Satellite digital elevation models (DEMs) are used for decision-making in various fields. Therefore, evaluating and improving vertical accuracy of DEM can increase the quality of end products. This article aimed to increase the vertical accuracy of most popular satellite DEMs (i.e., the ASTER, Shuttle Radar Topography Mission [SRTM], Forest And Buildings removed Copernicus DEM [FABDEM], and Multi-Error-Removed Improved-Terrain [MERIT]) using the particle swarm optimization (PSO) algorithm. For this purpose, at first, the vertical error of DEMs was estimated via ground truth data. Next, a second-order polynomial was applied to model the vertical error in the study area. To select the polynomial with the highest accuracy, employed for vertical error modeling, the coefficients of the polynomial have been optimized using the PSO algorithm. Finally, the efficiency of the proposed algorithm has been evaluated by other ground truth data and in situ observations. The results show that the mean absolute error (MAE) of SRTM DEM is 4.83 m while this factor for ASTER DEM is 5.35 m, for FABDEM is 4.28, and for MERIT is 3.87. The obtained results indicated that the proposed model could improve the MAE of vertical accuracy of SRTM, ASTER, FABDEM, and MERIT DEMs to 0.83, 0.51, 0.37, and 0.29 m, respectively. 

Due to different structures of the Earth’s crust and mantle, there is a significant density contrast at their boundary, the Moho Density Contrast (or shortly MDC). Frequently one assumes that the MDC is about 600 kg/m3, but seismic and gravimetric data show a considerable variation from region to region, and today there are few such studies, and global models are utterly rare. This research determines a new global model, called MDC21, which is a weighted least-squares combination of three available MDC models, pixel by pixel at a resolution of 1° × 1°. For proper weighting among the models, the study starts by estimating lacking standard errors and (frequently high) correlations among them. The numerical investigation shows that MDC21 varies from 21 to 504 kg/m3 in ocean areas and ranges from 132 to 629 kg/m3 in continental regions. The global average is 335 kg/m3. The standard errors estimated in ocean regions are mostly less than 40 kg/m3, while for continental regions it grows to 80 kg/m3. Most standard errors are small, but they reach to notable values in some specific regions. The estimated MDCs (as well as Moho depths) at mid-ocean ridges are small but show significant variations and qualities. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2022.

In this study, we present a new Moho depth model in Fennoscandia and its surroundings. The model is tailored from data sets of XGM2019e gravitationl field, Earth2014 topography and seismic crustal model CRUST1.0 using the Vening Meinesz-Moritz model based on isostatic theory to a resolution of 1° × 1°. To that end, the refined Bouguer gravity disturbance is determined by reducing the observed field for gravity effect of topography, density heterogeneities related to bathymetry, ice, sediments, and other crustal components. Moreover, stripping of non-isostatic effects of gravity signals from mass anomalies below the crust due to crustal thickening/thinning, thermal expansion of the mantle, Delayed Glacial Isostatic Adjustment (DGIA), i.e., the effect of future GIA, and plate flexure has also been performed. As Fennoscandia is a key area for GIA research, we particularly investigate the DGIA effect on the gravity disturbance and gravimetric Moho depth determination in this area. One may ask whether the DGIA effect is sufficiently well removed in the application of the general non-isostatic effects in such an area, and to answer this question, the Moho depth is determined both with and without specific removal of the DGIA effect prior to non-isostatic effect and Moho depth determinations. The numerical results yield that the RMS difference of the Moho depth from our model HVMD19 vs. the seismic CRUST19 and GRAD09 models are 3.8/4.2 km and 3.7/4.0 km when the above strategy for removing the DGIA effect is/is not applied, respectively, and the mean value differences are 1.2/1.4 km and 0.98/1.4 km, respectively. Hence, our study shows that the specific correction for the DGIA effect on gravity disturbance is slightly significant, resulting in individual changes in the gravimetric Moho depth up to − 1.3 km towards the seismic results. On the other hand, our study shows large discrepancies between gravimetric and seismic Moho models along the Norwegian coastline, which might be due to uncompensated non-isostatic effects caused by tectonic motions.

As recovering the crust-mantle/Moho density contrast (MDC) significantly depends on the properties of the Earth’s crust and upper mantle, varying from place to place, it is an oversimplification to define a constant standard value for it. It is especially challenging in Antarctica, where almost all the bedrock is covered with a thick layer of ice, and seismic data cannot provide a sufficient spatial resolution for geological and geophysical applications. As an alternative, we determine the MDC in Antarctica and its surrounding seas with a resolution of 1°x 1° by the Vening Meinesz-Moritz gravimetric-isostatic technique using the XGM2019e Earth Gravitational Model and Earth2014 topographic/bathymetric information along with CRUST1.0 and CRUST19 seismic crustal models. The numerical results show that our model, named HVMDC20, varies from 81 kg m-3 in the Pacific Antarctic mid-oceanic ridge to 579 kg m-3 in the Gamburtsev Mountain Range in the central continent with a general average of 403 kg m-3. To assess our computations, we compare our estimates with those of some other gravimetric as well as seismic models (KTH11, GEMMA12C, KTH15C and CRUST1.0), illustrating that our estimates agree fairly well with KTH15C and CRUST1.0 but rather poor with the other models. In addition, we compare the geological signatures with HVMDC20, showing how the main geological structures contribute to the MDC. Finally, we study the remaining glacial isostatic adjustment effect on gravity to figure out how much it affects the MDC recovery, yielding a correlation of the optimum spectral window (7< n <12) between XGM2019e and W12a GIA models of the order of ~0.6 contributing within a negligible \pm 14 kg m-3 to the MDC. 

Isostasy is a key concept in geoscience in interpreting the state of mass balance between the Earth's lithosphere and viscous asthenosphere. A more satisfactory test of isostasy is to determine the depth to and density contrast between crust and mantle at the Moho discontinuity (Moho). Generally, the Moho can be mapped by seismic information, but the limited coverage of such data over large portions of the world (in particular at seas) and economic considerations make a combined gravimetric-seismic method a more realistic approach. The determination of a high-resolution of the Moho constituents for marine areas requires the combination of gravimetric and seismic data to diminish substantially the seismic data gaps. In this study, we estimate the Moho constituents globally for ocean regions to a resolution of 1° × 1° by applying the Vening Meinesz-Moritz method from gravimetric data and combine it with estimates derived from seismic data in a new model named COMHV19. The data files of GMG14 satellite altimetry-derived marine gravity field, the Earth2014 Earth topographic/bathymetric model, CRUST1.0 and CRUST19 crustal seismic models are used in a least-squares procedure. The numerical computations show that the Moho depths range from 7.3 km (in Kolbeinsey Ridge) to 52.6 km (in the Gulf of Bothnia) with a global average of 16.4 km and standard deviation of the order of 7.5 km. Estimated Moho density contrasts vary between 20 kg m-3 (north of Iceland) to 570 kg m-3 (in Baltic Sea), with a global average of 313.7 kg m-3 and standard deviation of the order of 77.4 kg m-3. When comparing the computed Moho depths with current knowledge of crustal structure, they are generally found to be in good agreement with other crustal models. However, in certain regions, such as oceanic spreading ridges and hot spots, we generally obtain thinner crust than proposed by other models, which is likely the result of improvements in the new model. We also see evidence for thickening of oceanic crust with increasing age. Hence, the new combined Moho model is able to image rather reliable information in most of the oceanic areas, in particular in ocean ridges, which are important features in ocean basins.

The determination of the oceanic Moho (or crust-mantle) density contrast derived from seismic acquisitions suffers from severe lack of data in large parts of the oceans, where have not yet been sufficiently covered by such data. In order to overcome this limitation, gravitational field models obtained by means of satellite altimetry missions can be proficiently exploited, as they provide global uniform information with a sufficient accuracy and resolution for such a task. In this article, we estimate a new Moho density contrast model named MDC2018, using the marine gravity field from satellite altimetry in combination with a seismic-based crustal model and Earth's topographic/bathymetric data. The solution is based on the theory leading to Vening Meinesz-Moritz's isostatic model. The study results in a high-accuracy Moho density contrast model with a resolution of 1° × 1° in oceanic areas. The numerical investigations show that the estimated density contrast ranges from 14.2 to 599.7 kg/m3 with a global average of 293 kg/m3. In order to evaluate the accuracy of the MDC2018 model, the result was compared with some published global models, revealing that our altimetric model is able to image rather reliable information in most of the oceanic areas. However, the differences between this model and the published results are most notable along the coastal and polar zones, which are most likely due to that the quality and coverage of the satellite altimetry data are worsened in these regions.

In this research, we present a local Moho model, named MOHV19, including Moho depth and Moho density contrast (or shortly Moho constituents) with corresponding uncertainties, which are mapped from altimetric and gravimetric data (DSNSC08) in addition to seismic tomographic (CRUST1.0) and Earth topographic data (Earth2014) to a resolution of 1° × 1° based on a solution of Vening Meinesz-Moritz' theory of isostasy. The MOHV19 model covers the area of entire European plate along with the surrounding oceans, bounded by latitudes (30 °N–82 °N) and longitudes (40 °W–70 °E). The article aims to interpret the Moho model resulted via altimetric and gravimetric information from the geological and geophysical perspectives along with investigating the relation between the Moho depth and Moho density contrast. Our numerical results show that estimated Moho depths range from 7.5 to 57.9 km with continental and oceanic averages of 41.3 ± 4.9 km and 21.6 ± 9.2 km, respectively, and an overall average of 30.9 ± 12.3 km. The estimated Moho density contrast ranges from 60.2 to 565.8 kg/m3, with averages of 421.8 ± 57.9 and 284.4 ± 62.9 kg/m3 for continental and oceanic regions, respectively, with a total average of 350.3 ± 91.5 kg/m3. In most areas, estimated uncertainties in the Moho constituents are less than 3 km and 40 kg/m3, respectively, but they reach to much more significant values under Iceland, parts of Gulf of Bothnia and along the Kvitoya Island. Comparing the Moho depths estimated by MOHV19 and those derived by CRUST1.0, MDN07, GRAD09 and MD19 models shows that MOHV19 agree fairly well with CRUST1.0 but rather poor with other models. The RMS difference between the Moho density contrasts estimated by MOHV19 and CRUST1.0 models is 49.45 kg/m3.