The direct spectral element method for the calculation of synthetic seismograms in self-gravitating, spherically symmetric planets

TL;DR

This paper introduces a spectral element method for calculating synthetic seismograms in self-gravitating, spherically symmetric planets, extending previous approaches by using a displacement formulation to fully account for self-gravitation.

Contribution

It develops a displacement-based spectral element implementation for the direct solution method, enabling accurate modeling of self-gravitation and fluid stratification in planetary seismology.

Findings

Code $ exttt{DSpecM1D}$ shows excellent agreement with $ exttt{MINEOS}$ and $ exttt{YSpec}$.

Method accurately models elastic and anelastic planetary structures.

Extension to fluid stratification enhances modeling capabilities.

Abstract

This paper describes the implementation of the direct solution method (DSM) using radial spectral elements for the calculation of synthetic seismograms in self-gravitating, spherically symmetric, non-rotating, anelastic, and transversely isotropic Earth models. In contrast to previous implementations of the DSM that used a potential formulation within fluid regions, we use a displacement formulation throughout. It is this feature that allows us to extend the DSM to account fully for self-gravitation along with arbitrary fluid stratification. Our code, $\texttt{DSpecM1D}$, is benchmarked against the normal mode summation code $\texttt{MINEOS}$ as well as the direct radial integration code $\texttt{YSpec}$. Agreement between the codes is excellent for both elastic and anelastic models.