波动方程数值模拟的三种方法及对比

波动方程数值模拟方法是研究地震波场传播的一种重要手段,本文采用交错网格高阶有限差分方法分别对双程声波方程和双程弹性波方程进行了波场数值模拟,并且根据定位原理采用傅立叶有限差分算子进行了单程波方程数值模拟,在分析定位原理的基础上,对其计算过程稍作修改,将延拓到地面的波场直接由每个检波点接收,无需横向叠加过程,得到了单程声波方程共炮记录.基于不同波动方程的数值模拟结果表明,双程波方程结果包含直达波、多次波等干扰波,信噪比低;单程波数值模拟结果只包含了介质分界面的一次反射波,信噪比高,但对于大角度入射波误差较大,并且对于同一个地质模型而言,双程弹性波方程计算速度最慢,双程声波方程次之,单程声波方程计算速度最快.因此对于复杂地质模型,三种模拟方法可以取长补短,综合应用.

Three methods of wave equation forward modeling and comparisons

Wave equation forward modeling is a very important way to study the seismic propagation underground. In this paper, seismic forward modeling based on two-way acoustic wave equation and two-way elastic wave equation is done using the staggered-grid high-order difference method. Besides, according to the positioning principle, simulation based on one-way acoustic wave equation is made by the Fourier finite difference propagator. In the progress of computing, each geophone directly receives the wave field that has been extrapolated to the surface of the model without lateral stacking. The three simulation results show that two-way wave equations generate directive wave and multiple wave which reduce the SNR severely, while the one-way wave equation method gives a higher SNR with only reflected wave, but it creates larger errors with wide-angle incident wave. For the same model, two-way elastic wave equation algorithm costs the most computational time, one-way acoustic wave equation algorithm costs the least and two-way acoustic wave equation algorithm in between. So for a complex structure model, the three modeling methods can be used simultaneously with different advantages and disadvantages.