逆散射级数法预测层间多次波的算法改进及其策略
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摘要
波动方程预测层间多次波有两类算法.一是由Berkhout和Verschuur(1998)提出的基于CFP(共聚焦点)延拓的算法,另一是由Weglein(1997)等人提出的基于逆散射级数法的算法.ISS(逆散射级数)算法具有不依赖速度模型的优点,但是其计算成本很高.本文改进了Weglein提出的1-D预测公式,提高了计算效率.从理论方面。改进算法的计算速度提高了大约12倍.实际结果表明其计算速度更快,提高近80倍左右,主要原因在于后者的空间复杂度小.此外,由于时间-空间域比伪深度-波数域的层间多次波预测有更多的优点,本文推导了1.5-D时间-空间域ISS层间多次波预测算法,该算法有计算速度快、预测噪音小、适应观测系统能力强和不依赖地震子波等优点.在实际应用中,计算成本高是ISS预测层间多次波算法的主要障碍.因此,本文还讨论了预测层间多次波的策略.结合本文提出的改进算法和应用策略,能够在实际地震资料处理中较好地应用ISS预测层间多次波.
There are two wave-equation methods to attenuate internal multiples.One is CFP (common focus point)continuation method which is proposed by Berkhout and Verschuur (1998).The other is ISS(inverse scattering series)method which is proposed by Weglein etc. (1997).ISS method is independent of velocity.But the computing cost is very high.Firstly,we deduce a new algorithm based on the 1D ISS predicting formula given by Weglein et al.The new algorithm is about 12 times more efficient than the old algorithm in theory.Actually testing result shows that it is faster,nearly 80 times.In addition,internal multiple prediction in temporal spatial domain has more advantages than in pseudo-depth wavenumber domain.We deduce 1.5D ISS predicting formulation in temporal spatial domain from the 2D ISS formulation given by Weglein et al.The new formulation has some important merits,for example,high computing efficiency,little predicting noise,easiness to suit to geometry and independence of seismic wavelet.It is difficult to use old ISS algorithm to predict internal multiples of field data because of high computing cost.Based on the modified algorithm,we discuss the strategy of internal multiple prediction to make it usable on field data.
There are two wave-equation methods to attenuate internal multiples.One is CFP (common focus point)continuation method which is proposed by Berkhout and Verschuur (1998).The other is ISS(inverse scattering series)method which is proposed by Weglein etc. (1997).ISS method is independent of velocity.But the computing cost is very high.Firstly,we deduce a new algorithm based on the 1D ISS predicting formula given by Weglein et al.The new algorithm is about 12 times more efficient than the old algorithm in theory.Actually testing result shows that it is faster,nearly 80 times.In addition,internal multiple prediction in temporal spatial domain has more advantages than in pseudo-depth wavenumber domain.We deduce 1.5D ISS predicting formulation in temporal spatial domain from the 2D ISS formulation given by Weglein et al.The new formulation has some important merits,for example,high computing efficiency,little predicting noise,easiness to suit to geometry and independence of seismic wavelet.It is difficult to use old ISS algorithm to predict internal multiples of field data because of high computing cost.Based on the modified algorithm,we discuss the strategy of internal multiple prediction to make it usable on field data.
引文
[1]Berkhout A J,Versehuur D J.Estimation of multiple scattering by iterative inversion,part I:theoretical considerations.Geophysics,1997,62(5):1586～1595
[2]Weglein A B,Gasparotto F A,Carvalho P M,et al.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62:1975～1989
[3]Moses H E.Calculation of scattering potential from reflection coefficients.Phys.Rev.,1956,102:559～567
[4]Razavy M.Determination of the wave velocity in an inhomogeneous medium from reflection data.J.Acoust.Soc. Am.,1975,58:956～963
[5]Stolt R H,Jacobs B.Inversion of seismic data in a laterally heterogeneous medium.SEP Rep.,1980,24:135～152
[6]Carvalho P M,Weglein A B,Stolt R H.Examples of a nonlinear inversion method based on the T matrix of scattering theory:application on multiple suppression.61st Ann.Int.SEG Mtg.,1991,319～322(Expanded Abstracts)
[7]Carvalho P M,Weglein A B,Stolt R H.Nonlinear inverse scattering for multiple suppression:application to real data: partⅠ.62nd Ann.Int.SEG Mtg.,1992,1093～1095 (Expanded Abstracts)
[8]Matson K.The relationship between scattering theory and the primaries and multiples of reflection seismic data.J. Seism.Explor.,1996,5:63～78
[9]Aráujo F V,Weglein A B,Carvalho P M,et al.Internal multiple attenuation.56th Meeting of Association of Exploration Geophysicists,Session H036,1994
[10]Malcolm A E,de Hoop M V.A method for inverse scattering based on the generalized Bremmer coupling series.Submitted to Inverse Problems,CWP-486.2005
[11]Weglein A B,Matson K.Inverse-scattering interval multiple attenuation:an analytic example and subevent interpretation. Mathematical Methods in Geophysical Imaging(Proc.SPIE vol.3453)ed Hassanzadeh S(Bellingham,WA:SPIE), 1998.1008～1017
[2]Weglein A B,Gasparotto F A,Carvalho P M,et al.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62:1975～1989
[3]Moses H E.Calculation of scattering potential from reflection coefficients.Phys.Rev.,1956,102:559～567
[4]Razavy M.Determination of the wave velocity in an inhomogeneous medium from reflection data.J.Acoust.Soc. Am.,1975,58:956～963
[5]Stolt R H,Jacobs B.Inversion of seismic data in a laterally heterogeneous medium.SEP Rep.,1980,24:135～152
[6]Carvalho P M,Weglein A B,Stolt R H.Examples of a nonlinear inversion method based on the T matrix of scattering theory:application on multiple suppression.61st Ann.Int.SEG Mtg.,1991,319～322(Expanded Abstracts)
[7]Carvalho P M,Weglein A B,Stolt R H.Nonlinear inverse scattering for multiple suppression:application to real data: partⅠ.62nd Ann.Int.SEG Mtg.,1992,1093～1095 (Expanded Abstracts)
[8]Matson K.The relationship between scattering theory and the primaries and multiples of reflection seismic data.J. Seism.Explor.,1996,5:63～78
[9]Aráujo F V,Weglein A B,Carvalho P M,et al.Internal multiple attenuation.56th Meeting of Association of Exploration Geophysicists,Session H036,1994
[10]Malcolm A E,de Hoop M V.A method for inverse scattering based on the generalized Bremmer coupling series.Submitted to Inverse Problems,CWP-486.2005
[11]Weglein A B,Matson K.Inverse-scattering interval multiple attenuation:an analytic example and subevent interpretation. Mathematical Methods in Geophysical Imaging(Proc.SPIE vol.3453)ed Hassanzadeh S(Bellingham,WA:SPIE), 1998.1008～1017
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