Wave-Equation Datuming on a Micro-Computer

Abstract

Wave-equation datuming is a simple concept which can be used to correct seismic data recorded in areas where there are strong near-surface lateral velocity contrasts. In particular, the idea lends itself to correcting marine data recorded over near-surface limestone reefs which give rise to rapid changes in the sea-floor profile. A post-stack two-dimensional (2D) Kirchhoff implementation has been designed to run efficiently on an 80386-based micro-computer with or without an attached array processor (AP). It can be generalized readily to pre-stack application or to three-dimensional (3D) application and serves to demonstrate many of the features of these more numerically intensive implementations. The data flow is based on the semi-circle superposition rather than the hyperbola-sum approach to Kirchhoff summation (Claerbout, 1985). This is a single trace input, multiple trace output design which has the main advantages: (1) relaxed requirements on input data organization; (2) streamlined trace interpolation for time-shifting. In this 2D implementation, a spatially variant convolution in time serves to perform the off-line (y-direction) summation under the assumption of an earth model which is constant in y (Berryhill, 1979). The length of this convolver is the most critical parameter affecting performance. For reef structures which are not strictly 2D, convolver lengths can be set so that the resulting accuracy is commensurate with the limitation of the 2D assumption. Seismic data acquired in areas in the Timor Sea where reefs are a problem are ideal for demonstrating the applicability of this 2D post-stack datuming algorithm. A model consisting of point diffractors under a typical reef profile can be processed with wave-equation datuming so that migrated images of these diffractors are equally well resolved at different horizontal positions along the profile.