Parallel LSQR Algorithms Used in Seismic Tomography

作者：Jingsong Liu, Futian Liu, Jun Liu, Tian-Yao HAO · 发表于：Chinese Journal of Geophysics · 年份：2006 · DOI：10.1002/cjg2.858 · 被引用次数：14 · 研究领域：Statistical and numerical algorithms、Seismic Imaging and Inversion Techniques、Image and Signal Denoising Methods

Abstract This paper addresses the LSQR algorithms used in earthquake travel time tomography. We keep the epicenter terms in the equation for regional events, and then use orthogonal projection method to eliminate the epicenter terms; for tele‐events, the classic smoothing process is used. The number of non‐zero elements in partial derivative matrix is increased a couple of times because of the orthogonal projection and smoothing process. For a large scale inversion problem, the amount of non‐zero elements can be dozens of Gigabytes or hundreds of Gigabytes. The huge amount of memory requirement becomes the bottle neck of LSQR algorithms. To solve this problem, we studied the distribution property of non‐zero elements in partial derivative matrix , designed an efficient data structure for the sparse matrix, used a distributed memory and computation scheme for matrix computation, and implemented it on a multi‐processor super computer. We derived an estimation formula of parallel efficiency and tested two real tomography models.