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

Abstract

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.

Reformulation of the Vening-Meinesz Moritz Inverse Problem of Isostasy for Isostatic Gravity Disturbances

“…, r g  at a point The gravity disturbance  is computed using the following expression [1] Tenzer et al [22] developed and applied the uniform mathematical formalism of computing the topographic and density contrasts stripping gravity corrections. It utilizes the expression for computing the gravitational attraction g (defined approximately as a negative radial derivative of the respective potential ; i.e., V g V r     ) generated by an arbitrary volumetric mass layer with a variable depth and thickness while having a laterally distributed vertical density variation.…”

“…This is due to the fact that GPS observations provide the geodetic heights above the reference ellipsoid surface, while the definition of gravity anomalies requires topographic heights with respect to sea level. Tenzer et al [20][21][22] utilized the definition of gravity disturbances in the forward modeling of gravitational field generated by major known crustal density structures. Following this concept, here we define the VMM inverse problem of isostasy by means of the isostatic gravity disturbances.…”

Isostatic Crustal Thickness Under The Tibetan Plateau And Himalayas From Satellite Gravity Gradiometry Data

“…For this purpose, we combine three recently developed numerical methods for a regional determination of the Moho geometry from the isostatic gravity gradient. The computation of the gravity gradient is realized according to the approach introduced by Tenzer et al (2012a). They presented a uniform mathematical formalism of computing the gravity corrections and respective corrected gravity field.…”

“…Appendix A: Gravimetric forward modeling Tenzer et al (2012a) developed and applied a uniform mathematical formalism of computing the gravity corrections. It utilizes the expression for the gravitational potential V generated by an arbitrary volumetric mass layer with a variable depth and thickness while having laterally distributed vertical mass density variations.…”

Global Isostatic Gravity Maps From Satellite Missions and Their Applications in the Lithospheric Structure Studies

“…APPENDIX A GRAVIMETRIC FORWARD MODELING Tenzer, Novák, Vajda, Gladkikh, and Hamayun[48] developed and applied a uniform mathematical formalism of computing the gravity corrections. It utilizes the expression for the gravitational potential V generated by an arbitrary volumetric mass layer with a variable depth and thickness while having laterally distributed vertical mass density variations.…”