基于波数域梯度场分解的多尺度波形反演方法

全波形反演是一种建立高精度速度模型的有力工具，是偏移模式和层析模式的联合.然而，当初始模型较差、数据缺失低频成分和大偏移距数据缺失时，常规波形反演的层析成分更新较弱.因此，反演过程以偏移模式为主，容易导致反演快速陷入局部极小值.本文发展了基于波数域梯度场分解的多尺度波形反演方法（WGDFWI），从梯度场中分离出层析成分，在反演的初期主要依赖层析分量更新背景速度场，为常规全波形反演建立良好的初始模型.首先，基于一种高效的隐式波场分离方法，将梯度场分解为层析成分和偏移成分.然后在层析梯度上应用二维波数域滤波器，以缓解偏移成分泄露的问题，并利用多尺度反演策略，增强反演的稳定性.利用双层模型和Marmousi模型进行试算的结果表明，该方法可以有效重构背景速度模型，为常规波形反演提供良好的初始模型，有效提高反演精度.

Multi-scale full waveform inversion based ongradient decomposition in wavenumber domain

Full Waveform Inversion (FWI) is a powerful tool to reconstruct velocity model with high resolution. It is the combination of tomography mode and migration mode, however, the update of tomographic component is relatively weak, compared to that of migration component. When the initial velocity model is far away from the true velocity model, or the data lack low-frequency and large-offset information, FWI will be dominated by migration mode updating high-wavenumber information of the velocity model. In this way, the inversion will fall into a local minimum, generating a poor inversion result. To prevent the reconstructed model from being trapped into a local minimum, we develop a multi-scale full waveform inversion method based on gradient decomposition in wavenumber domain. Firstly, we decompose the FWI gradient into two parts, tomographic component and migration component, based on an implicit wavefield decomposition method. The tomographic component is extracted from FWI gradient. With a 2D filter in wavenumber domain, the migration component leakage can be mitigated, and the high-wavenumber noise can be effectively removed from tomographic gradient. We also use a multi-scale strategy to improve inversion stability. The tomographic updates are enhanced during the early stages of inversion to invert for a background velocity model, which will be used as the initial model for conventional FWI. Numerical results of two-layer model and Marmousi model tests demonstrate the effectiveness of multi-scale full waveform inversion based on gradient decomposition in wavenumber domain. The proposed method enhances the low-wavenumber updates and provides a more accurate initial model for subsequent FWI. The final inverted velocity model is more accurate than the conventional FWI result.