Summary Kirchhoff 3D prestack depth migration has become an extensively used tool in seismic data processing, because of its relative accuracy, efficiency and flexibility. However, a common concern in depth imaging projects are the limitations of the methods involved and the Kirchhoff algorithm is no exception This study will focus on improvements within Kirchhoff migration that are related to approximations used in the evaluation of the Kirchhoff integral rather than the fundamental limitations in its derivation. It will be shown that by more careful numerical evaluation of the Kirchhoff integral we can remove some of the commonly observed problems related to irregular sampling of the integral in Kirchhoff migration. Consequently, we observe improved amplitude behaviour and reduced levels of noise.

Summary Geologic data are usually measured or interpreted at isolated, irregular points in the earth. We present a geologic modeling system that can accept such data and construct a coherent 3-D model from it. The modeling system is based on topological data structures that are used in computer-aided geometric design. The explicit representation of the model’s topology in the data structures is crucial for carrying out the construction and manipulation of the model 3-D velocity fields can be constructed from isolated velocity points (v i , x i , y i , z i ) and 3-D surfaces can be constructed from a collection of points on the surface (x i , y i , z i ). In our examples, velocity is trilinearly interpolated between the specified points on a Delauney tetrahedral tessellation of the points, and a surface is constructed as the set of smallest-perimeter faces of the Delauney tessellation that defines a continuous, simply connected surface passing through the data points. These functions are illustrated with the representation of a salt structure from the Gulf of Mexico.