I. Inverse scattering subseries for removal of internal multiples and depth imaging primaries; II. Green's theorem as the foundation of interferometry and guiding new practical methods and applications.

摘要

This dissertation extends the current theory and algorithm to attenuate internal multiples, based on inverse scattering, to an eliminator of these events in the data. I identified, for the first time, the terms in the inverse scattering series corresponding to diagrams beyond the first term in a series that eliminates internal multiples. I was able to write those identified terms that take attenuation towards elimination of internal multiples in a closed form. This new capture represents an eliminator of all internal multiples generated at the shallowest reflector and further reduces internal multiples generated at deeper reflectors.;The second main result of this dissertation develops two new theories for data extrapolation: (1) constant velocity data extrapolation using the first inverse scattering equation, and (2) data-driven data extrapolation and regularization with Green's theorem and seismic interferometry.