Research On Direction And Inversion Methods Of Wave Equation Based On Genetic Algorithm

It is very important to study the propagation of waves in underground media in geological exploration.Wave distribution can be understood well by constantly updating and advancing current theories and methods.The research of two-dimensional wave equation has been widely applied in many fields.The wave equation forward modeling process and numerical inversion algorithm is of important theoretical significance and practical application value.This paper mainly studies the propagation law and characteristics of wave equation in inversion and analysis of the forward modeling and inversion algorithm with the mathematical model of two-dimensional wave equation as a research problems.Firstly,this paper briefly introduces the research background of wave equation,mainly introduces the research progress of numerical inversion method of wave equation,and describes the main difficulties in solving the inverse problem of wave equation.Secondly,this paper introduces the basic theory of genetic algorithm,including the principle of the algorithm and the applied operator,the operation process of the algorithm and the theoretical research and application value of the algorithm,and analyzes the advantages and disadvantages of the genetic algorithm.Besides,in this paper,the finite difference method is used to discrete the mathematical model of the two-dimensional wave equation.The explicit calculation format of equation is received.Various boundary conditions are handled and the corresponding forward numerical simulation of the two-dimensional wave equation are carried out.The resulting error between them is compared and analyzed.Finally,this paper proposes to use the genetic algorithm to solve the velocity inversion problem of two-dimensional wave equation,and improves the basic genetic algorithm accordingly,and designs the algorithm to solve the velocity inversion problem.The numerical simulation results follows show that the genetic algorithm can converge to the global optimal solution faster than the traditional inversion algorithm.To verify the feasibility,validity and stability of the proposed inversion algorithm in practical application,three-layer structure model and single anomalous body model are selected to simulate the velocity inversion of two-dimensional wave equation.The simulation results indicate the feasibility and efficiency of the algorithm and that the genetic algorithm has the best velocity inversion effect for solving two-dimensional wave equation,which solves the problems encountered in the inversion calculation to a certain extent.