Laterally varying velocity estimation

Abstract

Lateral velocity variations in the subsurface are a departure from the simple horizontally layered model on which the extraction of NMO velocities and interval velocities are based. Significant differences between stacking velocity and interval velocity may result in complex geological areas when the estimation is based on this horizontally layered media assumption. In this paper methods are presented of velocity estimation that are both quick and accurate in the presence of lateral velocity variations. The method developed here solves an analytic expression by fitting an unknown smooth velocity function, and also determines the reflector depth using only two simple assumptions: (1) that the ray in the laterally varying medium travels along the same path as in the homogeneous medium; and (2) that the subsurface velocity can be approximated by a smoothly varying lateral velocity function. Assumption (1) is shown to introduce only higher order correction terms to the travel time for a given source-receiver pair. It is demonstrated by assumption (2) how the use of a stable, smooth and continuous velocity function across the section results in a better migration velocity than a velocity analysis performed at an isolated CDP location. By estimating the degree of lateral velocity variation across the seismic section at an early stage in the processing sequence, a decision on whether to use pre- or post-stack migration can be made with reliable velocity information. This method has the advantage of using an analytic expression for the travel time instead of complicated ray tracing by solving differential equations. This makes it useable in an interactive velocity analysis mode. An example using field data from the North West Shelf of Australia shows how the new travel time equation can improve the velocity analysis over a fault zone.