Preliminary Discussion On Application Of Waveform Inversion

With the exploration of the unknown subsurface environment,the development of economic and the increased demand of resource,it is becoming more important to find an accurate and efficient way to describe the subsurface.Accurate velocity is essential for subsurface imaging,that's the reason why we always pay attention to building an excellent velocity model.Full waveform inversion has potential in processing the inversion of velocity and other parameters in detail.It uses its amplitude and phase information,which combine characteristics of seismic wave kinematics and dynamics,updating parameters iteratively by wave equation matching,so that residual of modeled data and real data is at the minimum.And then complete inversion and obtain parameters.This paper studies on FWI theory.Basic formula of modeling and inversion based on wave equation in both time domain and frequency domain is deduced in detail.And I also show the basic framework of FWI.And then,several key issues such as gradient,step,inversion strategy is introduced.We realized FWI in both time domain and frequency domain,and established different parallel inversion process.We use MPI parallel inversion strategy based on shots in time domain.On the other hand,we choose MPI plus MUMPS parallel inversion method in frequency domain.The difference is,wave field is divided into several parallel region in frequency domain,and we get the these different part of wave filed of all shots simultaneously by parallel computing while in time domain we compute each shot in one node.In this way we not only reduce the memory consumption but also improve the efficiency.FWI is achieved by interaction between data domain and model domain.But the fact is,they are not always corresponding to each other.Therefore,the solution is complicated.There are many minimums near objective function,and waveform inversion is a strong nonlinear inversion.Therefore the method of multi-scale inversion strategy is studied in this paper.In order to solve the problems of effective convergence waveform inversion in the application,I also study the gradient optimization algorithm and realized the algorithm such as the conjugate gradient method,limited memory BFGS algorithm,approximate Hessian diagonal elements.As a kind of fine inversion,FWI can obtain good effect in theory,with endless potential.In spite of attracting people's eyes,it does not appear in industrial application.It exposes shortcomings in application.So this paper tried to test FWI with real data.And I analyze the problem during inversion and explain the reasons why waveform inversion method has not been used in industrial production.And on the problem of its dependence on initial model,I recommend the complex frequency domain method,and prove it works well on model test.For a better result,the scale method is used in processing the real data,providing large and small-scale information of early arrival wave and reflection wave respectly.