  A time-domain numerical modeling of Biot poroelastic waves is presented. The
viscous dissipation occurring in the pores is described using the dynamic
permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the
coefficients in the Biot-JKD model are proportional to the square root of the
frequency: in the time-domain, these coefficients introduce order 1/2 shifted
fractional derivatives involving a convolution product. Based on a diffusive
representation, the convolution kernel is replaced by a finite number of memory
variables that satisfy local-in-time ordinary differential equations. Thanks to
the dispersion relation, the coefficients in the diffusive representation are
obtained by performing an optimization procedure in the frequency range of
interest. A splitting strategy is then applied numerically: the propagative
part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a
Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with
analytical solutions show the efficiency and the accuracy of this approach.
