Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion

In full waveform inversion(FWI)high-resolution subsurface model param-eters are sought.FWI is normally treated as a nonlinear least-squares inverse problem,in which the minimum of the corresponding misfit function is found by updating the model parameters.When multiple elastic or acoustic properties are solved for,simple gradient methods tend to confuse parameter classes.This is referred to as parameter cross-talk;it leads to incorrect model solutions,poor convergence and strong dependence on the scaling of the different parameter types.Determining step lengths in a subspace domain,rather than directly in terms of gradients of different parameters,is a potentially valuable approach to address this problem.The particular subspace used can be defined over a span of different sets of data or different parameter classes,provided it involves a small number of vectors compared to those contained in the whole model space.In a subspace method,the basis vectors are defined first,and a local min-imum is found in the space spanned by these.We examine the application of the sub-space method within acoustic FWI in determining simultaneously updates for velocity and density.We first discuss the choice of basis vectors to construct the spanned space,from linear updates by distinguishing only the contributions of different parameter classes towards nonlinear updates by adding the contributions of higher-order pertur-bations of each parameter class.The numerical character of FWI solutions generated via subspace methods involving different basis vectors is then analyzed and compared with traditional FWI methods.The subspace methods can provide better reconstructions of the model,especially for the velocity,as well as improved convergence rates,while the computational costs are still comparable with the traditional FWI methods.