Total variation regularized full waveform inversion based on gradient projection method
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摘要: 为降低地震全波形反演的不适定性,常用方法是引入未知模型的先验信息,从而将反演问题正则化。但是,传统正则化方法在包含多个先验信息的情况下,仍然面临挑战。本文提出一种扩展的全波形反演公式,其中包含对模型的凸集约束。本文以慢度平方作为反演的模型参数,展示了如何在施加全变差约束的同时,施加边界约束令其保持在一个物理意义上的可行范围内。为验证本文所提算法的适用性,分别开展简单模型及国际标准地质模型数值实验研究,结果表明,全变差正则化的引入可以提高光滑背景模型下高速扰动体的重构效果。Abstract: To reduce the ill-posedness of seismic full waveform inversion,a common method is to introduce prior information to regularize the inversion problem.Traditional regularization methods still face challenges even when they contain multiple prior information.This study proposed an extended full waveform inversion formula,which includes the convex set constraints on models.Specifically,this study showed how to constrain the total variation of the slowness square while forcing the constraint to keep it within a physical reality range.To verify the applicability of the algorithm proposed in this study,numerical experiments on simple models and international standard geological models were carried out.The results show that the introduction of total variation regularization can improve the reconstruction of high-speed disturbances under smooth background models.
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