Scattering theory is a natural framework within which to directly pose the time-lapse seismic inverse problem. Within that theory, if time-lapse difference data are identified with the scattered field, the perturbation becomes a direct measure of the time-lapse acoustic/elastic property and structural changes within the Earth volume of interest. A wavetheoretic relationship of this kind, free of nonphysical artifacts, is not easy to deduce otherwise: think of propagating a 2-way wave through a difference model with a single mobile interface, and the spurious multiples that would be created between the interface and itself at a later time. The main complication in the scattering description lies in the heterogeneity of the reference medium, which generates roughly as many reflections as the perturbed medium. Since most existing inverse scattering imaging/inversion methods assume a smooth, non-reflecting reference, the problem would appear to require a complete reformulation. Doing this provides us with both inversion methods of increased accuracy, and an explanation of why inconsistently posed methods do better than one might imagine they should. The complicating influence of the heterogeneous reference medium is suggestive that inversion be considered within certain special cases: multidimensional structural inversion within the linearized regime only, and linear or nonlinear inversion when analyzing a single isolated primary event to determine mechanical property variations within a known, fixed target.
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