Seismic data are primarily used in studies of the Earth's inner structure. Since large parts of the world are not yet sufficiently covered by seismic surveys, products from the Earth's satellite observation systems have more often been used for this purpose in recent years. In this study we use the gravity-gradient data derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the elevation data from the Shuttle Radar Topography Mission (SRTM) and other global datasets to determine the Moho density contrast at the study area which comprises most of the Eurasian plate (including parts of surrounding continental and oceanic tectonic plates). A regional Moho recovery is realized by solving the Vening Meinesz-Moritz's (VMM) inverse problem of isostasy and a seismic crustal model is applied to constrain the gravimetric solution. Our results reveal that the Moho density contrast reaches minima along the mid-oceanic rift zones and maxima under the continental crust. This spatial pattern closely agrees with that seen in the CRUST1.0 seismic crustal model as well as in the KTH1.0 gravimetric-seismic Moho model. However, these results differ considerably from some previously published gravimetric studies. In particular, we demonstrate that there is no significant spatial correlation between the Moho density contrast and Moho deepening under major orogens of Himalaya and Tibet. In fact, the Moho density contrast under most of the continental crustal structure is typically much more uniform.

Satellite gradiometry data provide the framework for estimating and validating Earth's gravity field from second and third order derivatives of the Earth's gravitational potential. Such procedures are especially useful when applied locally, as they relate to local and regional characteristics of the real gravity field. In the present study a joint inversion procedure is proposed for the estimation of gravity anomalies at sea surface level from second and third order potential derivatives, based on a standard Gauss-Markov estimation model. The estimation procedure is applied for a test area stretching over Iran involving simulated grids from GOCE-only model GGM_TIM_R05 at GOCE altitude and gravity anomalies recovered at sea level. In order to validate the proposed estimation three different reductions have been considered independently, namely the removal of the long-wavelength part of the observed field through a global gravity model, the removal of the high-frequency part of the field through the incorporation of a topographic/isostatic gravity model and the application of variance component estimation. The application of a global gravity model leads to an improvement in the individual component estimation of the order of magnitude 3 per cent to 73 per cent, with a significant reduction in bias to 4 mGal. Smoother gradient components can come out according to removing the topography and taking into account for isostasy that improved up results of recovery to 25 per cent for the radial second order derivative. Finally, the implementation of variance component estimation leads to no significant improvement in results of recovered gravity anomalies.

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Summary Second and third-order gravitational potential derivatives can be employed for the determination of the medium and high frequency parts of the Earth's gravity field. Due to the GOCE mission, second-order derivatives (SOD) in particular, express currently observed functionals of high accuracy and global coverage. Third-order derivatives (TOD), or gravitational curvature data, provide significant gravity field information when applied regionally. The absence of directly observed TOD data underlines the importance of investigating the relationship between SOD and TOD. This paper discusses the combination of simulated SOD in order to obtain TOD at satellite altitude by applying the spectral combination method. For the determination of TOD integral equations are developed that utilize SOD data at satellite altitude, thus extending the well-known Meissl spectral scheme. The performance of the derived mathematical models is investigated numerically for the test area of Himalayas and the Tibet region. Two different TOD computational strategies are examined. First, we define a deterministic approach that recovers TOD data from noise free simulated SOD data. Results show that retrieved TOD data at satellite level reach an agreement of the level of 1 × 10−17 m−1s−2 when compared with the true TOD data. Secondly, we propose a new mathematical model based on the spectral combination of integral relations and noisy SOD data with Gaussian noise for recovering TOD. Integral estimators of biased and unbiased types are examined in the cases of SOD data at satellite altitude. The used vertical SOD components show differences between the recovered and true vertical TOD components in the order of 1 × 10−17 m−1s−2 in magnitude, proving the vertical-vertical component of SOD as the best for validating purposes.