Simultaneous Source for non-uniform data variance and missing data
E. Haber and M. Chung Department of Mathematics、Department of Earth and Ocean Science, The University of British Columbia, Vancouver, BC, Canada, V6T-1Z4, Phone: +1 (604) 822-9068, Fax: +1 (604) 822-2545 Department of Mathematics, Virginia Tech 474 McBryde, Stanger Street, Blacksburg, VA 24061, USA, Phone: +1 (540) 231-3446 Fax : +1 (540) 231-5960
Abstract
The use of simultaneous sources in geophysical inverse problems has revolutionized the ability to deal with large scale data sets that are obtained from multiple source experiments. However, the technique breaks when the data has non-uniform standard deviation or when some data are missing. In this paper we develop, study, and compare a number of techniques that enable to utilize advantages of the simultaneous source framework for these cases. We show that the inverse problem can still be solved efficiently by using these new techniques. We demonstrate our new approaches on the Direct Current Resistivity inverse problem.
中文速览
地球物理勘探中，用多个震源同时采集数据可以大幅提升反演效率，但当不同数据点的测量精度不一致、或部分数据缺失时，传统的"同时震源"方法就会失效。针对这一问题，作者系统地提出并比较了四种解决思路：用低维正演模型补全缺失数据、对权重矩阵做低秩分解、对数据矩阵做随机近似、以及每次随机抽取部分震源子集来迭代求解，并将这些方法统一纳入随机规划（stochastic programming）框架，通过样本均值近似（Sample Average Approximation）高效求解目标函数。以直流电阻率（Direct Current Resistivity）反演为测试平台，数值实验表明这些新技术在保持同时震源方法计算优势的同时，能够正确处理非均匀噪声和数据缺口，避免了简单忽略数据差异所导致的重建伪像。这项工作填补了同时震源框架在实际非理想数据条件下的方法空白，对地震成像、电磁成像等大规模多源反演问题具有直接的实用价值。
原文 arXiv:1404.5254;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1404.5254v1