Full Waveform Inversion Of Wave Equation Based On The Finite-difference Contrast Source Method

Full-waveform inversion(FWI) seismic imaging is a seismic tomography technology, which is based on the optimization of a data fitting objective function. This inversion method can fully take advantage of the full information of seismic wavefield, such as amplitude, phase and so on, it thus has the ability of reconstructing high resolution of the subsurface structure. However, the huge forward modelling computation and the highly nonlinearity for the corresponding misfit functional hinder its wide applications in seismic exploration. When FWI involving in multi-component wave equation, the computation,the requirement for memory storage and the computing time may be out of our affordability. At present, most methods are based on the scalar acoustic model in the seismic imaging of the full waveform inversion, which can not interpret the complex seismic data well.Additionally, another difficulty for FWI is the influence between parameters, especially involving the density inversion. In this thesis, based on the multi-component acoustic and elastic wave equations, we discuss the fast and efficient multi-parameter finite-difference contrast source inversion method. Only one full forward modeling is required throughout the inversion processing for the finite-difference contrast source inversion method. Hence,the inversion method is very efficient in terms of calculation.Firstly,we carry out the study for fast and high efficient forward algorithms which are based on acoustic and elastic wave equations. Considering the intensive forward modeling computation of FWI, the parallel algorithm with high accuracy are discussed. These methods are based on the staggered-grid finite difference method, which may provide a theoretical and technical support for FWI.Secondly, based on acoustic wave equation, the acoustic multi-parameter finitedifference contrast source inversion algorithm is proposed in this thesis, which provides a theoretical basis for the development of the elastic wave equation multi-parameter finitedifference contrast source inversion algorithm. The first-order acoustic wave equation is rewritten as a pseudo-conservative form by using matrix-vector representation. By introducing the contrast source vector and contrast matrix, the corresponding minimization objective functional is established. In order to reconstruct the discontinuous information of the inversion model and to improve the resolution for this inversion method,multiplicative regularization method is incorporated into the acoustic multi-parameter inversion algorithm. The regularization method does not require the selection for the regularization parameters and it can greatly improve the inverting resolution. For the multi-component and multi-parameter inversion problem, the acoustic multi-parameter finite-difference contrast source inversion method is implemented parallelly by using the domain decomposition method and the distributed memory management strategy, which greatly improves the efficiency of the inversion algorithm. In numerical experiments, the two-phase inversion strategy is represented to deal with the cross talk effects between different parameters. This inversion strategy can mitigate the influences to some extent and improve the reconstruction resolution. The convergence and feasibility of this inversion algorithm are verified by the Marmousi model numerical results.Furthermore, based on elastic wave equation, the finite-difference contrast source inversion is extended to elastic wave density inversion, which is greatly helpful for the development of the elastic multi-parameter finite-difference contrast source inversion algorithm. The biggest obstacle for applying the monoparametric finite-difference contrast source inversion method to elastic wave equation case is to find the corresponding contrast source differential equation. Therefore, the elastic equation is represented by using matrix-vector form. The monoparametric finite-difference contrast source inversion method is successfully employed to invert the density by using this matrix-vector form.For the ill-posedness of this inverse problem, this thesis has also developed a monoparametric version multiplicative regularization method, and this regularization method greatly improve the accuracy for this inversion algorithm. The numerical results fully indicate that the finite-difference inversion method can be used for the elastic wave equation density inversion.Finally, the elastic multi-parameter finite-difference contrast source inversion is proposed based on elastic wave equation. Since the conventional elastic wave equation can not satisfy the contrast source differential equation, an invertible linear transformation is employed on the multi-component wavefield to transform the elastic wave equation to a pseudo-conservative elastic wave equation. By introducing the contrast source vector field and contrast function matrix, then the elastic multi-parameter contrast source inversion method is established. Considering the local convergence and initial guess dependence of the multi-parameter inversion method, an initialization strategy using wave backpropagation technology is presented. At the same time, in order to further improve the resolution of the inversion method, the elastic wave multiplicative regularization method for this finite-difference contrast source inversion method has also developed. Considering the large calculation for elastic wave multi-parameter inversion, the original problem is solved parallelly using the domain decomposition strategy, and this technique can improve the computation efficiency and the scalability. For the numerical instability resulting from the different magnitudes of multi-component wavefields, the normalized wavefield strategy is employed. In addition, in order to reduce the effects between different parameters, the corresponding two-phase inversion strategy is proposed, which improves the reconstruction resolution for the elastic multi-parameter inversion method. In the numerical experiments, the numerical results of the Marmousi2 and other models show that the elastic multi-parameter finite-difference contrast source inversion has the ability to reconstruct high resolution inversion results for the complex geological models.