全波形反演中最优化传输函数研究

不精确的初始速度模型、不完备的数据采集和不准确的物理模拟使全波形反演(FWI)易陷于局部极值, 影响着FWI的实用化。发展凸性更优的目标函数是解决此问题的关键。近几年, 最优化传输函数提供了新的途径。在全波形反演方法简介的基础上, 探讨最优化传输函数的模式匹配特性, 重点研究了包括一维和二维算法在的W2, BFM, KR-OT, GS-1D和GS-2D共5种最优化传输函数, 阐述其基本原理, 从理论上分析了其优、缺点。采用透射模型和SEAM Ⅱ Foothill模型, 实现了这5个函数的FWI; 根据反演剖面, 对5种最优化传输函数的凸性进行了测试和对比分析, 结果表明, 2D的最优化传输函数优于1D, BFM函数优于W2, GS-2D技术优于GS-1D技术。最优化传输函数的凸性主要取决于范数、预处理和时间空间坐标是否引入最优化传输目标函数等因素。

Full waveform inversion is a powerful imaging tool in geophysics.However, it suffers from local minimum issues owing to inaccurate starting models, the absence of low-frequency data, and inaccurate physical simulation.Convex objective functions have been studied for several decades.Over the past few years, geophysicists have achieved remarkable success with optimal transport functions, which has motivated the geophysics community to explore new formulations for optimal transport functions.In this study, five optimal transport functions, namely W2, BFM, KR-OT, GS-1D, and GS-2D(including 1D and 2D algorithms), were reviewed, and their convexities were compared and analyzed through synthetic tests.These full waveform inversion tests demonstrated that the 2D optimal transport function was superior to that of the 1D algorithm.Specifically, the BFM function was better than the W2 function and the GS-2D function was better than the GS-1D function.