The Earth topographic masses are compensated by an isostatic adjustment. According to the isostatic hypothesis a mountain is compensated by mass deficiency beneath it, where the crust is floating on the viscous mantle. For study of the impact of the compensating mass on the topographic mass a crustal thickness (Moho boundary) model is needed. A new gravimetric-isostatic model to estimate the Moho depth, Vening Meinesz-Moritz model, and two well-known Moho models (CRUST2.0 and Airy-Heiskanen) are used in this study. All topographic masses cannot be compensated by simple isostatic assumption then other compensation mechanism should be considered. In fact small topographic masses can be supported by elasticity of the larger masses and deeper Earth’s layers. We discuss this issue applying spatial and spectral analyses in this study. Here we are going to investigate influence of the crustal thickness and its density in compensating the topographic potential. This study shows that the compensating potential is larger than the topographic potential in low-frequencies vs. in high-frequencies which are smaller. The study also illustrates that the Vening Meinesz-Moritz model compensates the topographic potential better than other models, which is more suitable for interpolation of the gravity field in comparison with two other models. In this study, two methods are presented to determine the percentage of the compensation of the topographic potential by the isostatic model. Numerical studies show that about 75% and 57% of the topographic potentials are compensated by the potential beneath it in Iran and Tibet. In addition, correlation analysis shows that there is linear relation between the topographic above the sea level and underlying topographic masses in the lowfrequencies in the crustal models. Our investigation shows that about 580±7.4 metre (in average) of the topographic heights are not compensated by variable the crustal root and density.
The gravimetric model of the Moho discontinuity is usually derived based on isostatic adjustment theories considering floating crust on the viscous mantle. In computation of such a model some a priori information about the density contrast between the crust and mantle and the mean Moho depth are required. Due to our poor knowledge about them they are assumed unrealistically constant. In this paper, our idea is to improve a computed gravimetric Moho model, by the Vening Meinesz-Moritz theory, using the seismic model in Fennoscandia and estimate the error of each model through a combined adjustment with variance component estimation process. Corrective surfaces of bi-linear, bi-quadratic, bi-cubic and multi-quadric radial based function are used to model the discrepancies between the models and estimating the errors of the models. Numerical studies show that in the case of using the bi-linear surface negative variance components were come out, the bi-quadratic can model the difference better and delivers errors of 2.7 km and 1.5 km for the gravimetric and seismic models, respectively. These errors are 2.1 km and 1.6 km in the case of using the bi-cubic surface and 1 km and 1.5 km when the multi-quadric radial base function is used. The combined gravimetric models will be computed based on the estimated errors and each corrective surface.
The Moho depth can be determined using seismic and/or gravimetric methods. These methods will not yield the same result as they are based on different hypotheses as well as different types, qualities and distributions of data. Here we present a new global model for the Moho computed based on a stochastic combination of seismic and gravimetric Moho models. This method employs condition equations in the spectral domain for the seismic and gravimetric models as well as degree-order variance component estimation to optimally weight the corresponding harmonics in the combination. The preliminary data for the modelling are the seismic model CRUST2.0 and a new gravimetric Moho model based on the inverse solution of the Vening Meinez-Moritz isostatic hypothesis and the global Earth Gravitational Model EGM08. Numerical results show that this method of stochastic combination agrees better with the seismic Moho model (3.6 km rms difference) than the gravimetric one. The model should be a candidate for dandifying the frequently sparsely data CRUST2.0. We expect that this way of combining seismic and gravimetric data would be even more fruitful in a regional study.