全波形反演的一个新目标函数：数据域中的微分相似优化

A new objective function for full waveform inversion:differential semblance optimization in data domain

全波形反演(full waveform inversion,FWI)目前已有广泛的工业实践,但因其本质上的非线性,不如走时层析成像等传统速度建模技术稳健,非线性程度也因目标函数不同而不同。研究分析了FWI中几种不同目标函数的性质,基于定义在数据域中的微分相似概念,提出了一种新的目标函数。初步试验表明,这种目标函数对于比较大范围的数据残差都有凸状性质,基于梯度优化法时使用该目标函数的FWI比传统FWI更稳健,而且波形反演的良好分辨率基本得以保留。

Full Waveform Inversion（FWI）,while now widely practiced industrially,is less robust than many conventional velocity model building techniques,such as travel time tomography,due to its high non-linearity.Different objective functions in FWI have different degrees of non-linearity.In this study,we investigate the behavior of FWI with different objective functions and propose a new objective function based on differential semblance defined in the data domain.Preliminary tests suggest that this objective function is convex for a large range of data residuals.Gradient-based optimization schemes are therefore more robust than for the standard least-squares formulation;however,the good resolving power of waveform inversion is mostly retained.