对从各向同性到各向异性带来的几个问题的初探

文中根据应力与位移关系,导出了各向异性介质的波动方程(i=1,2,3;k=1,2,3)在二维平面(x-z平面)与铅直方向异性、横向同性(TI)介质的构造走向垂直,且TI介质的对称轴与z轴平行的情况下,可得出二维椭圆各向异性介质中SH波的波动方程,根据平面波理论,由此方程导出了速度函数。文中参考声波方程相移法正、反演原理,提出了各向异性波动方程正、反演的方法,并在各向同性和各向异性情况下,讨论了速度对偏移结果的影响。文中通过实例分析证实,如果被处理数据的假设前提和使用的处理软件的假设前提一致,则用各向异性波动方程偏移,其偏移成像结果是正确的;反之,将会导致明显的误差。即使在弱各向异性情况下,此种误差也是不容忽视的。

Discussion on some problems involved in transition from isotropic medium to anisotropic medium.

With the use of relation between stress and displacement, we derive the following wave equation in anisotropic medium (i=1,2,3;k=1,2,3)SH-wave equation in two-dimensional elliptic anisotropic medium can be derived when x-z plane is normal to structural trend in TI medium which is vertically anisotropic and laterally isotropic, and when the symmetric axis of TI medium is parallel to z axis. In terms of plane wave theory, velocity function is derived from this wave equation. Forward and inverse modeling methods which use wave equation in anisotropic medium are given by consulting forward and inverse modelings which use acoustic wave equation phase-shift.The influence of velocity upon migration is discussed in the cases of isotropic medium and anisotropic medium respectively. Illustrative analyses lead to the conclusion:if the assumptive premise of seismic data to be processed accords with that of data processing softwares we use, the migration result obtained by using anisotropic wave equation is correct; and if not, there will occur obvious error, which can not be neglected even in the case of weak anisotropic medium.