虚谱法无反射速度-应力方程地震数值模拟

Non-reflection numerical simulation of zero offset seismic wavefield with velocity-stress equation based on pseudo spectral method

基于单程波波场延拓算子的零偏移距地震数值模拟方法难以适应复杂地质条件下地震波速度的空间剧烈变化,且其最大成像角度有不同程度的限制。本文依据地震反射的形成机理,重置模型空间的密度分布,使得模型空间内纵波阻抗为常量以压制层间多次波;采用虚谱法可得到高精度的地震波场空间导数,因此可有效抑制空间数值频散,同时提高了数值模拟的垂向分辨率。数值模拟结果表明,得到的零偏移距地震记录绕射波场完整,偏移归位效果优于频率-波数域或频率-空间域的单程波模拟结果。无反射一阶应力-速度方程零偏移距数值模拟可有效压制多次反射波,在较大网格间距时,虚谱法仍可有效抑制数值频散。

Since the wavenumber in z axis may not be calculated directly and correctly when P-wave velocity varies dramatically in x-y plane, zero offset seismic numerical simulation based on one-way wave equation is not suitable in the complex geological areas, and the maximum imaging angle of wavefield extrapolation operators based on one-way wave equation is limited. According to the formation mechanism of seismic reflection, the density distribution is calculated manually to make the P-wave impedance is constant in the model space, thus the multiple reflections generated from impedance interfaces are decreased. The precision of spatial derivative of the seismic wave field calculated by pseudo spectral method is higher than that of finite difference, therefore, the numerical dispersion is suppressed effectively, and the vertical resolution is enhanced. Numerical simulation results show that the diffraction wave field in zero offset seismic data is abundant, and the effect of seismic migration is better than that of frequency wave number domain or frequency space domain based on one-way wave equation.