VTI介质频率-空间域准P波正演模拟

Quasi P-wave forward modeling in frequency-space domain in VTI media.

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.