VTI介质频率-空间域准P波正演模拟
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摘要
本文从VTI介质弹性波波动方程出发,借助VTI介质弹性参数和Thomsen参数,结合Kelvin-Christoffel方程,推导了VTI介质中准P波波动方程,并对VTI介质准P波进行了正演模拟。在正演模拟中,为了克服常规差分算子的数值频散,采用了25点优化差分算子;再依据最优化理论求取的优化系数建立了频率-空间域中准P波波动方程的差分格式;为了消除人为边界反射,根据特征分析方法并利用Kelvin-Christoffel方程,构建了VTI介质中准P波方程在不同边界和角点处的边界条件;再由准P波波动方程和边界条件,通过频率-空间域有限差分法,对准P波在均匀VTI介质、层状VTI介质和凹陷模型中的传播过程进行了数值正演模拟。通过正演模拟,得到了单频波波场、时间切片和共炮点记录,为研究地震成像及反演等提供了依据。
Coming from elastic wave equation in VTI me- dia,by the aid of elastic parameters of VTI media and Thomsen parameters and combining with Kelvin-Christoffel equation, the paper deduced quasi P-wave equation in VTI media and implemented its forward simulation. During the process of forward simulation ,in order to overcome the numeric dispersion in ordinary finite-difference operator, we adopted optimized 25 points finite-difference operator; differential format of quasi P-wave equation in frequency-space domain was created on the basis of optimum coefficients computed by way of optimization theory;in order to eliminate the reflections from the artificial boundary,the boundary conditions in different boundaries and corners for quasi P-wave equation in VTI media were constructed according to eigenvalue analysis and by using Kelvin-Christoffel equation; coming from the quasi P-wave equation and boundary conditions, the numeric forward simulations were conducted for the quasi P-wave propagation in homogeneous VTI medium,layered VTI medium and sag model separately by finite-difference algorithm in frequency-space domain. Single-frequency wavefields, time slices and common-shot-point records were obtained by forward simulation that provided a foundation for studying seismic imaging and inversion.
Coming from elastic wave equation in VTI me- dia,by the aid of elastic parameters of VTI media and Thomsen parameters and combining with Kelvin-Christoffel equation, the paper deduced quasi P-wave equation in VTI media and implemented its forward simulation. During the process of forward simulation ,in order to overcome the numeric dispersion in ordinary finite-difference operator, we adopted optimized 25 points finite-difference operator; differential format of quasi P-wave equation in frequency-space domain was created on the basis of optimum coefficients computed by way of optimization theory;in order to eliminate the reflections from the artificial boundary,the boundary conditions in different boundaries and corners for quasi P-wave equation in VTI media were constructed according to eigenvalue analysis and by using Kelvin-Christoffel equation; coming from the quasi P-wave equation and boundary conditions, the numeric forward simulations were conducted for the quasi P-wave propagation in homogeneous VTI medium,layered VTI medium and sag model separately by finite-difference algorithm in frequency-space domain. Single-frequency wavefields, time slices and common-shot-point records were obtained by forward simulation that provided a foundation for studying seismic imaging and inversion.
引文
[1] Alkhalifah T. Acoustic approximation for processing in transversely isotropic media. Geophysics, 1998. 63 (2):623-631
[2] Alkhalifah T. An acoustic wave equation for anisotro- pic media. Geophysics,2000,65(4) :1239-1250
[3] Alkhalifah T. An acoustic wave equation for orthorho- mbic media.Geophysics,2003,68(4):1169-1172
[4] Pratt R G. Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging. Geophysics, 1990,55(5) :626-632
[5] Thomsen L. Weak elastic anisotropy. Geophysics, 1986,51(10):1954-1966
[6] Min D-J et al. Improved frequency-domain elastic wave modeling using weighted-averaging difference operators. Geophysics,2000,65(3) :884-895
[7]张宝金．地震波参数反演及其可信度分析．同济大学博 士学位论文,2003:62-73
[8]董良国．地震波数值模拟与反演中的几个关键问题研 究．同济大学博士学位论文,2003:44-60
[9]刘洋等．任意偶数阶精度有限差分数值模拟．石油地球 物理勘探,1998,33(1):1-10
[2] Alkhalifah T. An acoustic wave equation for anisotro- pic media. Geophysics,2000,65(4) :1239-1250
[3] Alkhalifah T. An acoustic wave equation for orthorho- mbic media.Geophysics,2003,68(4):1169-1172
[4] Pratt R G. Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging. Geophysics, 1990,55(5) :626-632
[5] Thomsen L. Weak elastic anisotropy. Geophysics, 1986,51(10):1954-1966
[6] Min D-J et al. Improved frequency-domain elastic wave modeling using weighted-averaging difference operators. Geophysics,2000,65(3) :884-895
[7]张宝金．地震波参数反演及其可信度分析．同济大学博 士学位论文,2003:62-73
[8]董良国．地震波数值模拟与反演中的几个关键问题研 究．同济大学博士学位论文,2003:44-60
[9]刘洋等．任意偶数阶精度有限差分数值模拟．石油地球 物理勘探,1998,33(1):1-10
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