The adjoint method applied to time-distance helioseismology

Shravan Hanasoge, Aaron Birch, Laurent Gizon, Jeroen Tromp

    Research output: Contribution to journalArticle

    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 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 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 three-dimensional 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.

    Original languageEnglish (US)
    Article number100
    JournalAstrophysical Journal
    Volume738
    Issue number1
    DOIs
    StatePublished - Sep 1 2011

    Fingerprint

    adjoint method
    helioseismology
    inversions
    sensitivity
    wave spectrum
    wave excitation
    partial differential equations
    gradients
    optimization
    evaluation
    prediction
    predictions
    interactions
    inversion

    Keywords

    • magnetohydrodynamics (MHD)
    • Sun: dynamo
    • Sun: helioseismology
    • Sun: interior
    • Sun: oscillations
    • waves

    ASJC Scopus subject areas

    • Space and Planetary Science
    • Astronomy and Astrophysics
    • Nuclear and High Energy Physics

    Cite this

    The adjoint method applied to time-distance helioseismology. / Hanasoge, Shravan; Birch, Aaron; Gizon, Laurent; Tromp, Jeroen.

    In: Astrophysical Journal, Vol. 738, No. 1, 100, 01.09.2011.

    Research output: Contribution to journalArticle

    Hanasoge, Shravan ; Birch, Aaron ; Gizon, Laurent ; Tromp, Jeroen. / The adjoint method applied to time-distance helioseismology. In: Astrophysical Journal. 2011 ; Vol. 738, No. 1.
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