几种单程波动方程解法的对比
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摘要
在均匀介质条件下,比较了ω-k域内Stolt算法和Gazdag相移法、t-x域内部分分式算法、混合域内SSF算法和FFD算法的计算流程,零炮间距叠后时间偏移的单位脉冲响应、脉冲振幅变化、中心地震道数据的子波振幅变化和脉冲波场频谱特征等体现了波场动力学特性的信息。分析表明,在均匀介质条件下,ω-k域方法在脉冲响应、振幅变化和频谱特征方面能得到较好的结果,但该方法的子波分辨率相对其他方法较低,无法应用于横向速度变化介质问题,所以复杂地质问题应采用FFD法进行处理。同时以Stolt算法为例具体分析了子波振幅、子波频谱在偏移过程中的变化。
The authors compare the calculation processes of Stolt method and Gazdag phase—shift method in ω—k domain,partial fraction method in t—x domain and SSF and FFD methods in complex domain under uniform medium condition.The impulse response of post-stack time migration in the zero offset,impulse amplitude change,wavelet amplitude change of centre seismic trace data and spectral characteristics of impulse wave all express the wave field dynamics characteristics.The analysis reflects that the methods in ω—k domain under uniform medium condition have good results in impulse response、amplitude change and spectral characteristics,but the wavelet resolution is worse than other methods and can not applied in the media of lateral velocity variation,so that the method of FFD is better for complex geological problems.Meanwhile,the variation of wavelet amplitude and spectrum in offset process have been analyzed taking Stolt as an example.
The authors compare the calculation processes of Stolt method and Gazdag phase—shift method in ω—k domain,partial fraction method in t—x domain and SSF and FFD methods in complex domain under uniform medium condition.The impulse response of post-stack time migration in the zero offset,impulse amplitude change,wavelet amplitude change of centre seismic trace data and spectral characteristics of impulse wave all express the wave field dynamics characteristics.The analysis reflects that the methods in ω—k domain under uniform medium condition have good results in impulse response、amplitude change and spectral characteristics,but the wavelet resolution is worse than other methods and can not applied in the media of lateral velocity variation,so that the method of FFD is better for complex geological problems.Meanwhile,the variation of wavelet amplitude and spectrum in offset process have been analyzed taking Stolt as an example.
引文
[1]Zhang Y,Zhang G Q,Norman B.Theory of true ampli-tude one-way wave operator[J].Institute of PhysicsPublishing,2003,19(3):1113-1118.
[2]Gazdag J.Wave-equation migration with the phase-shiftmethod[J].Geophysics,1978,43:1342-1351.
[3]Stolt R H.Migration by Fourier transform[J].Geophys-ics,1978,43:23-48.
[4]Claerbout J F.Imaging the earth s interior[M].Oxford:Blackwell Scientific Publications,1985:4-30.
[5]Stoffa P L,Fokkema J T,Luna F,et al.Split-step Fou-rier migration[J].Geophysics,1990,55:410-421.
[6]Ristow D,Ruhl T.Fourier finite-difference migration[J].Geophysics,1994,59:1882-1893.
[7]Berkhout AJ.Ware field extrapolation techniques in seis-mic migration[J].Geophysics,1981,46:1638-1656.
[8]李世雄.波动方程的高频近似与辛几何[M].北京:科学出版社,2001:80-120.LI Shi-xiong.Approximate of wave equation in the high-frequency and symplectic[M].Beijing:Science Press,2001:80-120.
[9]Myung W L,Sang Y S.Optimization of one-way wave e-quations[J].Geophysics,1985,50:1634-1637.
[10]马在田.地震成像技术有限差分法偏移[M].北京:石油工业出版社,1989:121-143.MA Zai-tian.Finite-difference migration in seismic ima-ging technology[M].Beijing:Petroleum IndustryPress,1989:121-143.
[11]Zhang Y,Zhang G,Bleistein N.Theory of true ampli-tude one-way wave equations and true amplitude com-mon-shot migration[J].Geophysics,2005,70(3):1-10.
[12]陈胜昌,曹进忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J].地球物理学进展,2003,18(2):210-217.CHEN Sheng-chang,CAO Jin-zhong,MA Zai-tian.Mixed-domain one-way wave propagator and its applica-tion in migration image[J].Progress in Geophysics,2003,18(2):210-217.
[13]郑海山.地震偏移技术研究进展[J].世界地质,2000,19(4):392-395.ZHENG Hai-shan.Study development of seismic mirga-tion[J].World Geology,2000,19(4):392-395.
[14]刘军,侯平,魏茂林.地震波动力学参数在砂体预测中的应用[J].世界地质,2002,21(2):185-188.LIU Jun,HOUPing,WEI Mao-lin.Application of seis-mic dynamic parameters in sandstone prediction[J].World Geology,2002,21(2):185-188.
[15]谢忠求.浅层地震探测技术应用中的分辨率问题[J].矿产与地质,1999,70(13):112-116.XIE Zhong-qiu.Resolution problems about the applica-tion of shallowseismic prospecting technique[J].Min-eral Resources and Geology,1999,70(13):112-116.
[2]Gazdag J.Wave-equation migration with the phase-shiftmethod[J].Geophysics,1978,43:1342-1351.
[3]Stolt R H.Migration by Fourier transform[J].Geophys-ics,1978,43:23-48.
[4]Claerbout J F.Imaging the earth s interior[M].Oxford:Blackwell Scientific Publications,1985:4-30.
[5]Stoffa P L,Fokkema J T,Luna F,et al.Split-step Fou-rier migration[J].Geophysics,1990,55:410-421.
[6]Ristow D,Ruhl T.Fourier finite-difference migration[J].Geophysics,1994,59:1882-1893.
[7]Berkhout AJ.Ware field extrapolation techniques in seis-mic migration[J].Geophysics,1981,46:1638-1656.
[8]李世雄.波动方程的高频近似与辛几何[M].北京:科学出版社,2001:80-120.LI Shi-xiong.Approximate of wave equation in the high-frequency and symplectic[M].Beijing:Science Press,2001:80-120.
[9]Myung W L,Sang Y S.Optimization of one-way wave e-quations[J].Geophysics,1985,50:1634-1637.
[10]马在田.地震成像技术有限差分法偏移[M].北京:石油工业出版社,1989:121-143.MA Zai-tian.Finite-difference migration in seismic ima-ging technology[M].Beijing:Petroleum IndustryPress,1989:121-143.
[11]Zhang Y,Zhang G,Bleistein N.Theory of true ampli-tude one-way wave equations and true amplitude com-mon-shot migration[J].Geophysics,2005,70(3):1-10.
[12]陈胜昌,曹进忠,马在田.混合域单程波传播算子及其在偏移成像中的应用[J].地球物理学进展,2003,18(2):210-217.CHEN Sheng-chang,CAO Jin-zhong,MA Zai-tian.Mixed-domain one-way wave propagator and its applica-tion in migration image[J].Progress in Geophysics,2003,18(2):210-217.
[13]郑海山.地震偏移技术研究进展[J].世界地质,2000,19(4):392-395.ZHENG Hai-shan.Study development of seismic mirga-tion[J].World Geology,2000,19(4):392-395.
[14]刘军,侯平,魏茂林.地震波动力学参数在砂体预测中的应用[J].世界地质,2002,21(2):185-188.LIU Jun,HOUPing,WEI Mao-lin.Application of seis-mic dynamic parameters in sandstone prediction[J].World Geology,2002,21(2):185-188.
[15]谢忠求.浅层地震探测技术应用中的分辨率问题[J].矿产与地质,1999,70(13):112-116.XIE Zhong-qiu.Resolution problems about the applica-tion of shallowseismic prospecting technique[J].Min-eral Resources and Geology,1999,70(13):112-116.
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