Seismic reflection and transmission within an extended scatterer

Kristopher A. H. Innanen

A range of methods for making FWI stable in its construction of long wavelength model components in deep regions of the model (relative to maximum offset) have been introduced over the last several years, as discussed and presented by Geng, Almuteri and Innanen in CREWES. Many of these either quantitatively or qualitatively invoke multiple scattering. Using multiple scattering formalisms to model wave fields is not straightforward when the model error or perturbation is large, however. In this paper a Matlab code that quickly models the nth order truncated Born series approximation of a 1D wave field is written and used to flesh out some of the ways the series goes about creating events like direct arrivals and coda contributions. The main conclusion is a reminder not to say things like "the series did not converge by Nth order", but only things like “the series only converged to a maximum frequency fn by nth order”.