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According to the least square criterion of minimizing the misfit between modeled and observed data,this paper provides a preconditioned gradient method to invert the visco-acoustic velocity structure on the basis of using sparse matrix LU factorization technique to directly solve the visco-acoustic wave forward problem in space-frequency domain.Numerical results obtained in an inclusion model inversion and a layered homogeneous model inversion demonstrate that different scale media have their own frequency responses,and the strategy of using low-frequency inverted result as the starting model in the high-frequency inversion can greatly reduce the non-uniqueness of their solutions.It can also be observed in the experi-ments that the fast convergence of the algorithm can be achieved by using diagonal elements of Hessian matrix as the pre-conditioned operator,which fully incorporates the advantage of quadratic convergence of Gauss-Newton method.
According to the least square criterion of minimizing the misfit between modeled and observed data, this paper provides a preconditioned gradient method to invert the visco-acoustic velocity structure on the basis of using sparse matrix LU factorization technique to directly solve the visco-acoustic wave forward problem in space-frequency domain. Numerical results obtained in an inclusion model inversion and a layered homogeneous model inversion demonstrate that different scale media have their own frequency responses, and the strategy of using low-frequency inverted results as the starting model in the high- frequency inversion can greatly reduce the non-uniqueness of their solutions. It can also be observed in the experi-ments that the fast convergence of the algorithm can be achieved by using diagonal elements of Hessian matrix as the pre-conditioned operator, which fully incorporates the advantage of quadratic convergence of Gauss-Newton method.