Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to stu...Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.展开更多
In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. ...In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually</span><span style="font-family:"">,</span><span style="font-family:""> the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.展开更多
Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse ...Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.展开更多
文摘Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.
文摘In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually</span><span style="font-family:"">,</span><span style="font-family:""> the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.
基金Supported by the National Natural Science Foundation of China (69983005)
文摘Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.
