Band-limited local plane wave propagator and migration
Liu Shaoyong1,2, Han Bingkai1,2, Gu Hanming1,2, Song Guiqiao3
1. Institute of Geophysics and Geomatics, China University of Geosciences(Wuhan), Wuhan, Hubei 430074, China; 2. Hubei Subsurface Multi-scale Imaging Key Laboratory, Wuhan, Hubei 430074, China; 3. Exploration & Development Department, SINOPEC, Beijing 100728, China
Abstract：The seismic signal is a kind of band-limited signal,and it limits the application of ray-based operators to seismic wave propagation and migration under the infinite high-frequency approximation.With the framework of conventional ray theory,this paper proposes a band-limited local plane wave propagator.Characterized by local space linearity and implementation flexibility,the propagator can effectively perform band-limited seismic wavefield propagation and migration.Based on the propagation characteristics of high-frequency rays between intervals,the band-limited Snell's law is obtained for the central ray propagation with the relationship between the first Fresnel zone and the frequency band of signals.Then,the band-limited local plane wave propagator can be built with paraxial approximation under the local plane wave assumption.Finally a band-limited beam migration method is developed.Numerical experiments demonstrate that the band-limited beams have better illumination in ray-shadow areas and are beneficial to improve the imaging resolution in complex structures.
Babich V M and Buldyrev V S.Asymptotic Methods in Problems of Diffraction of Short Waves.Nauka,Moscow,1972.
[2]
Woodward M J.Wave-equation tomography.Geo-physics,1992,57(1):15-26.
[3]
Biondi B.Solving the frequency dependent eikonal equation.SEG Technical Program Expanded Abstracts,1992,11:1315-1319.
[4]
Hogan C M,Margrave G F.Ray-tracing and eikonal solutions for low-frequency wavefields.CREWES Research Report,2007.
[5]
Foreman T.A Frequency Dependent Ray Theory[D].The University of Texas at Austin,1987.
[6]
Protasov M,Gadylshin K.Exact frequency dependent rays on the basis of Helmholtz solver.SEG Technical Program Expanded Abstracts,2015,34:3739-3743.
[7]
Lomax A.The wavelength-smoothing method for approximating broad-band wave propagation through complicated velocity structures.Geophysical Journal International,1994,117(2):313-334.
[8]
Lomax A,Snieder R.Estimation of finite-frequency waveforms through wavelength-dependent averaging of velocity.Geophysical Journal International,1996,126(2):369-381.
[9]
Protasov M I,Yarman C E,Nichols D et al.Frequency-dependent ray-tracing through rugose interfaces.SEG Technical Program Expanded Abstracts,2011,30:2992-2996.
[10]
Protasov M I,Osypov K S.Frequency dependent ray tracing for irregular boundaries.Seismic Technology,2014,11(3):1-11.
[11]
Yarman C E,Cheng X,Osypov K et al.Band-limited ray tracing.Geophysical Prospecting,2013,61(6):1194-1205.
[12]
Červený V,Popov M M,Psencik I.Computation of wave fields in inhomogeneous media-Gaussian beam approach.Geophysical Journal International,1982,70(1):109-128.
[13]
Hill N R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[14]
Hill N R.Prestack Gaussian-beam depth migration.Geophysics,2001,66(4):1240-1250.
[15]
Hale D.Migration by the Kirchhoff,slant stack,and Gaussian beam methods.CWP Annual Project Review Meeting,Colorado,1992.
[16]
Gray S H.Gaussian beam migration of common-shot records.Geophysics,2005,70(1):953-959.
[17]
邓飞,刘超颖,赵波等.高斯射线束正演与偏移.石油地球物理勘探,2009,44(3):265-269.Deng Fei,Liu Chaoying,Zhao Bo et al.Gaussian beams forward simulation and migration.OGP,2009,44(3):265-269.
[18]
李振春,岳玉波,郭朝斌等.高斯波束共角度保幅深度偏移.石油地球物理勘探,2010,43(3):360-365.Li Zhenchun,Yue Yubo,Guo Chaobin et al.Gaussian beam common angle preserved-amplitude migration.OGP,2010,45(3):360-365.
[19]
Zhu T,Gray S H,Wang D.Prestack Gaussian-beam depth migration in anisotropic media.Geophysics,2007,72(3):S133-S138.
[20]
韩建光,王赟,张晓波等.VTI介质高斯束叠前深度偏移.石油地球物理勘探,2015,50(2):267-273.Han Jianguang,Wang Yun,Zhang Xiaobo et al.Gaussian beam prestack depth migration in VTI media.OGP,2015,50(2):267-273.
[21]
刘强,张敏,李振春等.各向异性介质共炮域高斯束偏移.石油地球物理勘探,2016,51(5):930-937.Liu Qiang,Zhang Min,Li Zhenchun et al.Common-shot domain Gaussian beam migration in anisotropic media.OGP,51(5):930-937.
[22]
代福材,黄建平,李振春等.角度域黏声介质高斯束叠前深度偏移方法.石油地球物理勘探,2017,52(2):283-293.Dai Fucai,Huang Jianping,Li Zhenchun et al.Angle domain prestack Gaussian beam migration for visco-acoustic media.OGP,2017,52(2):283-293.
[23]
Hu C S,Stoffa P L.Slowness-driven Gaussian-beam prestack depth migration for low-fold seismic data.Geophysics,2009,74(6):WCA35-WCA45.
[24]
Liu J,Palacharla G.Multiarrival Kirchhoff beam migration.Geophysics,2011,76(5):WB109-WB118.
[25]
Bube K P,Washbourne J K.Wave tracing:Ray tracing for the propagation of band-limited signals:Part 1-Theory.Geophysics,2008,73(5):VE377-VE384.
[26]
Washbourne J K,Bube K P,Carillo P et al.Wave tra-cing:Ray tracing for the propagation of band-limited signals:Part 2-Applications.Geophysics,2008,73(5):VE385-VE393.
[27]
Gray S H,Xie Y,Notfors C et al.Taking apart beam migration.The Leading Edge,2009,28(9):1098-1108.
[28]
Elad M.Sparse and Redundant Representations:from Theory to Applications in Signal and Image Processing.Springer Science & Business Media,2010.
[29]
Liu S Y,Gu H and Feng B.Characteristic wave imaging in TTI media via compressed sensing.SEG Technical Program Expanded Abstracts,2016,35:4424-4429.
[30]
Schneider W A.Integral formulation for migration in two and three dimensions.Geophysics,1978,43(1):49-76.
[31]
Popov M M,Semtchenok N M,Popov P M et al.Depth migration by the Gaussian beam summation method.Geophysics,2010,75(2):S81-S93.
