文章基本信息

标题：Seismic Waveform Inversion by Stochastic Optimization
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作者：Tristan van Leeuwen ; Aleksandr Y. Aravkin ; Felix J. Herrmann 等
期刊名称：International Journal of Geophysics
印刷版ISSN：1687-885X
电子版ISSN：1687-8868
出版年度：2011
卷号：2011
DOI：10.1155/2011/689041
出版社：Hindawi Publishing Corporation
摘要：We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.