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.     

The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

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.     

Global Crust-Mantle Density Contrast Estimated from EGM2008, DTM2008, CRUST2.0, and ICE-5G

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/m³. 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/m³. The estimated values of 485 kg/m³ (for the refined gravity disturbances) and 481?kg/m³ (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480?kg/m³, 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.     

Roughness of three types of gravity disturbances and their correlation with topography in rugged mountains and flat regions

We investigate the roughness of and the correlation with topography of the observed, topographically corrected (T), and bathymetrically and topographically corrected (BT) gravity disturbances. The numerical investigation is carried out for the gravity disturbances at the Earth’s surface and for the upward continued gravity disturbances at different altitudes. The area of study comprises a rough part of the Canadian Rockies surrounded by flat regions. The smoothest at the Earth’s surface are the BT gravity disturbances. The evolution of roughness with altitude shows an interesting phenomenon, diverse for the three types of gravity disturbances. The correlation with topography over the study area of the observed gravity disturbances is bellow 0.6, and of the BT gravity disturbances approximately −0.6. The largest absolute value, of about −0.75, is found between the topography and the T gravity disturbances. This large negative correlation indicates a presence of the isostatic compensation in mountainous regions of the Canadian west coast.     

Spectral harmonic analysis and synthesis of Earth’s crust gravity field

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 crust-corrected 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 ice-thickness (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.