The relationship between "direct, discrete" and "iterative, continuous" one-dimensional inverse methods

Abstract The two approaches are shown to be equivalent in two important respects. First, each method can be recovered from the other; second, because of the first equivalence, each method uses the same amount of information in reconstructing a profile to a certain depth z or traveltime tau into the medium. This information is the reflection data received for times less than 2tau . In particular, neither approach uses the "redundant data" received after time 2T in an inversion for a profile which is known to vary only for depths which correspond to traveltime T.--Modified journal abstract.