慢度法全波场模拟及其水平慢度积分的实现
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摘要
叠前地震数据的反演需要以某种正演算法为基础。本文从弹性动力学方程出发,采用慢度法计算层状介质的叠前地震记录。同反射率法一样,慢度法也能够提供地震波场的完全解,包括地震波在地层中传播时形成的一次波、多次波和转换波信息,而且其中间结果容易解释。具体实现步骤为:①通过傅立叶变换和汉克尔交换将本构方程和弹性动力学方程变换到频率-慢度域;②在频率-慢度域得到反射、透射系数矩阵递推公式;③分别对频率和慢度进行积分变换得到时-空域的地震道集。文中还讨论了慢度积分计算中解的稳定性问题。
The inversion of pre-stack seismic data necds to take some forward algorithms as a basis. Start-ing from elastic dynamic equations, the paper adopted slovvness method to compute the pre-stack seismic records in layered medium. The slovvness method can provide the complete solu-tion for seismic wavefield like reflectivity method , including the information of primary reflection, multiple and converted wave resulted from propa-gation of seismic wave in beds and inlermediate results can be easily interpreted. The concrete steps of realization is as follows:①the constitu-tive equations and elastic dynamic equations are transformed into frequency-slowness domain by Fourier transform and Hankel transform;②the recursive formulas of reflectivity and transmissivi-ty matrixes are resulted in frequency-slowness domain;③the seismic data gathers can be resulted from integral transformation for frequency and slovvness separately. The stability problem on so-lution in computing slowness is also discussed in the paper.
The inversion of pre-stack seismic data necds to take some forward algorithms as a basis. Start-ing from elastic dynamic equations, the paper adopted slovvness method to compute the pre-stack seismic records in layered medium. The slovvness method can provide the complete solu-tion for seismic wavefield like reflectivity method , including the information of primary reflection, multiple and converted wave resulted from propa-gation of seismic wave in beds and inlermediate results can be easily interpreted. The concrete steps of realization is as follows:①the constitu-tive equations and elastic dynamic equations are transformed into frequency-slowness domain by Fourier transform and Hankel transform;②the recursive formulas of reflectivity and transmissivi-ty matrixes are resulted in frequency-slowness domain;③the seismic data gathers can be resulted from integral transformation for frequency and slovvness separately. The stability problem on so-lution in computing slowness is also discussed in the paper.
引文
[1] Aki K and Richards P G. Quantitative seismology ,1980
[2] 寻浩等.各向异性介质中反射率法波场模拟及体波辐射图案.石油地球物理勘探,1997,32(5) :605-614
[3] Chapman C H. A new method for computing seismo-grams.Geophys J R astr Soc, 1978,84(2) :481-518
[4] Fryer G J. A slowness approach to the reflectivity method of seismogram synthesis. Geophys J R astr Soc, 1980,86(3) :747-758
[5] Kennett B L N. Reflections,rays and reverberations. Bull Seism Soc Am, 1974,64(6) :1685-1696
[6] 孙成禹.球面波分解理论及其倾斜叠加的实现.石油地球物理勘探,2000,35(6) :723～729
[7] 姜建国等.信号与系统分析基础.北京:清华大学出版社,1997
[8] Ostrander W J. Plane-wave reflection coefficients for gas sands at non-normal incidence. Geophys J R astr Soc, 1984,90(10) :1637-1648
[2] 寻浩等.各向异性介质中反射率法波场模拟及体波辐射图案.石油地球物理勘探,1997,32(5) :605-614
[3] Chapman C H. A new method for computing seismo-grams.Geophys J R astr Soc, 1978,84(2) :481-518
[4] Fryer G J. A slowness approach to the reflectivity method of seismogram synthesis. Geophys J R astr Soc, 1980,86(3) :747-758
[5] Kennett B L N. Reflections,rays and reverberations. Bull Seism Soc Am, 1974,64(6) :1685-1696
[6] 孙成禹.球面波分解理论及其倾斜叠加的实现.石油地球物理勘探,2000,35(6) :723～729
[7] 姜建国等.信号与系统分析基础.北京:清华大学出版社,1997
[8] Ostrander W J. Plane-wave reflection coefficients for gas sands at non-normal incidence. Geophys J R astr Soc, 1984,90(10) :1637-1648
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