中文摘要：

声波各向异性数值模拟对地震数据处理和解释起着重要的作用。基于Tsvankin提出的精确色散关系,通过平方根近似,在时间-波数域中推导出二维TTI介质纯P波声波波动方程,并利用快速展开法（Rapid Expansion Method,REM）进行了数值模拟。与传统的有限差分法求解二维TTI介质耦合方程和傅里叶有限差分法在时间上进行波场外推相比,该方法的模拟结果精度更高,计算速度更快,并且成功去除横波分量。

英文摘要：

Anisotropic numerical simulation of acoustic wave plays an important role in seismic data processing and interpreta- tion. Starting with the exact dispersion relationship derived by Tsvankin and a square root approximation, we proposed a pure P-wave acoustic equation for 2D TTI medium in time-wavenumher domain, then the rapid expansion method （REM） is ap- plied for numerical simulation. Compared with the conventional finite difference method to solve the 2D TTI medium coupled equations and Fourier finite difference to implement wavefield extrapolation in time, the synthetic data test results of our method is advanced in high precision and fast computing speed; what＇ s more, the SV-wave component has been removed successfully.