Propagation of seismic waves through a spatio-temporally fluctuating medium: Homogenization

TL;DR

This paper develops a homogenization approach to model seismic wave propagation through a rapidly fluctuating, evolving medium like the Sun, revealing anisotropic effects and wave decoherence that impact seismic interpretation.

Contribution

It introduces a homogenization framework for seismic waves in spatio-temporally varying media, deriving effective models and highlighting anisotropic wave speeds and wavefield decoherence.

Findings

Effective tensorial wave speeds in fluctuating media

Decoherence linked to wave attenuation in the Sun

Homogenization applicable to periodic and random media

Abstract

Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally stationary medium is almost universally invoked. However, the Sun is in a constant state of evolution, on a broad range of spatio-temporal scales. At the zero wavelength limit, i.e., when the wavelength is much shorter than the scale over which the medium varies, the WKBJ (ray) approximation may be applied. Here, we address the other asymptotic end of the spectrum, the infinite wavelength limit, using the technique of homogenization. We apply homogenization to scenarios where waves are propagating through rapidly varying media (spatially and temporally), and derive effective models for the media. One consequence is that a scalar sound speed becomes a tensorial wavespeed in the effective model and anisotropies can be induced depending on the nature of the perturbation. The second term in this asymptotic two-scale expansion, the so-called corrector, contains contributions due to higher-order scattering, leading to the decoherence of the wavefield. This decoherence may be causally linked to the observed wave attenuation in the Sun. Although the examples we consider here consist of periodic arrays of perturbations to the background, homogenization may be extended to ergodic and stationary random media. This method may have broad implications for the manner in which we interpret seismic measurements in the Sun and for modeling the effects of granulation on the scattering of waves and distortion of normal-mode eigenfunctions.