Minimum-phase Property of Memory Functions in the Wave Equation

Minimum-phase Property of Memory Functions in the Wave Equation

Van Dalen, K.N.
Slob, E.C.
Schoemaker, F.C.

Civil Engineering and Geosciences

Geoscience & Engineering

2012-06-04

Memory functions occur in the wave equation as time-convolution operators and generally account for the instantaneous and non-instantaneous responses of a medium. The specific memory function that is causal and stable, and the inverse of which is also causal and stable, is conventionally referred to as minimum phase. In this paper we present "extended minimum-phase relations" between the amplitude and phase spectra of a memory function that has different properties. The considered memory function and its inverse are both causal, but they do not need to be stable. We still address the function as minimum phase because the phase spectrum exhibits minimum group delay, like a conventional minimum-phase function. We have successfully tested the derived relations for the well-known Maxwell and Kelvin-Voigt models. The relations have potential applications in acoustics, seismology, poroelasticity, electromagnetics, electrokinetics and any other effective-medium theory that employs memory functions.

memory function
relations between amplitude and phase

http://resolver.tudelft.nl/uuid:2a526e59-ccf8-4d5d-97e3-6806c97ab70c

74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012, Copenhagen, Denmark, 4-7 June 2012

Institutional Repository

conference paper

(c) 2012 Van Dalen, K.N.
Slob, E.C.
Schoemaker, F.C.