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A time-domain numerical modeling of Biot poroelastic waves is presented. Theviscous dissipation occurring in the pores is described using the dynamicpermeability model developed by Johnson-Koplik-Dashen (JKD). Some of thecoefficients in the Biot-JKD model are proportional to the square root of thefrequency: in the time-domain, these coefficients introduce order 1/2 shiftedfractional derivatives involving a convolution product. Based on a diffusiverepresentation, the convolution kernel is replaced by a finite number of memoryvariables that satisfy local-in-time ordinary differential equations. Thanks tothe dispersion relation, the coefficients in the diffusive representation areobtained by performing an optimization procedure in the frequency range ofinterest. A splitting strategy is then applied numerically: the propagativepart of Biot-JKD equations is discretized using a fourth-order ADER scheme on aCartesian grid, whereas the diffusive part is solved exactly. Comparisons withanalytical solutions show the efficiency and the accuracy of this approach.

Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives