In exploration seismology, we record the response of the earth to various controlled seismic energy sources applied at or near the earth's surface. Since the earth is an imperfect elastic half-space, usually containing many internal boundaries and irregularities, the seismic response recorded at the surface consists of many different modes of wave propagation, some related to the surface of the half-space, others generated by the internal structure. Typically, we are primarily interested in using various back-scattered modes, like reflections, to construct images of the internal structure of the earth, so we need to separate one or more of these modes from the full seismic response for further processing. The separation is often accomplished using various mathematical transforms which take advantage of some unique characteristic of one or more of the modes.
In this work, we show how to apply some relatively simple geometric distortions to the X-T plane in which we usually display seismic data, to separate wavefield components for further processing. Since these distortions are all implemented as point-to-point re-mappings and interpolations in the plane, they can be reversed, with the relative fidelity depending only upon the interpolation method. We thus avoid integral transforms, since these can exhibit undesirable artifacts related to the transform aperture, caused by operations applied in the transform domain, or caused by irregularities in the original data domain.
We use physical model data for our demonstrations. Hence, techniques which perform well on these data should be effective as well on actual seismic field data.
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