Acoustic Full Waveform Inversion Methods Based On Robust Objective Functions

In recent years,full-waveform inversion（FWI）has been the research focus of seismic exploration due to its ability to accurately estimate subsurface parameters,making it a highly advanced geophysical model building technique.The objective function of FWI is created by comparing the observed and simulated seismic data,and the optimization of the objective function yields precise inversion results.However,when low-frequency information is not available,FWI,as a nonlinear inversion method,is prone to the cycle skipping problem,resulting in imprecise inversion outcomes.Employing a more convex and robust objective function in FWI can effectively mitigate the issue of cycle skipping.In recent years,the newly proposed optimal transport distance objective function has been one research hotpot due to its remarkable convexity performance compared to other robust objective functions.This paper conduct FWI based on two optimal transport distance objective functions,namely the entropy regularized optimal transport distance（Sinkhorn distance）objective function and the Wasserstein-2 distance（W₂ distance）objective function.Despite the fact that the aforementioned two objective functions can successfully weaken the cycle skipping,they are still unable to address the issues of imprecise wavelet estimation which may result in inadequately accurate inversion outcomes.Furthermore,the weakening of seismic wave due to viscoacoustic medium will reduce the amplitude of objective function’s gradient and impede convergence rate of inversion.Hence,enhancing the effectiveness of FWI for viscoacoustic medium is also a major topic of this paper.This paper begins by introducing the forward simulation methods of acoustic and visco-acoustic wave equations,and then goes on to explain the theory of FWI.This paper conducts the researches on the problems of insufficient inversion accuracy,inaccurate wavelet estimation,and low efficiency of FWI for viscoacoustic medium.This paper proposes an energy correction data preprocessing technique,which is based on the entropy regularization of the optimal transport distance objective function,resulting in a marked improvement of inversion accuracy of deep part compared to the traditional method.Then,for enhancing inversion accuracy,this paper further incorporates the patch-ordering regularization method to perform edge-preserving smoothing on the inversion results of this objective function,and finally obtains the high-precision inversion results with more consistent stratigraphic trends and more distinct stratigraphys.Subsequently,this paper suggests an FWI technique of the convolutional optimal transport distance objective function originaled from Wasserstein-2distance objective function,which is not reliant on an accurate practical wavelet,to tackle the issue of precise wavelet estimation.The inversion results show that,even if the wavelet estimation is wrong,this method can still obtain more accurate inversion results in the case of low-frequency information missing.In addition,this paper presents a gradient preprocessing technique utilizing a stabilized Q compensation approach for viscoacoustic media,in which the inversion gradient is obtained by cross-correlating the second-order partial derivative of the source wavefield with respect to time and the Q-compensated adjoint wavefield.To address the instability problem in the Q compensation,this paper proposes a stabilizing compensation strategy based on the constant fractional order Laplacian viscoacoustic wave equation.The numerical examples verify that the gradient preprocessing method based on this compensation strategy can boost the inversion efficiency and enhance the quality of FWI for viscoacoustic media with negligible additional calculations.