基于各向异性全变分约束的多震源弹性波全波形反演

多震源编码技术可以提高全波形反演的计算效率，但同时会引入串扰噪声使反演结果质量降低. 全变分约束可以有效地压制层内噪声并突出模型界面，其与多震源技术的结合，能在大大提高弹性波全波形反演效率的同时提高反演质量. 本文提出了一种高效的动态多震源全波形反演策略，可以在离散串扰噪声的同时保证照明的均匀性. 根据残留串扰噪声的分布特征，构建了与之匹配的基于各向异性全变分约束的弹性波全波形反演方法. 为了减少周期跳跃效应，将基于稀疏约束的低频重构算法应用于弹性波地震记录，给出了利用快速梯度投影算法求解各向异性全变分约束的全波形反演流程. 模型数据测试结果表明本文的方法不仅能有效地抑制多震源方法导致的串扰噪声，同时也能降低观测数据中的噪声对反演结果的影响.

Multi-source elastic full waveform inversion based on the anisotropic total variation constraint

The multi-source encoding technology can improve the calculation efficiency of the full waveform inversion, but the crosstalks caused by the source aliasing can reduce the quality of inversion results. The total variation (TV) constraint can suppress the noise within the layer and sharp the model interfaces. The combination of TV constraint and multi-source technology can not only greatly improve the calculation efficiency of the elastic full waveform inversion, but also ensure the inversion quality. In this paper, an efficient dynamic multi-source full waveform inversion strategy is proposed, which can disperse the crosstalks while ensuring uniform illumination. Then, we analyze the characteristics of the crosstalks, and establish the corresponding TV constraint elastic full waveform inversion method. To avoid cycle-skipping, we apply the low frequency reconstruction method based on the sparse constraint to elastic seismic data, and propose a new elastic multiscale inversion strategy. We also give the workflow for solving the anisotropic TV constraint full waveform inversion problem by the fast gradient projecting algorithm. The numerical tests show that our method can not only suppress the crosstalks caused by source aliasing, but also reduce the effect of the noise in observations on the final inversion results.