Abstract：When perturbed model is described with Gabor frames,the scatter waves can be calculated with Gaussian beam in the frequency domain or Gaussian packet in the time domain.For this case the precondition is that signals of the incident background wave-field should be short-duration in the time domain and broad-band in the frequency domain.With the above-mentioned modeling method an effective scatterer imaging algorithm is put forward.A common-shot-gather is decomposed with characteristic Gaussian packet firstly.All of the Gaussian packets that describe the common-shot-gather are back-propagated and projected into the model domain independently.The final scatterer is obtained by integrating all of the Gabor-scatterers that projected from Gaussian packets.One of the scatterer imaging method's key points is how to project Gaussian packet into the model domain.The scatterer imaging method is composed by 3 parts of the imaging algorithm,the projection theory from a Gaussian packet to a Gabor-scatterer,and the back-propagation scheme of Gaussian packet.The proposed scatterer imaging method gives the image that has the dimension in the model domain.Gaussian packet shares higher efficiency and better flexibility compared with wave equation.The accuracy of the proposed scatterer inversion method is tested and analyzed with a single Gabor-scatterer model in the numerical experiment.The scatterer inversion scheme is also applied in synthetic models and promising results is presented.Both of the experiments show that the proposed method shares high efficiency,and the algorithm is suitable for general models.
李辉, 殷俊锋, 王华忠, 刘守伟, 刘太臣. 高斯波包散射体成像方法[J]. 石油地球物理勘探, 2017, 52(2): 273-282.
Li Hui, Yin Junfeng, Wang Huazhong, Liu Shouwei, Liu Taichen. A scatterer imaging method based on Gaussian packet. OGP, 2017, 52(2): 273-282.
Fu Jiyou,Li Zhenchun,Yang Guoquan et al. Wave equation reflection travel-time inversion in acoustic media. OGP,2015,50(6):1134-1140.
[5]
Li H,Wang H Z,and Yin J F. Background velocity model building with Gaussian packet reflection traveltime inversion. 80th EAGE Annual International Meeting Extended Abstracts,2016.
[6]
Zhou H B,Amundsen L,Zhang G. Fundamental issues in full waveform inversion. SEG Technical Program Expanded Abstracts,2012,31:1-5.
[7]
Claerbout J F. Toward a unified theory of reflector mapping. Geophysics,1971,36(3):467-481.
[8]
Chang W,McMechan G A. Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,1986,51(1):67-84.
[9]
Cohen J K,Bleistein N. An inverse method for determining small variations in propagation speed. SIAM Journal on Applied Mathematics,1977,32(4):784-799.
[10]
Bleistein N,Cohen J K. Direct inversion procedure for Claerbout's equations. Geophysics,1979,44(6):1034-1040.
[11]
Bleistein N,Cohen J K,Hagin F G. Two and one-half dimensional Born inversion with an arbitrary reference. Geophysics,1987,52(1),26-36.
[12]
Beylkin G,Burridge R.Linearized inverse scattering problems in acoustics and elasticity. Wave Motion,1990,12(1):15-52.
[13]
Plessix R E,Mulder W A. Frequency-domain finite-difference amplitude-preserving migration. Geophysical Journal International,2004,157(3):975-987.
Chen Yunfeng,Wang Huazhong,Ren Haoran et al. Matrix representation of least square prestack migration based on linearization. OGP,2014,49(6):1091-1096.
[15]
胡江涛. 最小二乘逆时偏移及角度道集提取方法研究[学位论文]. 上海:同济大学,2015.
[16]
Klimeš L. Sensitivity of seismic waves to structure. Studia Geophysica et Geodaetica,2012,56(2):483-520.
Li Hui,Wang Huazhong. A scattering wave modeling method using Gaussian beam and Gaussian packet in the Gabor domain. Chinese Journal of Geophysics,2015,58(4),1317-1332.
[18]
?ervený V,Popov M M,Psencik I.Computation of wave fields in inhomogeneous media-Gaussian beam approach. Geophysical Journal Royal Astronomical Society,1982,70(1):109-128.
[19]
Popov M M. A new method of computation of wave fields using Gaussian beams. Wave motion,1982,4(1):85-97.
[20]
Ralston J.Gaussian beams and the propagation of singularities:Studies in partial differential equations. MAA Studies in Mathematics,1983,23(1):206-248.
Li Hui,Wang Huazhong,Feng Bo et al. Efficient pre-stack depth migration method using characteristic Gaussian packets. Chinese Journal of Geophysics,2014,57(7):2258-2268.
[23]
?ervený V. Seismic Ray Theory. Cambridge University Press,Cambridge,2001,417-419.
[24]
de Bruin C G M,Wapenaar C P A,Berkhout A J. Angle dependent reflectivity by means of prestack migration. Geophysics,1990,55(9):1223-1234.
[25]
Zhu X,McMechan G A. Stretch-free migration imaging condition. Geophysics,2013,78(4):1-8.
