| In the vigorous development of geophysics for decades,seismic exploration is an indispensable part.It needs to deeply study the propagation of seismic waves in underground unknown media.The structure of underground media has very complex properties.The wave equation inversion method can properly use the characteristics of seismic wave field dynamics to identify the parameters of underground media.Therefore,this paper takes the wave equation as the mathematical model.The inversion of the wave equation needs the forward modeling of the wave equation as an important part.The results can be used to simulate the real situation underground.Therefore,the research of this paper has application value.Firstly,this paper introduces the basic theory of inverse problems in mathematical physics,the theory and research progress of wave equation inversion method and multi-scale method,and introduces the basic theoretical knowledge required in this paper in detail.Then,the trust region algorithm is used to solve the inversion problem,and some improvements are made,that is,in the process of numerical simulation,the velocity value of the boundary is assigned,the gradient and Jacob matrix of the objective function value are obtained by the secant method,and the regularization parameters are adjusted to half of the original each time in each iteration,The improved single-scale trust region algorithm is better applied to the model in this paper.The single-scale trust region inversion algorithm is combined with the multi-scale method,that is,the iteration is carried out in the double grid.Firstly,the single-scale trust region inversion algorithm is used to iterate on the fine grid,in order to smooth the initial solution as much as possible and limit the obtained solution to the coarse grid by using the restriction operator,Continue to use the single-scale trust region inversion algorithm iteration to obtain the approximate solution on the coarse grid.The change of the solution on the coarse grid is interpolated to the fine grid by the interpolation operator.The purpose of the coarse grid iteration is to make the correction solution fall within the field of the optimal solution.Finally,use the single-scale trust region inversion algorithm iteration on the fine grid to get the correction solution closer to the optimal solution.In this paper,the two inversion algorithms are used to simulate the wave equation in the case of single anomaly,multi anomaly and three-layer medium.Through the analysis of the inversion numerical results,it shows that the single-scale trust region inversion algorithm and multi-scale trust region inversion algorithm are feasible and adaptive. |
