Minimum-phase Property of Memory Functions in the Wave Equation

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.Geoscience & EngineeringCivil Engineering and Geoscience

Generalized minimum-phase relations for memory functions associated with wave phenomena

Structural EngineeringCivil Engineering and Geoscience

Experimental validation of the electrokinetic theory and development of seismoelectric interferometry by cross-correlation

We experimentally validate a relatively recent electrokinetic formulation of the streaming potential (SP) coefficient as developed by Pride (1994). The start of our investigation focuses on the streaming potential coefficient, which gives rise to the coupling of mechanical and electromagnetic fields. It is found that the theoretical amplitude values of this dynamic SP coefficient are in good agreement with the normalized experimental results over a wide frequency range, assuming no frequency dependence of the bulk conductivity. By adopting the full set of electrokinetic equations, a full-waveform wave propagation model is formulated. We compare the model predictions, neglecting the interface response andmodeling only the coseismic fields, with laboratory measurements of a seismic wave of frequency 500 kHz that generates electromagnetic signals. Agreement is observed between measurement and electrokinetic theory regarding the coseismic electric field. The governing equations are subsequently adopted to study the applicability of seismoelectric interferometry. It is shown that seismic sources at a single boundary location are sufficient to retrieve the 1D seismoelectric responses, both for the coseismic and interface components, in a layered model.Geoscience & EngineeringCivil Engineering and Geoscience

Electrokinetic fields and waves: Theory, experiments and numerical modeling

Geoscience & EngineeringCivil Engineering and Geoscience