Research On The Total Variation Regularization Simulation And Inversion Method Of Two-dimensional Wave Equations

The study of Two-Dimensional Wave Equation is widely applied in many fields,especially in its inversion, such as in the studies of geological exploration, tunnel earthquake,ultrasound CT imaging etc. However, due to the difficult nonlinear and discomfort as well as the large amount of calculation in many fields, it has theoretical significance and practical value to study the forward procedure of wave equation and numerical inversion algorithm.The paper mainly studies the spreading rules and characteristics of the wave equation in its inversion and analyzes its forward and inversion algorithms using Two-Dimensional Wave Equation as the main mathematical model.Firstly, the paper introduces the research background and its progress of the wave equation and gives the basic theory of the study, including Finite Difference Method,Regularization Method and Numerical Method. Secondly, it discretes the different finite difference methods applied in the mathematical models of Two-Dimensional Wave Equation,mainly including explicit and implicit formats, and solves the different boundary conditions of the two formats. Meanwhile, the corresponding models and parameters are simulated using the forward numerical value of the Two-Dimensional Wave Equation, and the errors are analyzed. It has been found that the higher accuracy is, the more accurate the results are.Finally, the Two-Dimensional Nonlinear Wave Equation is standardly processed and reduced to small problems. The medium parameters of the problems studied in the paper is not continuous, and the advantages of the Regularization Method is that it can handle the problems of discontinuous functions, so the paper tackles the problem using Total Variation Regularization and Finite Volume Method. Furthermore, the corresponding Iterative Inversion is constructed based on nonlinear optimization algorithm, including Steepest Descent Method,NeM wton method,Conjugate Gradient Method etc.In order to test the feasibility, effectiveness, and stability in the practical application of Iterative Inversion deduced herein, three-medium models and single abnormal body models are selected respectively to simulate the numerical value of the parameters of Two-Dimensional Wave Equation. The simulation results are that the feasibility and efficiency of the algorithm are strongly explained by the numerical simulation results, and that Total Variation Conjugate Gradient Method is the best for the effect of Inversion and solve the problems of Inversion.