic compensation. Results: Figure 1 shows the transient crater (Dt) , the diameter of the largest crustal thickness (DLCT), and the diameter of the Bouguer anomaly from basin formation models (DBA-mod) as a function of impactor size (Limp). Apparently, Dt, DLCT, DBA-mod depend on the target's thermal state (indicated by the colors). For impactors larger than 40 km in diameter the thermal state affects the size of the Bouguer anomaly [5]. As examples, we discuss here the best-fit models for Korolev crater and Orientale basin: Figure 2 shows the model for the Korolev crater, assuming an impactor size of 50 km and a temperature profile at ca. 4.1 Ga. In Figure 3, the best-fit model for the Orientale basin formed by an impactor of 80 km in a cold lunar environment (3.8 Ga) is shown. The models are fitted to the observed gravity signal (Fig. 2a, 3a, dashed line). The green line (Fig. 2a, 3a) corresponds to the gravity anomaly derived from the basin formation model assuming constant densities in crust (ρc) and mantle (ρm) (Fig. 2b, 3b, left panel). The latter distinctly deviates from the density distribution in our basin formation models (Fig. 2b, 3b); however, we consider the usage of constant densities as a simple estimate of how Bouguer anomalies of our models may look like after cooling. The gravity signal (Fig. 2a, 3a; black line) based on the inhomogeneous density distribution due to the thermal expansion right after impact shows a much lower amplitude and a "plateau" in the basin center. A closer look to the temperature field (Fig. 2c, 3c) reveals that the "plateau" is directly related to the hot area of the temperature field. In order to assess the isostatic equilibrium of the basin formation models with the inhomogeneous density distribution, we determine the position of the crust-mantle-boundary according to the Airy concept (Fig. 2b, 3b, orange line). Our preliminary results show that the Korolev impact structure is almost in isostatic equilibrium, whereas large changes in the crust-mantle-boundary have to be assumed for the larger Orientale basin. Conclusion: By assuming constant densities in the target, we are able to fit the observed and modeled gravity signatures. But this method of gravity fitting is questionable because the observed gravity data are based on the current subsurface density field, whereas the basin formation models show the density field directly after impact. We expect that cooling of impact structures between the last 4.4 Ga and 3.8 Ga directly affects the density distribution concomitant with isostatic compensation processes changing the position of the crust-mantle-boundary. Thus, the position of the gravity signal will also change. Acknowledgements: We gratefully thank the developers of iSALE and the pySALEPlot tool. This work is funded by the Deutsche Forschungsgemeinschaft (Project-ID 263649064-TRR 170). References: [1] Wilhelms, D.E. (1987) USGS Professional Paper 1348. [2] Morbidelli, A. et al. (2018) Icarus, 305, 262-276. [3] Miljkovic, K. et al. (2016) J. Geophys. Res. Planets, 121, 1695-1712. [4] Potter, R.W.K. et al. (2015) GSA Special Papers, 518, SPE518-506. [5] Lompa, T. et al. (2021) LPSC, Abstract #1254. [6] Zuber, M.T. et al. (2013) Science, 339, 668-671. [7] Melosh, H.J. et al., (2013) Science, 340, 1552-1555. [8] Neumann, G.A., et al. (2015) Sci. Adv., 1, e1500852. [9] Freed, A.M. et al. (2014) J. Geophys. Res. Planets, 119.

We present a machine learning approach to statistically derive geothermal heat flow (GHF) for Antarctica. The adopted approach estimates GHF from multiple geophysical and geological data sets, assuming that GHF is substantially related to the geodynamic setting of the plates. We apply a Gradient Boosted Regression Tree algorithm to find an optimal prediction model relating GHF to the observables. The geophysical and geological features are primarily global data sets, which are often unreliable in polar regions due to limited data coverage. Quality and reliability of the data sets are reviewed and discussed in line with the estimated GHF model. Predictions for Australia, where an extensive database of GHF measurements exists, demonstrate the validity of the approach. In Antarctica, only a sparse number of direct GHF measurements are available. Therefore, we explore the use of regional data sets of Antarctica and its tectonic Gondwana neighbors to refine the predictions. With this, we demonstrate the need for adding reliable data to the machine learning approach. Finally, we present a new geothermal heat flow map, which exhibits intermediate values compared to previous models, ranging from 35 to 156 mW/m2, and visible connections to the conjugate margins in Australia, Africa, and India., Plain Language Summary: The heat energy transferred from the Earth's interior to the surface (geothermal heat flow) can substantially affect the dynamics of an overlying ice sheet. It can lead to melting at the base and hence, decouple the ice sheet from the bedrock. In Antarctica, this parameter is poorly constrained, and only a sparse number of thermal gradient measurements exist. Indirect methods, therefore, try to estimate the continental Antarctic heat flow. Here, we use a machine learning approach to combine multiple information on geology, tectonic setting, and heat flow measurements from all continents to predict Antarctic values. We further show that using reliable data is crucial for the resulting prediction and a mindful choice of features is recommendable. The final result exhibits values within the range of previously proposed heat flow maps and shows local similarities to the continents once connected to East Antarctica within the supercontinent Gondwana. We suggest a minimum and maximum heat flow map, which can be used as input for ice sheet modeling and sea level rise predictions., Key Points: A new geothermal heat flow map of Antarctica is established by adopting a machine learning approach. Input features include both global and regional geological and tectonic information, and heat flow observations. A Gondwana reconstruction shows connections of heat flow at the conjugate margins of East Antarctica., Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659

The Wilkes Subglacial Basin in East Antarctica hosts one of the largest marine-based and hence potentially more unstable sectors of the East Antarctic Ice Sheet (EAIS). Predicting the past, present and future behaviour of this key sector of the EAIS requires that we also improve our understanding of the lithospheric cradle on which it flows. This is particularly important in order to quantify geothermal heat flux heterogeneity in the region. The WSB stretches for almost 1600 km from the Southern Ocean towards South Pole. Like many intracratonic basins, it is a long-lived geological feature, which originated and evolved in different tectonic settings. A wide basin formed in the WSB in a distal back arc basin setting, likely in response to a retreating West Antarctic Paleo-Pacific active margin from Permo-Triassic times. Jurassic extension then led to the emplacement of part of a huge flood basalt province that extends from South Africa to Australia. The region was then affected by relatively minor upper crustal Mesozoic to Cenozoic(?) extension and transtension, producing narrow graben-like features that were glacially overdeepened, and presently steer enhanced glacial flow of the Matusevich, Cook and Ninnis glaciers.Here we present the results of our enhanced geophysical imaging and modelling in the WSB region performed within the 4D Antarctica project of ESA, which aims to help quantify the spatial variability in subglacial Antarctic geothermal heat flux (GHF), one of the least well constrained parameters of the entire continent.We exploit a combination of airborne radar and aeromagnetic data compilations and crustal and lithosphere thickness estimates from both satellite and airborne gravity and independent passive seismic constraints to develop new geophysical models for the region. To help constrain the starting models, including depth to basement beneath the Permian to Jurassic cover rocks, we applied a variety of depth to magnetic and gravity source estimation approaches from both line and gridded datasets. Given the huge differences between recent satellite gravity estimates of crustal thickness (Pappa et al., 2019, JGR) and sparse seismological constraints, we examine different scenarios for isostatic compensation of Rock Equivalent Topography and intracrustal loads, as a function of variable effective elastic thickness (Te) across the WSB and its flanks. Our models reveal a major lithospheric-scale boundary along the northeastern margin of the WSB, separating the Ross Orogen from a cryptic and composite Precambrian Wilkes Terrane. At the onset of enhanced flow for the central Cook ice stream, we image a Precambrian basement high with a felsic bulk composition. We suggest based on the similarity in potential field signatures that it represents late Paleoproterozoic to Mesoproterozoic igneous basement as exposed in South Australia, where it also associated with high GHF (80-120 mW/m2), primarily caused by anomalously radiogenic granitoids.We hypothesise that the differences in basement depth and metasediment/sediment thickness, coupled with differences in intracrustal heat production give rise to significantly greater heterogeneity in GHF beneath different sectors of the WSB than previously recognised. To help quantify such heterogeneity we develop a suite of new probabilistic thermal models for the study region.

We established a new Geothermal Heat Flow (GHF) model for Antarctica by using a machine learning approach. GHF is substantially related to the geodynamic setting of the plates, and global geophysical and geological data sets can provide information for remote regions like Antarctica, where only sparse direct measurements exist. We applied a Gradient Boosted Regression Tree algorithm in order to build an optimal prediction model relating GHF to the observables.Employed data sets are reviewed for their reliability and quality in polar regions and we emphasize the need for adding reasonable data to the algorithm. The validity of our approach is indicated by predictions for Australia, where an extensive database of GHF measurements exists. Our new estimated GHF map exhibits rather moderate values compared to previous models, ranging from 35 to 156 mWm-2, and shows visible connections to the conjugate margins in Australia, Africa, and India.Such estimates on the geothermal structure of Antarctica are for example needed for studies on ice sheet modeling. The internal thermal structure and the mass balance of the modeled Antarctic ice sheet (AIS) are significantly affected by the prescribed GHF distribution. Applying a wide range of possible GHF maps within estimated uncertainties to ice-sheet-shelf set-ups, the influence of GHF on the modeled AIS response to a variety of climate scenarios is quantified.

We explore the lithosphere structure of the Red Sea using gravity and magnetic data.We re-processed marine data form past surveys conducted during the 70’s and the 80’s, available at the NGDC database. By correcting the magnetic measurements according to the DGRF (definitive magnetic reference field), leveling and replacing the long wavelengths with satellite data (LCS1 model) we managed to generate a consistent magnetic anomaly map for the entire length of the Red Sea that is composed of 10 different surveys and contain overs 100,000 measuring points. The magnetic anomaly map highlights structural differences between the southern, central and northern parts of the Red Sea.Using forward gravity approach, constrains from seismic, wells and petrophysical data, and by integrating insights from magnetic analysis, we define the lithospheric model of the Red Sea to address key questions regarding rifting, sea floor spreading and transition processes. For example, the southern parts of the Red Sea are characterized by shallow and wide asthenosphere upwelling, while in the axial trough lithosphere is thin with thicknesses of less than 15 km. The lithosphere thickness increase asymmetrically towards the rift shoulders. In general, the lithosphere is thicker on the eastern sides than on the western sides. In the central parts of the Red Sea, the lithosphere structure is not significantly different from the southern parts, however, asthenosphere upwelling is slightly narrower. In northern parts of the Red Sea asthenosphere upwelling significantly narrows and focused mainly beneath the axial trough and the lithosphere is thicker. This architecture reflects the currently transition from continental rifting (in the north) to oceanic seafloor spreading (in the south) in the Red Sea.

The lithospheric structure of Greenland is still poorly known due to its thick ice sheet, the sparseness of seismological stations, and the limitation of geological outcrops near coastal areas. As only a few geothermal measurements are available for Greenland, one must rely on geophysical models. Such models of Moho and LAB depths and sub-ice geothermal heat-flow vary largely.Our approach is to model the lithospheric architecture by geophysical-petrological modelling with LitMod3D. The model is built to reproduce gravity observations, the observed elevation with isostasy assumptions and the velocities from a tomography model. Furthermore, we adjust the thermal parameters and the temperature structure of the model to agree with different geothermal heat flow models. We use three different heat flow models, one from machine learning, one from a spectral analysis of magnetic data and another one which is compiled from a similarity study with tomography data.For the latter, a new shear wave tomography model of Greenland is used. Vs-depth profiles from Greenland are compared with velocity profiles from the US Array, where a statistical link between Vs profiles and surface heat flow has been established. A similarity function determines the most similar areas in the U.S. and assigns the mean heat-flow from these areas to the corresponding area in Greenland.The geothermal heat flow models will be further used to discuss the influence on ice sheet dynamics by comparison to friction heat and viscous heat dissipation from surface meltwater.

The thickness of the magnetized layer in the crust (or lithosphere) holds valuable information about the thermal state and composition of the lithosphere. Commonly, maps of magnetic thickness are estimated by spectral methods that are applied to individual data windows of the measured magnetic field strength. In each window, the measured power spectrum is fit by a theoretical function which depends on the average magnetic thickness in the window and a ‘fractal’ parameter describing the spatial roughness of the magnetic sources. The limitations of the spectral approach have long been recognized and magnetic thickness inversions are routinely calibrated using heat flow measurements, based on the assumption that magnetic thickness corresponds to Curie depth. However, magnetic spectral thickness determinations remain highly uncertain, underestimate uncertainties, do not properly integrate heat flow measurements into the inversion and fail to address the inherent trade-off between lateral thickness and susceptibility variations.We present a linearized Bayesian inversion that works in space domain and addresses many issues of previous depth determination approaches. The ‘fractal’ description used in the spectral approaches translates into a Matérn covariance function in space domain. We use a Matérn covariance function to describe both the spatial behaviour of susceptibility and magnetic thickness. In a first step, the parameters governing the spatial behaviour are estimated from magnetic data and heat flow data using a Bayesian formulation and the Monte-Carlo-Markov-Chain (MCMC) technique. The second step uses the ensemble of parameter solution from MCMC to generate an ensemble of susceptibility and thickness distributions, which are the main output of our approach.The newly developed framework is applied to synthetic data at satellite height (300 km) covering an area of 6000 x 6000 km. These tests provide insight into the sensitivity of satellite magnetic data to susceptibility and thickness. Furthermore, they highlight that magnetic inversion benefits greatly from a tight integration of heat flow measurements into the inversion process.

Global gravity field data obtained by dedicated satellite missions is used to study the density distribution of the lithosphere. Different multi-data joint inversions are using this dataset together with other geophysical data to determine the physical characteristics of the lithosphere. The gravitational signal from the deep Earth is usually removed by high-pass filtering of the model and data, or by appropriately selecting insensitive gravity components in the inversion. However, this will remove any long-wavelength signal inherent to lithosphere. A clear choice on the best-suited approach to remove the sub-lithospheric gravity signal is missing. Another alternative is to forward model the gravitational signal of these deep situated mass anomalies and subtract it from the observed data, before the inversion. Global tomography provides shear-wave velocity distribution of the mantle, which can be transformed into density anomalies. There are difficulties in constructing a density model from this data. Tomography relies on regularisation which smoothens the image of the mantle anomalies. Also, the shear-wave anomalies need to be converted to density anomalies, with uncertain conversion factors related to temperature and composition. Understanding the sensitivity of these effects could help determining the interaction of the deep Earth and the lithosphere.In our study the density anomalies of the mantle, as well as the effect of CMB undulations, are forward modelled into their gravitational potential field, such that they can be subtracted from gravity observations. The reduction in magnitude of the density anomalies due to the regularisation of the global tomography models is taken into account. The long-wavelength region of the density estimates is less affected by the regularisation and can be used to fix the mean conversion factor to transform shear wave velocity to density. We present different modelling approaches to add the remaining dynamic topography effect in lithosphere models. This results in new solutions of the density structure of the lithosphere that both explain seismic observations and gravimetric measurements. The introduction of these dynamic forces is a step forward in understanding how to properly use global gravity field data in joint inversions of lithosphere models.

In this contribution, we examine the evolution of the South Atlantic passive margins, based on a new thermal lithosphere-asthenosphere-boundary (LAB) model. Our model is calculated by 1D advection and diffusion with rifting time, crustal thickness and stretching factors as input parameters. The initial lithospheric thickness is defined by isostatic equilibrium with laterally variable crustal and mantle density. We simulate the different rifting stages that caused the opening of the South Atlantic Ocean and pick the LAB as the T=1330° C isotherm. The modelled LAB shows a heterogeneous structure with deeper values at equatorial latitudes, as well as a more variable lithosphere along the southern part. This division reflects different stages of the South Atlantic opening: Initial opening of the southern South Atlantic caused substantial lithospheric thinning, followed by the rather oblique-oriented opening of the equatorial South Atlantic accompanied by severe thinning. Compared to global models, our LAB reflects a higher variability associated with tectonic features on a smaller scale. As an example, we identify anomalously high lithospheric thickness in the South American Santos Basin that is only poorly observed in global LAB models. Comparing the LAB of the conjugate South American and African passive margins in a Gondwana framework reveals a variable lithospheric architecture for the southern parts. Strong differences up to 80 km for selected margin segments correlate with strong gradients in margin width for conjugate pairs. This mutual asymmetry suggests highly asymmetric melting and lithospheric thinning prior to rifting.

We apply a Bayesian inversion based on the Monte Carlo Markov chain sampling scheme to magnetic anomaly data of Australia. In our inversion, we simultaneously solve for the susceptibility distribution and the thickness of the magnetic layer. Due to the excellent data coverage, we test our method for Australia. As data source, we use aeromagnetic data of Australia, which are conformed to the recent satellite magnetic model, LCS-1, by an equivalent dipole source approach combined with a spherical harmonic representation. The data are presented in different heights in order to minimize local scale features and to maximize sensitivity to the thickness of the magnetic layer. As constraint, we use estimates of the magnetic layer based on measurements of geothermal heat flow and crustal rock properties. Hereby, we assume that the Curie isotherm does coincide with the deepest magnetic layer. We systematically explore, the effect of increasing model resolution and of the geothermal heat flow values considering their accuracy and quality. The set-up will in the next step be applied to other continental areas of the Earth.