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arXiv 1602.01540physics.geo-phcs.NAmath.NA
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地震全波形反演中的最优传输

Optimal Transport for Seismic Full Waveform Inversion

The University of Texas at Austin(德克萨斯大学奥斯汀分校);New Jersey Institute of Technology(新泽理工学院)

Bjorn Engquist, Brittany D. Froese, Yunan Yang

AI总结:

本文提出利用最优传输中的Wasserstein度量来改进全波形反演中的反演问题,通过证明目标函数的凸性和对噪声的鲁棒性,提出求解Monge-Ampere方程的算法,并通过数值示例验证其有效性。

摘要:

全波形反演是一种通过地表测量确定地球性质的成功方法。该反问题通过求解一个受偏微分方程约束的优化问题来解决,其中未知系数在计算波场中被调整以最小化与测量数据的不匹配。本文提出使用与最优传输相关的Wasserstein度量来衡量这种不匹配。证明了目标函数的凸性和对噪声的鲁棒性。Wasserstein度量通过求解Monge-Ampere方程来计算。我们描述了用于优化的Frechet梯度计算算法。给出了数值示例。

英文摘要:

Full waveform inversion is a successful procedure for determining properties of the earth from surface measurements in seismology. This inverse problem is solved by a PDE constrained optimization where unknown coefficients in a computed wavefield are adjusted to minimize the mismatch with the measured data. We propose using the Wasserstein metric, which is related to optimal transport, for measuring this mismatch. Several advantageous properties are proved with regards to convexity of the objective function and robustness with respect to noise. The Wasserstein metric is computed by solving a Monge-Ampere equation. We describe an algorithm for computing its Frechet gradient for use in the optimization. Numerical examples are given.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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