Research On Elastic And Electromagnetic Full Waveform Inversion Problem Based On Variational Framework

The full waveform inversion(FWI)problem,which belongs to the non-linear least-square minimization problem,aims at reconstructing the distribution of media of true model by iteratively comparing the simulated data model with the observed data.Comparing to the Ray-tracing based tomography method,which only used a small portion of the information of the received waveform,the full waveform inversion method is able to achieve higher resolution and better imaging quality by makes use of all of the information of waveform.Therefore,the FWI method is widely adopted in seismic exploration and target detection.According to the type of waveform,FWI problems can be classified into two categories,which are elastic FWI and electromagnetic FWI problems.The common processing domain of the latter is frequency domain while the latter usually operates in the time domain.The general procedure of solving the FWI problem is as follows.Firstly,formulate the forward model based on the wave equations of elastic wave of electromagnetic wave,and then design a backward model which is used to simulate the real model.By optimizing the forward model iteratively,the parameter distribution of the simulated backward model can be used to approximate the one of the real models.In this thesis,we first proposed a conjugate gradient method based frequency domain elastic FWI algorithm,and modified the original FWI object function with an additive regularization under the variational framework.By minimizing the residual between simulated data and observed data,the parameter information of elastic waveform can be well reconstructed.By considering the Marmousi2 seismic model,the proposed FWI algorithm is able to recover the primary and secondary wave velocity as well as the density of elastic wave.Then we turned to the time domain FWI problems,involving both the elastic and electromagnetic waves.By using the time domain finite element method,we formulated the time domain forward model for elastic wave and proposed an L-BFGS method based FWI algorithm.As for the electromagnetic FWI problem,we derived the objective function concerning the residual between the observed scattering field and the simulated field,and then decompose the scattering field into the deterministic portion and ambiguous portion by using the subspace optimization method(SOM),where the fast Fourier transformation is performed to avoid the computation of singular value decomposition of Green’s function matrix.Moreover,different from the elastic FWI problems,the multiplicative regularization is considered in this case.In the simulation parts,the multi-scale method is further exploited by adjusting sampling frequency to gradually decrease the spatial scale of imaging area and thus achieve better inversion performance.