论文标题
通过最佳运输和软质编码分析地震反转的分析
Analysis of Seismic Inversion with Optimal Transportation and Softplus Encoding
论文作者
论文摘要
本文致力于对地震全波形反演（FWI）中局部最小问题的理论和数值研究。 本文提供了对最佳运输（OT）类型目标函数的不同性质的数学分析，并证明了在伴随状态方法中获得的梯度不取决于Kantorovich电位的特定选择。提出了一种使用软叠层编码方法的新方法，以概括并将OT度量施加在FWI上。这种方法改善了目标函数的凸度，并减轻了循环措施问题。通过基准Marmousi模型，在数值上证明了所提出方法的有效性。
This paper is devoted to theoretical and numerical investigation of the local minimum issue in seismic full waveform inversion (FWI). This paper provides a mathematical analysis of optimal transportation (OT) type objective function's differentiability and proves that the gradient obtained in the adjoint-state method does not depend on the particular choice of the Kantorovich potentials. A novel approach using the softplus encoding method is presented to generalize and impose the OT metric on FWI. This approach improves the convexity of the objective function and mitigates the cycle-skipping problem. The effectiveness of the proposed method is demonstrated numerically on an inversion task with the benchmark Marmousi model.
