| In recent years,mathematical physics inverse problem is one of the development and progress quickly.This is because it is driven by the urgent need of Engineering Mechanics and other disciplines,the issue by the vast number of scholars strongly praised and attaches great importance to.There are many different kinds of the most striking feature of the inverse problem is the problem and theory has a very wide range of fields involved,especially its inversion,for example geological exploration,tunnel earthquake,ultrasound CT imaging study,but due to the nonlinear and discomfort makes it difficult to add qualitative issues large,and for many areas of computationally intensive,so the research wave equation forward procedure has important theoretical and practical value and numerical inversion algorithm.The main rule of the spread of the wave equation inversion of this article and characteristics of two-dimensional wave equation as the main mathematical model to analyze the forward and inversion algorithms.Firstly,the research background and progress of the wave equation;gives the basic theory of this study,finite difference methods,and numerical methods regularization;Secondly,the mathematical model of two-dimensional wave equation finite difference different discrete methods,including explicit format,implicit scheme,and the different boundary conditions of these two formats are processed to solve,and the corresponding parameters of the model and the two-dimensional wave equation forward numerical simulation,and passed between them errors obtained were analyzed and found higher accuracy,more accurate results.finally,the two-dimensional nonlinear wave equation regularization process,which reduces to minimization problem,since the medium parameters studied in this article the problem is not continuous,and regularization advantage of the method is not able to handle Continuous Functions,so this combination of Total Variation Regularization and finite volume method to address this issue,and based on the steepest descent method,Newton method,conjugate gradient method of nonlinear optimization algorithms,construct the corresponding iterative inversion algorithm.In order to test the inferred herein iterative inversion algorithm feasibility,effectiveness,and stability in the practical application,we were selected three media models and model parameters of individual anomalies dimensional wave equation numerical simulation,from analog Looking at the results: numerical simulation results obtained strongly suggest the feasibility and efficiency of the algorithm,we can see the full variational conjugate gradient method for inversion of the best,and to a certain extent to solve the inverse problem encountered. |
