  In this paper, we derive the augmented Biot-JKD equations, where the memory
terms in the original Biot-JKD equations are dealt with by introducing
auxiliary dependent variables. The evolution in time of these new variables are
governed by ordinary differential equations whose coefficients can be
rigorously computed from the JKD dynamic tortuosity function $T^D(\omega)$ by
utilizing its Stieltjes function representation derived in
\cite{ou2014on-reconstructi}, where an algorithm for computing the pole-residue
representation of the JKD tortuosity is also proposed. The two numerical
schemes presented in the current work for computing the poles and residues
representation of $T^D(\omega)$ improve the previous scheme in the sense that
they interpolate the function at infinite frequency and have much higher
accuracy than the one proposed in \cite{ou2014on-reconstructi}.
