We developed and applied a novel numerical scheme for a gravimetric forward modelling of the Earth's crustal density structures based entirely on methods for a spherical analysis and synthesis of the gravitational field. This numerical scheme utilises expressions for the gravitational potentials and their radial derivatives generated by the homogeneous or laterally varying mass density layers with a variable height/depth and thickness given in terms of spherical harmonics. We used these expressions to compute globally the complete crustcorrected Earth's gravity field and its contribution generated by the Earth's crust. The gravimetric forward modelling of large known mass density structures within the Earth's crust is realised by using global models of the Earth's gravity field (EGM2008), topography/bathymetry (DTM2006.0), continental icethickness (ICE-5G), and crustal density structures (CRUST2.0). The crust-corrected gravity field is obtained after modelling and subtracting the gravitational contribution of the Earth's crust from the EGM2008 gravity data. These refined gravity data mainly comprise information on the Moho interface and mantle lithosphere. Numerical results also reveal that the gravitational contribution of the Earth's crust varies globally from 1,843 to 12,010 mGal. This gravitational signal is strongly correlated with the crustal thickness with its maxima in mountainous regions (Himalayas, Tibetan Plateau and Andes) with the presence of large isostatic compensation. The corresponding minima over the open oceans are due to the thin and heavier oceanic crust.
When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means of line integrals after applying the Gauss divergence theorem.
We investigate globally the correlation of the step-wise consolidated cruststripped gravity field quantities with the topography, bathymetry, and the Moho boundary. Global correlations are quantified in terms of Pearson's correlation coefficient. The elevation and bathymetry data from the ETOPO5 are used to estimate the correlation of the gravity field quantities with the topography and bathymetry. The 2×2 arc-deg discrete data of the Moho depth from the global crustal model CRUST 2.0 are used to estimate the correlation of the gravity field quantities with the Moho boundary. The results reveal that the topographically corrected gravity field quantities have the highest absolute correlation with the topography. The negative correlation of the topographically corrected gravity disturbances with the topography over the continents reaches -0.97. The ocean, ice and sediment density contrasts stripped and topographically corrected gravity field quantities have the highest correlation with the bathymetry (ocean bottom relief). The correlation of the ocean, ice and sediment density contrasts stripped and topographically corrected gravity disturbances over the oceans reaches 0.93. The consolidated crust-stripped gravity field quantities have the highest absolute correlation with the Moho boundary. In particular, the global correlation of the consolidated crust-stripped gravity disturbances with the Moho boundary is found to be -0.92. Among all the investigated gravity field quantities, the consolidated crust-stripped gravity disturbances are thus the best suited for a refinement of the Moho density interface by means of the gravimetric modeling or inversion.
We derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice functions combined with the spherical height functions describe the global thickness of the continental ice sheet. The newly derived formulas are utilized in the forward modelling of the gravitational field quantities generated by the ice density contrast. The 30×30 arc-sec global elevation data from GTOPO30 are used to generate the global elevation model (GEM) coefficients. The spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness data from the CRUST 2.0 global crustal model are used to generate the global lower-bound ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m 3 (i.e., difference of the reference constant density of the continental upper crust 2670 kg/m 3 and the density of glacial ice 917 kg/m 3 ) is adopted. The numerical examples are given for the gravitational potential and attraction generated by the ice density contrast computed globally with a low-degree spectral resolution complete to degree and order 90 of the GEM and GIM coefficients.
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