The Adjoint Method Applied to Timedistance Helioseismology
Abstract
For a given 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 toward a stationary point. The adjoint method, arising from partialdifferentialequationconstrained 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 waveexcitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an 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 (Fréchet derivatives) relative to threedimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 2011
 DOI:
 10.1088/0004637X/738/1/100
 arXiv:
 arXiv:1105.4263
 Bibcode:
 2011ApJ...738..100H
 Keywords:

 magnetohydrodynamics: MHD;
 Sun: dynamo;
 Sun: helioseismology;
 Sun: interior;
 Sun: oscillations;
 waves;
 Astrophysics  Solar and Stellar Astrophysics;
 Mathematical Physics
 EPrint:
 23 pages, 9 Figures, accepted by ApJ