Spectral-infinite-element Simulations of Self-gravitating Seismic Wave Propagation

Abstract:

Gravitational perturbations induced by particle motions are governed by the Poisson/Laplace equation, whose
domain includes all of space. Due to its unbounded nature, obtaining an accurate numerical solution is very
challenging. Consequently, gravitational perturbations are generally ignored in simulations of global seismic
wave propagation, and only the unperturbed equilibrium gravitational field is taken into account. This so-called
“Cowling approximation” is justified for relatively short-period waves (periods less than 250 s), but is invalid
for free-oscillation seismology. Existing methods are usually based on spherical harmonic expansions. Most
methods are either limited to spherically symmetric models or have to rely on costly iterative implementation
procedures. We propose a spectral-infinite-element method to solve wave propagation in a self-gravitating Earth
model. The spectral-infinite-element method combines the spectral-element method with the infinite-element
method. Spectral elements are used to capture the internal field, and infinite elements are used to represent the
external field. To solve the weak form of the Poisson/Laplace equation, we employ Gauss-Legendre-Lobatto
quadrature in spectral elements. In infinite elements, Gauss-Radau quadrature is used in the radial direction
whereas Gauss-Legendre-Lobatto quadrature is used in the lateral directions. Infinite elements naturally integrate
with spectral elements, thereby avoiding an iterative implementation. We demonstrate the accuracy of the
method by comparing our results with a spherical harmonics method. The new method empowers us to tackle
several problems in long-period seismology accurately and efficiently.