Global Earth Structure Recovery from State-of-the-art Models of the Earth's Gravity Field and Additional Geophysical Information

Currently, a tremendous improvement is observed in the accuracy and spatial resolution of global Earth’s gravity field models. This improvement is achieved due to using various new data, including those from satellite gravimetry missions (CHAMP, GRACE, and GOCE); terrestrial and airborne gravity data, as well as altimetry data. The new gravity field models can be applied, in particular, to improve our knowledge of the Earth’s interior structure. The aim of this study is to compile a global map of the Moho interface using a global gravity model and additional available information about the crust density structure. In our study, we use the gravity field model EIGEN-6C2 and the global crustal model CRUST1.0 derived from seismic data. In addition, we utilize seismic-based models of Moho as prior information: CRUST1.0 model, as well as the Crust07 model, which was derived by a fully non-linear inversion of fundamental mode surface waves. The observed gravity field contains nuisance signals from the topography and density heterogeneities related to bathymetry, ice, sediments, and other crustal components. Therefore, we model and sequentially subtract these signals by applying so-called stripping corrections. This results in crust-stripped gravity field quantities (gravity anomalies and gravity disturbances). In the course of research, we review different analytical, semi-analytical, and numerical forward modeling techniques to compute the gravitational attraction of a body. We also derive an analytical formula for the computation of gravitational potential generated by a polyhedral body having linearly varying density. We compute the correction to observed gravity field using the analytical methods in the vicinity of the body and using semi-analytical methods in the far zone. We demonstrate that the sequential correction of gravity disturbances and gravity anomalies for nuisance signals increases the correlation with the Moho depths. We use the corrected gravity field to find the global (mean) value for the crust-mantle density contrast using the Pearson's correlation method. We use an empirical technique in which the absolute correlation between the Moho depth from CRUST 1.0 model and the updated crust stripped gravity disturbances/anomalies is minimized. The updated stripped gravity disturbances/anomalies are obtained by adding a contribution (attraction) related to the density contrast between the reference crust and the upper most mantle to stripped gravity disturbances/anomalies. The recovery of the Moho geometry is based on solving a system of linear equations which relates the crust-stripped gravity field (represented in terms of spherical harmonic coefficients) and the geometry of the Moho interface (represented in terms of Moho depths at the nodes of an equiangular geographical grid). In this way, corrections to the prior Moho configuration are estimated. It is known that a stand-alone inversion of gravimetric data may lead to inaccurate results because it is impossible to separate the signal from the interface under consideration and gravimetric signals from other sources (particularly, those located deeper inside the Earth). To suppress the latter signals (e.g, related to inhomogeneities of the mantle density and deep Earth structure), we propose to eliminate the contribution of low-degree spherical harmonics from input gravity data. Furthermore, we apply degree-dependent weights to the remaining spherical harmonics coefficients. The weight matrix is designed in such a way that low degrees are weighted less and high degree more. We have developed an advanced inversion procedure in which gravity data and information from other (seismic) sources are exploited simultaneously, using zero-order and first-order Tikhonov regularization concepts. The variance components estimation (VCE) procedure is used for the estimation of relative weights of different data sets. We consider a number of inversion strategies based on different combinations of data sets, regularization types, degree-dependent weights applied to input gravity data, as well as input gravity data minimum and maximum truncation degrees. For the selection of optimal inversion parameters, we compare the developed Moho models with the two regional Moho models for the European crust. The two models includes the EuCrust07 and EuM09 developed by Magdala Tesauro et al. and Marek Grad et al., respectively. We find that the best model is obtain when using a joint inversion (gravity data plus CRUST 1.0 and CRUST07 seismic models), first-order Tikhonov regularization, degree-dependent weights proportional to the fourth power of the degree and setting the minimum and maximum truncation degree equal to 90 and 180, respectively. The final Moho model (DMM-1) is compared with two regional models: (1) for the South America and (2) for Africa. From the comparison and statistical analysis we found that our developed model DMM-1 have the best RMS fit with the two regional models as well as with observed point values.