Linearized inversion: a significant step beyond pre-stack migration, Geophys

One of the advantages of seismic inversion methods in petroleum exploration is the potential quantitative evaluation of the distributed parameters (propagation velocity, acoustic im-pedance) which characterize subsurface formations. Such methods are particularly attractive for detecting stratigraphic traps, which can be recognized by a lateral variation in these parameters. Consequently, they can yield a substantial improvement over conventional pre-stack migrations which only provide images of heterogeneities. Among inversion methods, the linearized inversion is arousing great interest because of simplifications it brings to computing. The disadvantage of this approach stems from the difficulty in finding a so-called reference medium, sufficiently close to the actual unknown medium as to justify the linearization. The first part of this work aims at providing a better understanding of the 2-D linearized forward problem and attempts to answer the following question: how close must the reference medium be to the exact medium for the linearization to be justified? The second part of this work examines the 2-D linearized inverse problem and analyses how errors resulting from the linearization can influence the solution of the problem. Numerical experiments show the effectiveness of the linearized inversion. More specifically it allows a quantitative identification of the heterogeneities, as well as a non-linear inversion does, when the reference medium accurately approximates the velocity of the actual medium. With a cruder reference medium the quantitative identification of the heterogeneities becomes usually less accurate, but at least the linearized inversion yields a substantially better image than the pre-stack migration. Key words: reflection seismology, seismic interpretation, seismic inversion, seismic migra-tion, seismic modelling, wave equation