Recovery of Moho’s undulations based on the Vening Meinesz–Moritz theory from satellite gravity gradiometry data: A simulation study

In the gravimetric approach to determine the Moho depth an isostatic hypothesis can be used. The Vening Meinesz–Moritz isostatic hypothesis is the recent theory for such a purpose. Here, this theory is further developed so that the satellite gravity gradiometry (SGG) data are used for recovering the Moho depth through a nonlinear integral inversion procedure. The kernels of its forward and inverse problems show that the inversion should be done in a larger area by 5° than the desired one to reduce the effect of the spatial truncation error of the integral formula. Our numerical study shows that the effect of this error on the recovered Moho depths can reach 6 km in Persia and it is very significant. The iterative Tikhonov regularization in a combination with either generalized cross validation or quasi-optimal criterion of estimating the regularization parameter seems to be suitable and the solution is semi-convergent up to the third iteration. Also the Moho depth recovered from the simulated SGG data will be more or less the same as that obtained from the terrestrial gravimetric data with a root mean square error of 2 km and they are statistically consistent.     

Integrated electro-hydraulic system modeling and analysis

The technical approach for the development of the computer model of an integrated electro-hydraulic system is presented. As an example, the development of the computer model of the Space Shuttle Electric Auxiliary Power Unit (EAPU) is discussed. The integrated model consists of power source, electric power distribution and control (EPD&C), and mechanical and hydraulic loads. The modeling and analysis results, model interface issues, EPD&C interactions with the power sources, and EPD&C interaction with the electro-hydraulic load are discussed . The selected computer tool facilitates the development of "submodel" corresponding to the subsystem in the integrated system. This modeling approach and the models developed for EAPU can be generalized and adapted for the detailed modeling, simulation, and analysis of other aerospace and commercial electro-mechanical systems     

Generation of vertical–horizontal and horizontal–horizontal gravity gradients using stochastically modified integral estimators

The Earth’s gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250 km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1 mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′ × 30′ gravity anomalies are required.