From Satellite Gradiometry Data to Subcrustal Stress Due to Mantle Convection
Abstract
Subcrustal stress induced by mantle convection can be determined by the Earth's gravitational potential. In this study, the spherical harmonic expansion of the simplified NavierStokes equation is developed further so satellite gradiometry data (SGD) can be used to determine the subcrustal stress. To do so, we present two methods for producing the stress components or an equivalent function thereof, the socalled S function, from which the stress components can be computed numerically. First, some integral estimators are presented to integrate the SGD and deliver the stress components and/or the S function. Second, integral equations are constructed for inversion of the SGD to the aforementioned quantities. The kernel functions of the integrals of both approaches are plotted and interpreted. The behaviour of the integral kernels is dependent on the signal and noise spectra in the first approach whilst it does not depend on extra information in the second method. It is shown that recovering the stress from the verticalvertical gradients, using the integral estimators presented, is suitable, but when using the integral equations the verticalvertical gradients are recommended for recovering the S function and the verticalhorizontal gradients for the stress components. This study is theoretical and numerical results using synthetic or real data are not given.
 Publication:

Pure and Applied Geophysics
 Pub Date:
 September 2014
 DOI:
 10.1007/s0002401408472
 Bibcode:
 2014PApGe.171.2391E
 Keywords:

 Closedform formulae;
 Downward continuation;
 Inversion;
 Integral equation;
 Spectra combination