三维正交各向异性介质三分量高精度有限差分正演模拟

Finite-difference forward modeling of three-component records with high precision in 3-D orthorhombic anisotropic media

三维各向异性正演模拟是研究各向异性介质中波场传播规律的重要方法。本文就三维正交各向异性介质给出了一种快速精确的有限差分正演方法。该方法采用了４阶精度的空间差分格式和２阶精度的时间差分格式，这既要提高了精度，也不增加过多计算量；另外还结合通量校正法来克服数值频散，使计算能以较大的网络步长进行，在减少了计算量的同时，还提高了精度。对边界反射，文中提出了一种简单实用的三维各向异性吸收边界条件，易于编程，且吸收效果明显；对数值计算的稳定性问题也作了一般讨论。数值算例验证了本文方法的正确性和有效性，并表明它具有精度高和边界吸收明显的优点。该方法不但可以用来合成三维各向异性介质的共炮点记录、ＶＳＰ三分量记录及零偏移距地震记录，而且还适用于其他各种类型的波场正演。

3-D anisotropic forward modeling is important method for studying rule of wave-field spreading in anisotropic media. The paper presented a rapid and precise finite-difference forward modeling method for 3-D orthorhombic anisotropic med ia. The method adopted the finite-different form with four-order precision in space and two order precision in time which both improves the precision of sol ution and is no much increase in computational effort; meanwhile, combining with flux-corrected transport method to overcome numerical dispersion and conductin g calculation by using large grid step (coarse grid), the method can not only re duce computational effort but also improve precision. The paper presented a simple and practical 3-D anisotropic absorbing boundary condition for boundary ref lection in order to program easily and have a good absorption effect. The paper also has a general discussion on stability in numerical calculation. The numeric al examples proved the correctness and the effectiveness of the method and showe d that it has advantages of high precision and good boundary absorption. The met hod can be used not only to make synthetic common shot records and three compon ent VSP records in 3-D anisotropic media, but also to make synthetic zero offs et seismogram; meanwhile, the method can also be used for forward problems of wa ve field in other different types.