层状半无限空间中波动问题的数值模拟

NUMERICAL MODELING FOR WAVE PROPAGATION IN A LAYERED HALF SPACE

摘要:

本文对波动方程首先进行富里叶-贝赛尔积分变换,在波数k域内构成(z,t)的有限差分隐格式进行迭代,由此计算出纵向非均匀的层状模型的合成地震图。对含有低速层和高速薄层的几种模型做了对比计算,通过时间场与空间场的波动分析,揭示了几种主要震相的传播与形成过程。计算结果表明,无论高速层的厚薄如何。反射波始终很强烈。但初至首波在薄层构造中不清晰,一种属转换型的续至薄层首波震相值得注意;低速层的顶界面难以形成能量较强的上行波,因此在推断低速层埋深上存在不确定性。

Abstract:

For a vertically inhomogeneous layered model, Fourier-Bessel integration transform is applied to the equation of wave propagation, after that a synthetic seismogram can be obtained by a finite-difference iteration in the wave number domain. Due to the separation between space and time variables after the transform, such algorithm is of stable and wide feasible. In the present paper some models involving a lower velocity layer(LVL) and a higher velocity thin-layer are studied for comparison. Through an analysis for wave propagation in space and time domain, the processes of propagation and generation of several prominent phases are revealed. Computational results indicate that no matter how much the thickness of higher velocity layer is the reflection wave is still strong, while the initial head wave from the thin-layer is not obvious. It is worthwhile to point out that there exists one kind of converted head wave in the thinlayer. It is found that the upward propagation wave with strong energy is hard to be formed at the top of LVL, which means that there is rather serious uncertainty at inferring the depth of LVL.