Abstract:The Gaussian packet and Gaussian beam methods in the frequency domain have been applied to seismic forward modeling for the past few years. However, Gaussian packet can only model the wave-field excited by Gabor wavelet source; and even though Gaussian beam in the frequency domain can model the wave-field of any source function, it needs lots of Fourier transformations, which is time-consuming. Aiming at the above problems, we propose a new forward modeling method with the space-time Gaussian beam in this paper. Based on unidimensional Gabor decomposition, seismic source function can be decomposed into a series of Gabor wavelet, the wave-field of which can be further decomposed into the space-time Gaussian beam with different emergency angles. According to the property of linear superposition of wave equation, the record at any point of subsurface or topography can be computed by the summation of the space-time Gaussian beams, which have different emergency angles and Gabor wavelets. Through the reconstruction of source wavelet, the proposed method can model the wave-fields of any seismic source, and needs no any Fourier transformations, which enhances the computing efficiency. Besides, its accuracy can be comparable to that obtained by the finite-difference method. Numerical examples of smoothed medium and layered models prove the validity and adaptability of the above conclusions.
Popov M M. A new method of computation of wave fields using Gaussian beams.Wave Motion,1982,4(1):85-97.
[2]
Popov M M.A new method of computing wave fields in the high-frequency approximation. Journal of Soviet Mathematics, 1982,20(1):1869-1882.
[3]
Cěrvený V,Popov M M,Pšen?ík I.Computation of wave fields in inhomogeneous media-Gaussian beam approach. Geophysical Journal International,1982,70(1):109-128.
[4]
Cěrvený V.Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method. Geophysical Journal International,1983,73(2): 389-426.
[5]
Cerveny V.Gaussian beam synthetic seismograms.Journal of Geophysical Research-Atmospheres, 1985, 58(1-3):44-72.
[6]
Klimeš L.Gaussian packets in the computation of seismic wavefields.Geophysical Journal International,1989,99(2):421-433.
[7]
Geng Y,Wu R S,Gao J.Efficient Gaussian packets representation and seismic imaging.SEG Technical Program Expanded Abstracts,2011,30:3398-3403.
Li Hui, Feng Bo, Wang Huazhong.A new wave field modeling method by using Gaussian packets.GPP, 2012, 51(4):327-337.
[9]
Hill N R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[10]
Hill N R.Prestack Gaussian-beam depth migration.Geophysics,2001,66(4):1240-1250.
[11]
Gray S H.Gaussian beam migration of common-shot records.Geophysics,2005,70(4):S71-S77.
[12]
Gray S H,Bleistein N.True-amplitude Gaussian-beam migration.Geophysics,2009,74(2):S11-S23.
[13]
Popov M M,Kachalov A P,Kachalov S A et al.Migration with Gaussian beams.9th International Congress of the Brazilian Geophysical Society,2005.
[14]
Popov M M,Semtchenok N M,Popov P M et al.Reverse time migration with Gaussian beams and velocity analysis applications.70th EAGE Conference & Exhibition,Rome Italy,2008.
[15]
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.
[16]
Popov M M.Summation of space-time Gaussian beams in problems of propagation of wave packets.Journal of Soviet Mathematics,1990, 50(6):2032-2043.
[17]
Popov M M.Summation of space-time Gaussian beams in problems of propagation of wave packets.Journal of Mathematical Sciences,1990,50(6):2032-2043.
[18]
Katchalov A P,Popov M M.Gaussian beam methods and theoretical seismograms.Geophysical Journal International,1988, 93(3):465-475.