A matched-filter approach to wave migration

Wave migration is a technique in which the reflectivity of the Earth is interpreted by extrapolating the fields measured on the surface into the ground. The motivation of this paper is to develop a generalized imaging algorithm based on a matched-filter that shows a mathematical connection between currently used migration techniques. The filter is determined by estimating the received signal when a specific test target exists in the ground. To keep the method general, a point scatterer is used as this target, while distributed objects are modeled without changing the filter characteristics by a collection of independent point scatterers. Also, the specific forms of the Green’s functions, which describe wave propagation in the ground, are not included in the formation of this approach leaving more freedom in the implementation. When the filter is applied to measured data of a monostatic survey, the resulting method becomes a forward scattering problem in which these data become time-reversed current sources. Next, specific forward scattering techniques are applied to this matched-filter approach and the resulting methods are compared to traditional migration techniques. In doing so, we find that the general form of most migration techniques can be shown using a matched-filter, while the major differences lie in the actual interpretation of the wave propagation that is used to implement the filter. The similarities of the matched-filter-based approaches to traditional techniques are used to show a connection and general overview of wave migration. Finally, these methods are applied to data collected over pipes buried in sand. q 2000 Elsevier Science B.V. All rights reserved.