Adaptive Choice Strategy Of Regularization Parameter For Wave Equation Inversion

Geophysical inverse problem has been a hot research subject as an edge discipline abstracted from the practice.Inverse problem of two-dimensional wave equation is studied in this paper as one of its branch.Since the most inverse problems may be ill-posed,there are a lot of difficulties in the actual solution process.Therefore,further study in inverse problem of wave equation has profound theoretical significance and broad application prospects.In this paper,owing to the characteristics of the wave equation,the two-dimensional elastic wave equation is selected as mathematical model.After the model is discreted with finite difference method,the regular processing is used for this nonlinear problem.Because the measured data has noise,an efficient model function approach without requiring knowledge of the noise level is proposed when a regularization parameters for wave equation is choosed.The approach only need to compute the residual and regularized solution norm,and the regularization parameter is updated iteratively.Compared with the traditional iterative method,it not only effectively avoids the problem that convergence is strongly dependent on select of the initial values,but also reduces cost of computation and ensures the convergence of the algorithm.To test the feasibility,efficiency and stability of the algorithm,we carry out numerical simulation to inverse parameters of two-dimensional elastic wave equation on a three-layer medium model.And the superiority of the algorithm proposed in this paper is shown by comparing separately with heuristics and L-curve method in chosen regularization parameter.The numerical simulation results robustly indicated feasibility and effect of the algorithm,which solve some difficulty in inversion to some extent.