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正则化是求解地震层析成像反演问题必须的。一般情况下,地震层析成像方程组非常庞大,合理选择正则化参数非常困难。本文提出一种在线性层析成像反演中实际选择正则化参数的算法。该算法基于大多数层析成像常用的数据统计假设。首先利用Lanczos双对角变换将方程组转换到Krylov子空间。在转换的子空间中,方程组转换成标准阻尼最小二乘正规方程。标准方程组的解可以写成正则化参数的显函数,这使得可以进行计算机方便的选取正则化参数。正则化参数选取的第二个准则是数字化模拟的研究。如果转换空间的维数远小于原始模型空间的维数,此算法的计算效果非常好,特别适用于大型地震层析成像问题。
Regularization is necessary to solve the seismic tomography inversion problem. In general, the seismic tomography equations are very large and it is very difficult to select the regularization parameters reasonably. This paper presents an algorithm for the actual selection of regularization parameters in linear tomography inversion. The algorithm is based on the statistical assumptions commonly used in most tomography. Firstly, the equations are transformed into Krylov subspaces by Lanczos diagonal transformation. In the transformed subspace, the system of equations is transformed into a standard damped least-squares normal equation. The solution of the standard equations can be written as the explicit function of the regularization parameter, which makes it possible to select the regularization parameters conveniently by computer. The second criterion for regularization parameter selection is the study of digital simulation. If the dimension of the transformation space is much smaller than the dimension of the original model space, this algorithm is very effective and suitable for large-scale seismic tomography.