利用低阶偏微分方程组的大倾角差分偏移

利用Claerbout方程进行地震资料偏移,只适用于小倾角的情况。为了克服这一限制,R.Stolt和A.Berkhout等人导出了高阶近似的单程波方程,它们是比较复杂的高阶偏微分方程,在数值求解上存在一定的困难。本文讨论了低阶方程组形式的高阶近似,对它们构造了一些合适的差分格式。提出了求解这些差分方程的具体算法,并与15°差分偏移算法相比较,分析了此算法的计算工作量。本文提出的大倾角差分偏移方法十分有效且容易实现。

STEEP DIP FINITE-DIFFERENCE MIGRATION USING THE SYSTEM OF LOWER-ORDER PARTIAL DIFFERENTIAL EQUATIONS

The Claerbout equation is applicable to migrate data with small dips. For larger dips,equations of second- and third-order approximations have been derived eorrespond-ly by E. Stolt and A. Berkhout in the form of higher order P. D. E.. In this article higher-order approximations in the form of system of lower-order P.D.E. are discussed. These equations are very simple,one is of the first-order and others are the one-dimensional wave equations. The latter can be further simplified into two first-order equations. From this system,an equation close to that of Claerbout is obtained. For these equations,some suitable finite-difference schemes are constructed. At the end,the numerical algorithm for solving the finite-difference equations is described and the increment of computation efforts in comparison with that of conventional 15-degree migration algorithm is discussed. The method presented in this article for migrating data with steep dips is very efficient and easily implemented.