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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-wave inversion (FWI) has a wide range of industrial practices, but its inherent nonlinearity is not as robust as conventional velocity modeling techniques such as time-lapse tomography. The degree of nonlinearity is also dependent on the objective function different. The properties of several different objective functions in FWI are studied and analyzed. Based on the concept of differential similarity defined in the data field, a new objective function is proposed. The preliminary experiments show that this objective function has a convexity for a relatively large range of data residuals. The FWI based on this objective function based on the gradient optimization method is more robust than the traditional FWI, and the good resolution of the waveform inversion is basically preserved .