A hybrid linear-hyperbolic radon transform

One application of the Radon transform (RT) is to map events with different curvature in the data space to different areas of a model space, where the se events can be separated or filtered before going back to the data space. This ability of the RT is in practice diminished by the fact that data con tain events with different shapes. Linear events due to ground roll (GR), f or example, are superimposed on hyperbolic events from reflections. Both ev ents cannot be simultaneously focused with the standard RT. A linear RT loc alizes the GR and not the reflections, and a parabolic RT for NMO corrected data does not localize the GR. In this paper we present a hybrid Radon tra nsform to perform a sparse representation in the model space of data contai ning events with different shape. The RT is performed by two operators, eac h one with a different set of basis functions. The same idea can be extende d to more than two operators for data with more complicated combinations of events.