层析反演中的正则化方法研究

The study of regularization in tomography

正则化可显著降低层析反演解的非唯一性,提高层析反演结果的质量。主要研究了模型参数正则化和数据正则化。地下介质参数之间的关联性如何加入模型正则化是讨论的问题之一;观测数据之间的关联性加入数据正则化的方法则是另一个主要议题。此外,讨论了Tikhonov正则化和预条件两种模型正则化实现策略,指出前者理论比较直观,后者计算效率更高,并证明了两者在理论上的等价性。模型正则化通过构造各向异性光滑算子加入地质构造特征,数据正则化则通过在层析矩阵中加入预先构造的数据预条件矩阵来实现。通过层析偏移速度分析给出了模型正则化和数据正则化的具体实现策略。理论分析和层析偏移速度分析的数值实验说明本文的模型正则化和数据正则化可显著提高层析反演的质量。

Regularization in tomography is able to weaken the non-uniqueness of tomography to improve the inversion result- The discussion of regularization in this paper includes model-regularization and data-regularization Model paramelers are not isolated, how to add the relationship of these parameters into tomography is one of the missions hereSimilarly, considering da- tum relationship in tomography is another problemThe so-called ＂straightforward regularization＂ and the ＂precondition regu- larization＂ are focused, and we achieve that the former is intuitionistic and the latter is more efficiencyAlso, we point out that the above two algorithms are equivalent to each other, and this will be shown in this paperThe geological structure characteristics of the medium can be integrated into the tomography using the model-regularization with anisotropic smooth matrix. The data-regularization is realized with another smooth operator which will be integrated into the tomographic matrix. The model-regularization and data-regularization are tested with tomographic migration velocity analysis （MVA） algorithm, The results of theory and numerical experiments with tomographic MVA show that the proposed model-regularization and the da- ta-regularization are both able to improve the quality of tomography obviously.