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Abstract
Discrete echoes in non-destructive testing are usually associated with a step change in impedance between two different lossless media. While maintaining the problem as a one-dimensional one, different refinements to this model are briefly summarised. These include a continuous spatial impedance variation, interfaces comprising discrete layers of finite thickness, the inclusion of losses in the media on the two sides of a discontinuous boundary, and lossy media in which the losses also vary continuously in space. Some of these models have found application in medical ultrasonics and underwater acoustics and may prove useful also in NDE.