The Adjoint Method Applied to Time-Distance Helioseismology

TL;DR

This paper discusses the application of the adjoint method to compute sensitivity kernels in time-distance helioseismology, enabling non-linear iterative inversions of solar interior models.

Contribution

It introduces an adjoint-based approach for efficiently calculating sensitivity kernels for 3D solar models, advancing helioseismic inversion techniques.

Findings

Derivation of the adjoint method for helioseismic applications

Framework for computing sensitivity kernels from wavefield interactions

Potential for non-linear iterative inversions in solar modeling

Abstract

For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely the average wave-excitation spectrum, resulting in the {\it forward wavefield}, and differences between predictions and observations, resulting in an {\it adjoint wavefield}. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Fr\'{e}chet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for non-linear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.