基于双对角通量校正的多尺度全波形反演

油气勘探的不断深入使地震勘探面临的问题越来越复杂。全波形反演(FWI)以其高精度优势成为一种极具潜力的速度建模方法，但其反演效果很大程度上受初始模型精度和炮记录频带范围的影响。在实际地震数据处理中，初始速度模型的精度往往不高，而精确的初始速度模型又是防止FWI陷入局部极值的关键，因此降低FWI对初始模型的依赖性至关重要。为此，提出一种基于双对角通量校正的多尺度FWI方法，利用通量校正运输技术对二维时间域声波方程进行校正，获得不同频率成分的校正波场，并据此推导出FWI梯度及步长计算公式，使用低频~高频的校正波场进行多尺度反演。为了验证该方法的有效性，利用改进Marmousi模型进行模拟测试。结果表明，该方法有效地拓展了波场的中低频成分，降低了FWI对初始模型的依赖性。

Multi-scale full waveform inversion based on double diagonal flux correction transport

The continuous furthering of oil and gas exploration exposes seismic exploration to increasingly complex issues. Full waveform inversion (FWI) has become a highly promising velocity modeling method due to its high accuracy. Nevertheless, its inversion effect is largely affected by the accuracy of the initial model and the frequency range of the shot record. In actual seismic data processing, the accuracy of the initial velocity model is often not high, despite that an accurate initial velocity model is the key to preventing FWI from falling into local extreme values. Therefore, reducing the depen-dence of FWI on the initial model is vital. For this reason, a multi-scale FWI method based on double-diagonal flux correction is proposed in this paper. Specifically, the two-dimensional time-domain acoustic wave equation is corrected by the flux-corrected transport technology to obtain the corrected wavefields of different frequency components. On this basis, the calculation formulas for FWI gradient and step size are derived, and multi-scale inversion is carried out with the corrected wavefields from low frequency to high frequency. Simulation tests with a modified Marmousi model are conducted to verify the effectiveness of the proposed method. The results show that the proposed method effectively expands the medium- and low-frequency components of the wavefield and reduces the dependence of FWI on the initial model.