[Amath-seminars] AMath Seminar by Yvonne Ou on Friday May 31

Randall J LeVeque rjl at uw.edu
Tue May 21 11:56:02 PDT 2013

Applied Mathematics Seminar

Speaker: Yvonne Ou, University of Delaware

Title: Dynamic permeability, Microstructure and dissipation in
Biot-JKD wave equations

Time: 2:30pm on Friday, May 31, 2013

Room: Savery 157

Abstract: In the geophysics and bone ultrasound applications of poroelastic
equations of Biot type, it has been observed that low-frequency Biot
equations underestimate the dissipation when compared with experimental
results. In contrast to the low-frequency theory, in which the dissipation
term is proportional to the relative fluid velocity, Biot did consider the
correction for dissipation term when the frequency is higher than a critical
value. As a consequence of this correction, the dissipation term in the
time-domain waves equations becomes a memory term. Johnson, Koplik and
Dashen (JKD) proposed a unified theory for frequency-dependent permeability,
which is termed 'dynamic' permeability, based on the causality argument.
Like high frequency Biot equations, the time domain Biot-JKD also contains a
memory term.

The focus of this talk will be on
(1) How is the microstructure of the pore space mathematically quantified in
the context of permeability?
(2) How does the causality built in the dynamic permeability provide an
efficient way for numerically handling the memory term in Biot-JKD
(3) How to go beyond the Biot-JKD parameter-fitting methodology to
construct a sample-specific permeability for a given microstructure? How to
solve the ill-posed inverse problem arising from this?

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