Computational Acoustics in Spherical Geometry: Steps toward Validating Helioseismology

Abstract

Throughout the past decade, detailed helioseismic analyses of observations of solar surface oscillations have led to advances in our knowledge of the structure and dynamics of the solar interior. Such analyses involve the decomposition of time series of the observed surface oscillation pattern into its constituent wave modes, followed by inversion procedures that yield inferences of properties of the solar interior. While this inverse problem has been a major focus in recent years, the corresponding forward problem has received much less attention. We aim to rectify this situation by taking the first steps toward validating and determining the efficacy of the helioseismic measurement procedure. The goal of this effort is to design a means to perform differential studies of various effects such as flows and thermal perturbations on helioseismic observables such as resonant frequencies, travel-time shifts, etc. Here we describe our first efforts to simulate wave propagation within a spherical shell, which extends from 0.2 to about 1.0004 R_solar (where R_solar is the radius of the Sun) and which possesses a solar-like stratification. We consider a model containing no flows that will serve as a reference model for later studies. We discuss the computational procedure, some difficulties encountered in a simulation of this kind, and the means to overcome them. We also present techniques used to validate the simulation.