| This article deals with time-domain numerical modeling of Biot poroelastic waves. The viscous dissipation inside the pores is described by the model of dynamic permeability of Johnson-Koplik-Dashen (JKD). Some coefficients of the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, they introduce shifted fractional derivatives of order $1/2$, which involves a convolution product. A diffusive representation replaces the convolution kernel by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Based on the dispersion relation, the coefficients of the diffusive representation are determined by optimization on the frequency range of interest. A numerical modeling based on a splitting strategy is proposed: the propagative part is discretized by a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions are proposed, demonstrating the efficiency and the accuracy of the approach. |
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