Fourier finite‐difference migration for steeply dipping reflectors with complex overburden1

Abstract

AbstractThe improvement in accuracy and efficiency of wave‐equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase‐shift and finite‐difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite‐difference migration’(FFD migration).In our approach we try to generalize and improve the split‐step Fourier migration method for strong lateral velocity variations using an additional finite‐difference correction term. Like most of the current migration methods in use today, our method is based on the one‐way wave equation. It is solved by first applying the square‐root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square‐root operator and this constant‐velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split‐step Fourier correction term.Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split‐step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase‐shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher‐order implicit FD schemes. These schemes use two cascaded downward‐continuation steps in order to attain comparable migration performance.