Research On Forward And Inverse Algorithm Of Wave Equation In Two-Phase Medium

There are saturated soil layers and unsaturated soil layers of different depths on the surface of the earth,whether it is an ocean plate or a continental plate.When the seismic wave passes through the soil layer,the liquid phase and solid phase in the soil layer will have an important impact on its propagation,so predicting the propagation path of the seismic wave is very important for the prevention and mitigation of earthquake disasters.The inverse problem of mathematical physics has always been a concern of scholars.The inversion problem of wave equation can be used to simulate the parameters of underground medium.Due to the complexity of the surface,the traditional wave equation model can not truly simulate the multiphase characteristics of surface soil medium.In this paper,the two-phase medium wave equation is selected as the model,and the forward and inversion research is carried out to simulate the real situation of the surface.These are of great significance in practical engineering applications.The solution of the inversion problem often requires the support of the forward process.Firstly,the forward problem of the two-phase medium wave equation is explored.In this paper,the finite difference method is used to deal with the forward process.In order to reduce the amount of calculation,the selected area is first unitized to improve the calculation efficiency.The half-step central difference scheme is used to ensure the second-order accuracy of the internal processing.Based on the Taylor expansion,a new second-order accuracy difference scheme is constructed to process the boundary,thus ensuring the accuracy of the difference scheme inside and at the boundary.Then the stability analysis is carried out to verify the rationality of the constructed discrete difference scheme,and the numerical simulation of the established forward model is carried out by computer to verify the feasibility of the constructed scheme.In order to explore the inversion problem of wave equation in two-phase media,according to the constructed forward model,the parameter identification inversion problem based on surface records is constructed.Since most of the inverse problems are ill-posed,the regularization method is used to overcome the ill-posedness of the inverse problem.Aiming at the problems given in this paper,a nonlinear optimization algorithm of regular-parabolic fitting is constructed.Through the deformation of surface parameters and the optimization of objective function coefficients,the optimal solution of the problem is obtained within the allowable error range.The algorithm effectively avoids the gradient calculation,so that the computer can deal with the problem quickly.The numerical simulation is carried out in the three layer medium model and the single abnormal body medium model,and good results are obtained.