The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi...The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational resources than the gradient method.展开更多
Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the one...Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the ones of virtual images in real mode(VIRM).The real images in real mode are the same as the conventional integral images.The virtual images in real mode are obtained by changing the coordinates of the corresponding points in elemental images which can be reconstructed by the lens array in virtual space.In order to reduce the spot size of the reconstructed images,the diffuser in conventional integral imaging is given up in the proposed method.Then the spot size is nearly1/20 of that in the conventional system.And an optical integral imaging system is constructed to confirm that our proposed method opens a new way for the application of the passive 3D display technology.展开更多
基金supported by the Open Foundation of Engineering Research Center of Nuclear Technology Application,Ministry of Education(No.HJSJYB2017-7)the Science and Technology Research project of the Jiangxi Provincial Education Department(No.GJJ170481)the National Natural Science Foundation of China(No.41874126)。
文摘The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational resources than the gradient method.
基金supported by the National Natural Science Foundation of China(No.11474169)
文摘Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the ones of virtual images in real mode(VIRM).The real images in real mode are the same as the conventional integral images.The virtual images in real mode are obtained by changing the coordinates of the corresponding points in elemental images which can be reconstructed by the lens array in virtual space.In order to reduce the spot size of the reconstructed images,the diffuser in conventional integral imaging is given up in the proposed method.Then the spot size is nearly1/20 of that in the conventional system.And an optical integral imaging system is constructed to confirm that our proposed method opens a new way for the application of the passive 3D display technology.
