In this thesis we present a new seismic data stacking method called Plane Wave Composition (PWC). This method, applicable in a bidimensional medium with lateral velocity gradients, is developed on the basis of physical and mathematical concepts on the plane wave decomposition of spherical wave fields. In the initial part of this work, we present a review on the conventional stacking method and on plane wave decomposition of the point-source seismograms. The stacking by plane wave composition is a method which produce a normal incidence (or zero offset) section by the application of the following main processes: A double plane wave decomposition, achieved by a slant stack along the shot array and another slant stack along the receiver array, followed by a plane wave composition achieved by an inverse slant stack. The PWC stacking method is theoretically formulated here on the basis of the scattering theory applied to seismic waves, within the constraint of the Born approximation. Initially, starting with the acoustic wave equation, for a finite source-receiver configuration, a solution for the direct single scatter (Born) model is derived. That result is reduced for the coincident source-receiver (zero offset) configuration. Afterward, the mathematical expression of PWC stacking method is solved replacing the observed data function by the scattered field obtained by the Born approximation. For most clarity, the algorithm to obtain the zero offset seismic section by the PWC stacking method is described by applying it to the data corresponding to a simple model. A successful application is performed using the Marmousi seismic data set, corresponding to a geological complex model. Finally, in the same data set, a noise analysis shows that this method increase the signal-noise ratio in the seismic trace. Thus, it has been showed that the PWC stacking method is an efficient alternative to process seismic data of complex models.
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