The Study For The Forward And Inverse Problem Of Elastic Wave Equation In Fluid-Saturated Porous Media

Fluid-saturated porous media are two-phase media composed of the solid and?uid. Biot theory considered that the subsurface solid is a porous elastic solid con-taining a compressible viscous ?uid. Compared with the single-phase medium theory,?uid-saturated porous media theory can describe the subsurface media more preciselyand the fluid-saturated porous medium elastic wave equation can describe more in-formation than ever. So, fluid-saturated porous media theory can be used widely ingeophysics exploration and earthquake engineering. Therefore, further research of theforward and inverse methods has theory and engineering significance for the elasticwave equation in fluid-saturated porous media.Wavelet analysis is an international forward research field in recent years. It notonly contains abundant mathematical theories, but also is a powerful method and toolin engineering and it brings new ideas to many fields. The homotopy method is awidely convergent method for solving the nonlinear operator equation and also hasimportant applications in many fields. Level set method has become an novel toolfor the computation of evolving boundaries and interfaces. Instead of tracking thesurfaces, we solve the resulting partial differential equation. Therefore, in this thesiswe compose the wavelet analysis and finite-difference method into the forward simu-lation. Then we draw the wavelet analysis, the adaptive homotopy method and levelset method into the inversion process, and carry out a series of studies of numericalinversion methods, which have the abilities of saving computational costs, noise sup-pression, global convergence and easy realization of the procedure consequently.Firstly, based on the Biot theory, a wavelet finite-difference method is proposedby combing the good properties of wavelet analysis and traditional finite-differencemethod. For the wavelet multi-resolution method, it owns a quick decomposition andreconstruction algorithm and the finite-difference method is simple and may be read-ily implemented. This algorithm is applied to simulate the propagation of 2-D elasticwave in fluid-saturated porous media for the homogenous and two-layer models. Theresulting synthetic seismograms are shown.Secondly, the principle of wavelet multi-scale inversion is introduced to the gen- eral estimation problem. Basing on this principle and the homotopy method modifiedthe homotopy parameter adaptively, we design a wavelet adaptive homotopy inversionmethod. Numerical simulations are carried out for the inverse problem of two dimen-sional elastic wave equation in fluid-saturated porous media in seismic prospecting.The numerical results and tests of noise suppression indicate the method's effective-nessThirdly, apply a level set regularization method to the inverse problem for 2-Dwave equation in Fluid-saturated media. we utilized the level set function to presentthe discontinuous parameter, and the regularization functional is applied to the levelset function. Numerical experiments show that the method can recover coefficientswith rather complicated geometry of noise in the observation data.Finally, the wavelet adaptive homotopy method is introduced to the time-lapseseismic inversion. we design a local inversion algorithm. According to the inversionresults of base model, we can obtain a small domain containing the oil reservoir, thenin this domain we apply the adaptive homotopy method to inverse the monitor model.The results show that this algorithm can improve the precision and decrease the runtime.