Similarity and the inverse Q filter: Some simple algorithms for inverse Q filtering

Abstract

A number of authors have addressed the issue of the time variance of the forward and inverse Q filter on the assumption of a frequency‐constant or nearly frequency‐constant Q factor. Early papers by Futterman (1962) and Carpenter (1966) derived time‐domain solutions for the forward Q filter, given an assumed behavior of Q at low and high frequencies, while Kjartansson (1979) used an assumed stress‐strain relationship to derive the forward Q filter for a precisely frequency‐constant Q. Bickel and Natarajan (1985) applied these earlier results to the derivation of various expressions for the inverse Q filter.