nan Hamayun

The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast

The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast 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/m3 (i.e., difference of the reference constant density of the continental upper crust 2670 kg/m3 and the density of glacial ice 917 kg/m3) 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.

A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST 2.0 Moho boundary

A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST 2.0 Moho boundary 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 Pearsons 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.

Spectral expressions for modelling the gravitational field of the Earth’s crust density structure

We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm−3. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure.

Global atmospheric effects on the gravity field quantities

Global atmospheric effects on the gravity field quantities We compile the global maps of atmospheric effects on the gravity field quantities using the spherical harmonic representation of the gravitational field. A simple atmospheric density distribution is assumed within a lower atmosphere (< 6 km). Disregarding temporal and lateral atmospheric density variations, the radial atmospheric density model is defined as a function of the nominal atmospheric density at the sea level and the height. For elevations above 6 km, the atmospheric density distribution from the United States Standard Atmosphere 1976 is adopted. The 5 × 5 arc-min global elevation data from the ETOPO5 are used to generate the global elevation model coefficients. These coefficients (which represent the geometry of the lower bound of atmospheric masses) are utilized to compute the atmospheric effects with a spectral resolution complete to degree and order 180. The atmospheric effects on gravity disturbances, gravity anomalies and geoid undulations are evaluated globally on a 1 × 1 arc-deg grid.

Global Topographically Corrected and Topo-Density Contrast Stripped Gravity Field from EGM08 and CRUST 2.0

We compute globally the topographically corrected and topo-density contrast stripped gravity disturbances and gravity anomalies taking into account the major known density variations within the topography. The topographical and topo-density contrast stripping corrections are applied to the EGM08 gravity field quantities in two successive steps. First, the gravitational contribution of the topography of constant average density 2,670 kg/m3 is subtracted. Then the ice, sediment, and upper crust topo-density contrast stripping corrections are applied to the topographically corrected gravity field quantities in order to model the gravitational contribution due to anomalous density variations within the topography. The coefficients of the global geopotential model EGM08 complete to degree 180 of spherical harmonics are used to compute the gravity disturbances and gravity anomalies. The 5 × 5 arc-min global elevation data from the ETOPO5 are used to generate the global elevation coefficients. These coefficients are utilized to compute the topographical correction with a spectral resolution complete to degree and order 180. The 2 × 2 arc-deg global data of the ice, sediment, and upper crust from the CRUST 2.0 global crustal model are used to compute the ice, sediment, and upper crust topo-density contrast stripping corrections with a 2 × 2 arc-deg spatial resolution. All data are evaluated globally on a 1 × 1 arc-deg grid at the Earth’s surface.