椭圆各向异性介质中SH波波场模拟

Modeling of SH wave fieid in elliptic anisotropic medium

在二维椭圆各向异性介质条件下,各向异性波动方程可以分解为一个独立的 SH 波波动方程和一个 P-SV 波波动方程组。本文用褶积求微分的有限差分方法实现了二维椭圆各向异性介质中 SH 波的共炮点记录的模拟。模拟结果的成败在于求解 SH 波波动方程时对边界条件的处理,文中分别给出内边界及边界端点的吸收公式;同时给出多种各向同性和椭圆各向异性介质中的共炮点记录和波场切片图(Snapshot),展示了椭圆各向异性 SH 波波场的特性。从中可以看出:①反射 SH 波的时距曲线并非双曲线;②各向异性波在界面上的反射和透射仍满足Snell 定律;③各向异性介质中的 SH 波和各向同性介质中的波型是完全对应的,只是两种介质中的同一类型的波在传播时间、传播速度和同相轴的形态及能量分布有所不同。

In the case of two-dimensional elliptic anisotropic medium,an anisotropic wave equation can be decomposed into a SH wave equation and a P-SV wave equation system.Common-shot SH wave records in two-dimensional elliptic anisotropic medium may be modelled by using the finite difference method which differentiates through convolution.Whether the modeling is successful or not depends on boundary condition treatment in solving SH wave equation.Giv- en in the paper are absorption formulae of inner boundary and boundary end points,various common shot records and wave field snapshots in isotropic and elliptic anisotropic media,some showing SH wave field property in elliptic anisotropic medium.From these figures we can see the following points:(1) time-distance curve of reflected SH wave is not hyperbolic,(2)reflected and transmitted waves at an interface in anisotropic medium still satisfy Snell's law, and(3)SH waves in anisotropic medium and isotropic medium have homolo- gous wave modes but their corresponding waves in the two different media are different in travel time,velocity,event shape and energy distribution.