An Estimate of the Effect of 3D Heterogeneous Density Distribution on Coseismic Deformation Using a Spectral Finite-Element Approach

Abstract

The advancement of the Global Geodetic Observing System (GGOS) has enabled monitoring of mass transport and solid-Earth deformation processes with unprecedented accuracy. Coseismic deformation is modelled as an elastic response of the solid Earth to an internal dislocation. Self-gravitating spherical Earth models can be employed in modelling regional to global scale deformations. Recent seismic tomography and high-pressure/high-temperature experiments have revealed finer-scale lateral heterogeneities in the elasticity and density structures within the Earth, which motivates us to quantify the effects of such finer structures on coseismic deformation. To achieve this, fully numerical approaches including the Finite Element Method (FEM) have often been used. In our previous study, we presented a spectral FEM, combined with an iterative perturbation method, to consider lateral heterogeneities in the bulk and shear moduli for surface loading. The distinct feature of this approach is that the deformation of the entire sphere is modelled in the spectral domain with finite elements dependent only on the radial coordinate. By this, self-gravitation can be treated without special treatments employed when using an ordinary FEM. In this study, we extend the formulation so that it can deal with lateral heterogeneities in density in the case of coseismic deformation. We apply this approach to a longer-wavelength vertical deformation due to a large earthquake. The result shows that the deformation for a laterally heterogeneous density distribution is suppressed mainly where the density is larger, which is consistent with the fact that self-gravitation reduces longer-wavelength deformations for 1-D models. The effect on the vertical displacement is relatively small, but the effect on the gravity change could amount to the same order of magnitude of a given heterogeneity if the horizontal scale of the heterogeneity is large enough.