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.

We compute globally the consolidated crust-stripped gravity disturbances/anomalies. These refined gravity field quantities are obtained from the EGM2008 gravity data after applying the topographic and crust density contrasts stripping corrections computed using the global topography/bathymetry model DTM2006.0, the global continental ice-thickness data ICE-5G, and the global crustal model CRUST2.0. All crust components density contrasts are defined relative to the reference crustal density of 2,670 kg/m 3 . We demonstrate that the consolidated crust-stripped gravity data have the strongest correlation with the crustal thickness. Therefore, they are the most suitable gravity data type for the recovery of the Moho density interface by means of the gravimetric modelling or inversion. The consolidated crust-stripped gravity data and the CRUST2.0 crust-thickness data are used to estimate the global average value of the crust-mantle density contrast. This is done by minimising the correlation between these refined gravity and crust-thickness data by adding the crust-mantle density contrast to the original reference crustal density of 2,670 kg/m 3 . The estimated values of 485 kg/m 3 (for the refined gravity disturbances) and 481 kg/m 3 (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480 kg/m 3 , which is adopted in the definition of the Preliminary Reference Earth Model (PREM). This agreement is more likely due to the fact that our results of the gravimetric forward modelling are significantly constrained by the CRUST2.0 model density structure and crust-thickness data derived purely based on methods of seismic refraction.

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.

Global maps of the step-wise topography corrected and crustal components stripped geoids using the CRUST 2.0 model We compile global maps of the step-wise topography corrected and crustal components stripped geoids based on the geopotential model EGM'08 complete to spherical harmonic degree 180 and the CRUST 2.0 global crustal model. The spectral resolution complete to degree 180 is used to compute the primary indirect bathymetric stripping and topographic effects on the geoid, while degree 90 for the primary indirect ice stripping effect. The primary indirect stripping effects of the soft and hard sediments, and the upper, middle and lower consolidated crust components are forward modeled in spatial form using the 2 × 2 arc-deg discrete data of the CRUST 2.0 model. The ocean, ice, sediment and consolidated crust density contrasts are defined relative to the adopted reference crustal density of 2670 kg/m 3 . Finally we compute and apply the primary indirect stripping effect of the density contrast (relative to the mantle) of the reference crust. The constant value of -520 kg/m 3 is adopted for this density contrast relative to the mantle. All data are evaluated on a 1 × 1 arc-deg geographical grid. The complete crust-stripped geoidal undulations, globally having a range of approximately 1.5 km, contain the gravitational signal coming from the global mantle lithosphere (upper mantle) morphology and density composition, and from the sub-lithospheric density heterogeneities. Large errors in the complete crust-stripped geoid are expected due to uncertainties of the CRUST 2.0 model, i.e., due to deviations of the CRUST 2.0 model density from the real earth's crustal density and due to the Moho-boundary uncertainties.

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 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.

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.