基于奇异值分解的地震走时层析成像重建算法

Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography.

作者信息

Song L P, Zhang S Y

出版信息

IEEE Trans Image Process. 1999;8(8):1152-4. doi: 10.1109/83.777099.

Abstract

A reconstruction method is given for seismic transmission traveltime tomography. The method is implemented via the combinations of singular value decomposition, appropriate weighting matrices, and variable regularization parameter. The problem is scaled through the weighting matrices so that the singular spectrum is normalized. Matching the normalized singular values, a regularization parameter varies within the interval [0, 1], and linearly increases with singular value index from a small, initial value rather than a fixed one to eliminate the impacts of smaller singular values' components. The experimental results show that the proposed method is superior to the ordinary singular value decomposition (SVD) methods such as truncated SVD and Tikhonov regularization.

摘要

给出了一种地震透射走时层析成像的重建方法。该方法通过奇异值分解、适当的加权矩阵和可变正则化参数的组合来实现。通过加权矩阵对问题进行缩放，以使奇异谱归一化。匹配归一化奇异值，正则化参数在区间[0, 1]内变化，并随着奇异值索引从一个小的初始值而不是固定值线性增加，以消除较小奇异值分量的影响。实验结果表明，所提出的方法优于普通奇异值分解（SVD）方法，如截断SVD和蒂霍诺夫正则化。