With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.T...With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L_(∞)-norm,respectively,where1<γ<2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.展开更多
A new theory for inverse problem of wave equation, that is, the union method for scattered wave extrapolation and velocity imaging, is proposed in this paper. This method is very different from the classical wave extr...A new theory for inverse problem of wave equation, that is, the union method for scattered wave extrapolation and velocity imaging, is proposed in this paper. This method is very different from the classical wave extrapolation for migration, because we relate directly the scattered wave extrapolation to velocity inversion. And also this method is different from any linearized inverse method of wave equation, because we needn′t use linearized approximation. Because of this, the method can be applied to strong scattering case effectively (i.e. the value of scattered wave is not small, which can not be neglected). This method, of course, is different from nonlinearized optimum inverse method, because in this paper, the nonlinear inverse problem is turned into two steps inverse problem, i.e. scattered wave extrapolated and velocity imaging, which can be solved easily. Hence, the problem how to get the global optimum solution by using the nonlinearized optimum inverse method doesn′t bother us by using the method in this paper.展开更多
An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on t...An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.展开更多
An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. Fr...An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. From the function approximation perspective, the OSA method shares the same separable approximation format to the one-way wave operator as other separable approximation methods but it is the only global function approximation among these methods. This leads to a difference in the phase error curve, impulse response, and migration result from other separable approximation methods. The difference is that the OSA method has higher accuracy, and the sensitivity to the velocity variation declines with increasing order.展开更多
This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave （PMMW） imaging. The poor spatial resolution, which is limited by antenna size, should be improved ...This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave （PMMW） imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient （CG） algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.展开更多
Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive p...Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive projected Landweber （APL） super-resolution algorithm using a spectral correction procedure, which attempts to combine the strong points of all of the projected Landweber （PL） iteration and the adaptive relaxation parameter adjustment and the spectral correction method, is proposed. In the algorithm, the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component. Then, the algorithm updates the relaxation parameter adaptively at each iteration. A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer. From experiments, it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error （MSE）. These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.展开更多
When seismic waves propagate through the geological formation,there is a significant loss of energy and a decrease in imaging resolution,because of the viscoacoustic properties of subsurface medium.This profoundly imp...When seismic waves propagate through the geological formation,there is a significant loss of energy and a decrease in imaging resolution,because of the viscoacoustic properties of subsurface medium.This profoundly impacts seismic wavefield propagation,imaging and interpretation.To accurately image the true structure of subsurface medium,the consensus among geophysicists is to no longer treat subsurface medium as ideal homogeneous medium,but rather to incorporate the viscoacoustic properties of subsurface medium.Based on the generalized screen propagator using conventional acoustic wave equation(acoustic GSP),our developed method introduces viscoacoustic compensation strategy,and derives a one-way wave generalized screen propagator based on time-fractional viscoacoustic wave equation(viscoacoustic GSP).In numerical experiments,we conducted tests on two-dimensional multi-layer model and the Marmousi model.When comparing with the acoustic GSP using the acoustic data,we found that the imaging results of the viscoacoustic GSP using the viscoacoustic data showed a significant attenuation compensation effect,and achieved imaging results for both algorithms were essentially consistent.However,the imaging results of acoustic GSP using viscoacoustic data showed significant attenuation effects,especially for deep subsurface imaging.This indicates that we have proposed an effective method to compensate the attenuated seismic wavefield.Our application on a set of real seismic data demonstrated that the imaging performance of our proposed method in local areas surpassed that of the conventional acoustic GSP.This suggests that our proposed method holds practical value and can more accurately image real subsurface structures while enhancing imaging resolution compared with the conventional acoustic GSP.Finally,with respect to computational efficiency,we gathered statistics on running time to compare our proposed method with conventional Q-RTM,and it is evident that our method exhibits higher computational efficiency.In summary,our proposed viscoacoustic GSP method takes into account the true properties of the medium,still achieves migration results comparable to conventional acoustic GSP.展开更多
Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unres...Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unresolved. To describe the seismic wave propagation in media with lateral velocity variations and to image high-angle structures, we propose the generalized screen propagator based on particle swarm optimization （PSO-GSP）, for the precise fitting of the single-square-root operator. We use the 2D SEG/EAGE salt model to test the proposed PSO-GSP migration method to image the faults beneath the salt dome and compare the results to those of the conventional high-order generalized screen propagator （GSP） migration and split-step Fourier （SSF） migration. Moreover, we use 2D marine data from the South China Sea to show that the PSO-GSP migration can better image strong reflectors than conventional imaging methods.展开更多
基金supported by the National Natural Science Foundation of China(grant number 11671081).
文摘With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L_(∞)-norm,respectively,where1<γ<2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.
文摘A new theory for inverse problem of wave equation, that is, the union method for scattered wave extrapolation and velocity imaging, is proposed in this paper. This method is very different from the classical wave extrapolation for migration, because we relate directly the scattered wave extrapolation to velocity inversion. And also this method is different from any linearized inverse method of wave equation, because we needn′t use linearized approximation. Because of this, the method can be applied to strong scattering case effectively (i.e. the value of scattered wave is not small, which can not be neglected). This method, of course, is different from nonlinearized optimum inverse method, because in this paper, the nonlinear inverse problem is turned into two steps inverse problem, i.e. scattered wave extrapolated and velocity imaging, which can be solved easily. Hence, the problem how to get the global optimum solution by using the nonlinearized optimum inverse method doesn′t bother us by using the method in this paper.
基金This research is sponsored by China National Natural Science Foundation （N0. 40474047）.
文摘An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.
基金sponsored by the National Natural Science Foundation of China (Nos. 40774069 and 40974074)the State Key Program of National Natural Science of China (No. 40830424)the National 973program (No. 007209603)
文摘An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. From the function approximation perspective, the OSA method shares the same separable approximation format to the one-way wave operator as other separable approximation methods but it is the only global function approximation among these methods. This leads to a difference in the phase error curve, impulse response, and migration result from other separable approximation methods. The difference is that the OSA method has higher accuracy, and the sensitivity to the velocity variation declines with increasing order.
基金supported partly by the State Key Program of National Natural Science Foundation of China(60632020)the Youth Science Foundation of University of Electronic Science and Technology of China(JX0823).
文摘This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave （PMMW） imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient （CG） algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.
基金the National Natural Science Foundation of China (60632020).
文摘Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive projected Landweber （APL） super-resolution algorithm using a spectral correction procedure, which attempts to combine the strong points of all of the projected Landweber （PL） iteration and the adaptive relaxation parameter adjustment and the spectral correction method, is proposed. In the algorithm, the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component. Then, the algorithm updates the relaxation parameter adaptively at each iteration. A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer. From experiments, it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error （MSE）. These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.
基金financially supported by the National Natural Science Foundation of China (grant Nos.42004103,42374149)Sichuan Science and Technology Program (grant No.2023NSFSC0257)CNPC Innovation Found (2022DQ02-0306)。
文摘When seismic waves propagate through the geological formation,there is a significant loss of energy and a decrease in imaging resolution,because of the viscoacoustic properties of subsurface medium.This profoundly impacts seismic wavefield propagation,imaging and interpretation.To accurately image the true structure of subsurface medium,the consensus among geophysicists is to no longer treat subsurface medium as ideal homogeneous medium,but rather to incorporate the viscoacoustic properties of subsurface medium.Based on the generalized screen propagator using conventional acoustic wave equation(acoustic GSP),our developed method introduces viscoacoustic compensation strategy,and derives a one-way wave generalized screen propagator based on time-fractional viscoacoustic wave equation(viscoacoustic GSP).In numerical experiments,we conducted tests on two-dimensional multi-layer model and the Marmousi model.When comparing with the acoustic GSP using the acoustic data,we found that the imaging results of the viscoacoustic GSP using the viscoacoustic data showed a significant attenuation compensation effect,and achieved imaging results for both algorithms were essentially consistent.However,the imaging results of acoustic GSP using viscoacoustic data showed significant attenuation effects,especially for deep subsurface imaging.This indicates that we have proposed an effective method to compensate the attenuated seismic wavefield.Our application on a set of real seismic data demonstrated that the imaging performance of our proposed method in local areas surpassed that of the conventional acoustic GSP.This suggests that our proposed method holds practical value and can more accurately image real subsurface structures while enhancing imaging resolution compared with the conventional acoustic GSP.Finally,with respect to computational efficiency,we gathered statistics on running time to compare our proposed method with conventional Q-RTM,and it is evident that our method exhibits higher computational efficiency.In summary,our proposed viscoacoustic GSP method takes into account the true properties of the medium,still achieves migration results comparable to conventional acoustic GSP.
基金supported by the 863 Program of China(No.2013AA064201)National Science and Technology Major Project(No.2016ZX05003-003)
文摘Various migration methods have been proposed to image high-angle geological structures and media with strong lateral velocity variations; however, the problems of low precision and high computational cost remain unresolved. To describe the seismic wave propagation in media with lateral velocity variations and to image high-angle structures, we propose the generalized screen propagator based on particle swarm optimization （PSO-GSP）, for the precise fitting of the single-square-root operator. We use the 2D SEG/EAGE salt model to test the proposed PSO-GSP migration method to image the faults beneath the salt dome and compare the results to those of the conventional high-order generalized screen propagator （GSP） migration and split-step Fourier （SSF） migration. Moreover, we use 2D marine data from the South China Sea to show that the PSO-GSP migration can better image strong reflectors than conventional imaging methods.
