Anisotropic wave propagation and zero-offset migration

Abstract

In reflection seismology, migration may be defined as the transformation of apparent reflector positions to their true positions. In practice this usually means that diffractions are collapsed and reflector dip angles are changed. When a medium is anisotropic, and the axes of velocity symmetry are tilted with respect to the horizontal, horizontal reflection events migrate laterally as well. The lateral migration of reflections from horizontal layers was studied by constructing an anisotropic scale model representing a medium in which the bedding is inclined to the surface. This situation may be classified as one of transverse isotropy with a tilted axis of symmetry. The elastic parameters of the anisotropic model were recovered by P- and SH-wave transmission measurements carried out to simulate a walk-away VSP. Numerical modelling of a P-wave CMP gather above a horizontal reflector in such a medium indicated that there would be an asymmetrical distribution of reflection points. The zero-offset reflection point was displaced laterally by a distance equal to more than 20% of the depth, and the spread of reflection points was 15% of the depth. The NMO velocity was found to be a function of offset. A zero-offset reflection survey was carried out on the model. The P-wave data were migrated with an anisotropic migration algorithm which may be applied to wavefronts of any shape. On the resulting section, the horizontal reflection features are moved laterally by a distance equal to 20% of the depth back to their correct positions. The lateral displacement of reflections from a horizontal reflector beneath a medium with tilted anisotropic velocity characteristics has significance for the selection of drill locations when such a situation is encountered in the field.