Linearized 2.5-dimensional parameter imaging inversion in anisotropic elastic media

ABSTRACT

In this paper we derive 2.5-D short-period seismic modelling and imaging-inversion formulae in the Born approximation for anisotropic elastic media. The 2.5-D approach encompasses 3-D wave scattering measured in a common-azimuth acquisition geometry subject to 2-D computations under appropriate assumptions. The lowest possible symmetry of the medium in this approach, in principle, is monoclinic, while the medium must be translationally invariant in the normal direction to the associated symmetry plane. In the presence of caustics, artefacts may be generated by the imaging-inversion procedures. We show that in the 2.5-D approach the analysis of artefacts in the 2-D symmetry plane implies the corresponding analysis in 3-D in the framework of the common-azimuth acquisition geometry. An interesting aspect of our results is the occurrence of out-of-plane geometrical spreading in the least-squares removal of the contrast source radiation patterns on the data. We finally introduce the 2.5-D generalized Radon transform that generates common-image-point gathers. The reconsideration of 2.5-D scattering theory is motivated by the increase in use of ocean-bottom acquisition technology. It is not uncommon for ocean bottom cable (OBC) seismic data to be collected along a single line, and the question arises of how to make optimal use of these data. We show the effect of the factors making up the amplitude in the 2.5-D generalized Radon transform on OBC field data from the North Sea.