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arXiv 1105.4263astro-ph.SRmath-phmath.MP
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时距日震学中的伴随方法

The Adjoint Method Applied to Time-Distance Helioseismology

Shravan Hanasoge, Aaron Birch, Laurent Gizon, Jeroen Tromp

摘要:

对于给定的{ \it失配函数},模型的指定最优性度量,其梯度描述了可以改变系统属性以向静止点前进的方式。伴随方法是从偏微分方程约束优化中产生的,描述了一种通过有限计算提取失配函数关于模型参数的导数的方法。它依赖于由两种类型的源驱动的波场的精确计算,即平均波激发谱,导致{ \it向前波场},以及预测和观测之间的差异,导致{ \it伴随波场}。所有的灵敏度内核相关的一个给定的测量出现直接从评估的相互作用积分涉及这些波场。该技术有助于计算相对于三维异质背景模型的灵敏度核(Fréchet导数),从而为非线性迭代反演铺平了道路。一个算法来执行这样的反演使用尽可能多的观察所需的讨论。

英文摘要:

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.

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