基于互相关目标函数的反射波波形反演

在速度—密度参数化模式下，传统全波形反演（FWI）得到的密度结果存在严重的偏移效应，即无法恢复模型中的低波数信息。反射波波形反演（RWI）能够反演密度模型的低波数分量，将其与FWI结合能够更准确地反演密度模型。为此，提出基于互相关目标函数的速度—密度双参数RWI方法。首先回顾了传统声波变密度方程双参数反演，并利用辐射模式分析了密度反演的偏移特征；然后在实施RWI过程中借助速度和密度高度耦合性，通过Gardner公式同步更新速度和密度参数；再将最终的反演结果作为输入模型进行传统速度—密度双参数FWI；最终建立了基于RWI+FWI的速度—密度双参数反演流程。简单双层模型和重采样的Sigsbee 2A模型测试结果表明，RWI可克服反演局部极值并减弱密度偏移特征，在实施RWI过程中利用Gardner经验公式同时对速度和密度进行更新，可精确地恢复速度、密度的低波数信息。

Reflection waveform inversion based on cross-correlation misfit function

On a velocity and density model,the density from conventional FWI (Full Waveform Inversion) is seriously migrated,namely low wavenumber information in the model hasn't been recovered. Since RWI (Reflection Waveform Inversion) can estimate low wavenumber component,the combination of RWI and FWI can invert the density model more accurately. A velocity-density RWI model based on crosscorrelation-based misfit function is proposed. This paper first reviews the two-parameter inversion based on the conventional acoustic wave equation,and analyze the migration characteristics of density inversion using a radiation mode;then synchronously updates velocity and density by the Gardner formula based on the high trade-off between velocity density model when running RWI,and input the RWI results as the initial model for traditional velocity-density FWI;and finally builds a velocity-density RWI+FWI inversion workflow. Application on a simple two-layer model and a resampled Sigsbee 2A model has proved that RWI could avoid inversion to be trapped in local minima and suppress density migration;and in the process of RWI,low wavenumber information of velocity and density could be accurately recovered by using the Gardner formula to update velocity and density at the same time.