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《Chinese Journal of Geophysics》 1986-03
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STEEP DIP FINITE-DIFFERENCE MIGRATION USING THE SYSTEM OF LOWER-ORDER PARTIAL DIFFERENTIAL EQUATIONS

ZHANG GUAN-QUAN (Computing Center, Academia Sinica)  
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.
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