The Adjoint Method Applied to Time-Distance Helioseismology

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 (Fréchet 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.

23 pages, 9 Figures, accepted by ApJ

References in corpus (5)

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• SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere
• Time-distance helioseismology: Sensitivity of f-mode travel times to flows
• Impact of Locally Suppressed Wave sources on helioseismic travel times
• An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer

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• Numerical simulations of multiple scattering of the $f-$mode by flux tubes
• Interpretation of Helioseismic Travel Times - Sensitivity to Sound Speed, Pressure, Density, and Flows
• Seismic probes of solar interior magnetic structure
• The Quest to Understand Supergranulation and Large-Scale Convection in the Sun
• Seismic sensitivity of Normal-mode Coupling to Lorentz stresses in the Sun
• Full Waveform Inversion for Time-Distance Helioseismology
• Finite-frequency sensitivity kernels in spherical geometry for time-distance helioseismology
• Propagating Linear Waves in Convectively Unstable Stellar Models: a Perturbative Approach
• Probabilistic Inversions for Time-Distance Helioseismology
• The Current State-Of-The-Art In Active Region Seismology
• Strategies in seismic inference of supergranular flows on the Sun
• Iterative inversion of synthetic travel times successful at recovering sub-surface profiles of supergranular flows
• Validating time-distance helioseismic inversions for non-separable subsurface profiles of an average supergranule
• Testing volume integrals of travel-time sensitivity kernels for flows