基于波场重建的时域全波形反演

摘要

全波形反演是一种高精度反演方法,但采用梯度类优化方法求解时,巨大的波场存储量是该方法的应用短板之一.首先根据拉格朗日乘子法推导了时域全波形反演的梯度公式,提出了一种基于波场重建方案,用以解决梯度计算的数据存储问题.根据有限差分的求解条件,确定所需保存的波场信息,满足波场精确重建需求,进而构建全波形反演的梯度数据,大幅降低了全波形反演方法对波场数据的存储需求.基于匀速模型和Marmousi模型的测试表明,该方法能精确重建波场,结合波场重建的时域全波形反演方法反演精度高,存储需求小.%Full waveform inversion is a high-resolution inversion method,but the large wave field storage is one of the application weakness when the gradient class optimization algorithm is used to solve the problem.In this paper,we know,on Lagrange multiplier method,the gradient formula of time domain full waveform inversion is deduced.A new method on wave field reconstruction is proposed to solve the data storage problem of gradient calculation.According to the condition of solving the finite difference,the information of the needed wave field is determined,and the exact reconstruction needs of the wave field are satisfied.Then the gradient data of the full waveform inversion is constructed,which greatly reduces the demand of the full waveform inversion method for the wave field data.The test based on homogeneous model and Marmousi Model shows that the proposed scheme in this paper can reconstruct the wave field accurately.Time domain waveform inversion method with wave field reconstruction has high-resolution and small storage demand.