混合全变差正则化的全波形反演
Full Waveform Inversion with Compound Total Variation Regularization
摘要: 全波形反演(FWI)是一个高度非线性和不适定的数学物理反问题。全变差(TV)正则化方法具有保持解的不连续的性质，然而其对具有一定倾斜角度(如分段线性)的区域会呈现阶梯状伪影。二阶TV (TV2)正则化方法可以减弱阶梯现象，同时很好地保留反演的边缘信息。但二阶TV正则化方法与传统TV正则化相比，其需要更多的计算量。因此，本文基于TV和TV2正则化方法，提出了混合的全变差正则化方法(HTV)。基于Marmousi2模型和Sigsbee模型进行数值实验，数值结果表明相对于TV和TV2正则化方法，HTV正则化方法在反演精度方面具有较好的计算表现。
Abstract: Full waveform inversion (FWI) is a highly nonlinear and ill-posed mathematical physics inverse problem. Total variation (TV) regularization method has the property of preserving the discontinuity of the solution. However, it leads to the stair-casing artifacts for regions with certain skew angles (e.g., piecewise linearity). The second-order TV (TV2) regularization method can attenuate the staircase phenomenon while preserving the edge information of the inversion resolution well. However, compared with the conventional TV regularization method, the TV2 regularization method requires large computation costs. Therefore, we combine the advantages of TV and TV2 regularization and propose a hybrid regularization (HTV) method. Numerical experiments based on the Marmousi2 model and the Sigsbee model are conducted, and the numerical results show that the HTV regularization method has better computational performance in terms of inversion accuracy compared with the TV and TV2 regularization methods.
文章引用：吴法选, 何清龙. 混合全变差正则化的全波形反演[J]. 现代物理, 2022, 12(5): 115-128. https://doi.org/10.12677/MP.2022.125012

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