Exponential asymptotically bounded velocity model: Part I — Effective models and velocity transformations

Abstract

A new compacted-sediment, vertical-velocity model that represents the effect of gradually increasing velocities with depth is proposed. An asymptotically bounded, exponential velocity model is defined by three intuitive parameters. For a given layer, the parameters are 1) the velocity, 2) its vertical gradient at the top interface, and 3) an upper-limit velocity value. Time-depth relations, velocity transformations, hyperbolic, and nonhyperbolic moveouts are derived. The entire vertical velocity profile is composed of a set of layers, where the velocity function for each layer is defined by the proposed model. This method provides a basis for describing the subsurface using a smaller number of thick layers rather than using the classical, linear velocity model.