Acoustic imaging of layered media

Abstract

This paper presents the echoes-to-impedance transform, a nonlinear transform designed for acoustic imaging of layered media—for example, sedimentary geological formations, biological tissue such as skin, or laminated structures in the built environment. The transform converts time domain digital reflection data directly into impedance as a function of spatial location, using minimal prior information about the source wavelet and no prepreprocessing. It is simple, fast, and, according to numerical experiments, highly accurate. More than this, physical structure is superresolved at a finer scale than that of the source wavelet. The derivation of the echoes-to-impedance transform stems from a recently developed numerical method for wave propagation in one dimension in conjunction with the theory of orthogonal polynomials on the unit circle.