Wavefield Simulation in Biot-Rayleigh-Based Double-Porosity Media

We develop a numerical algorithm for wave simulation in double-porosity media, based on Biot theory of poroelasticity and the Rayleigh model of bubble oscillations. Spherical inclusions embedded in a background medium oscillate to yield attenuation by mode conversion from fast P-wave energy to slow P-wave energy. The differential equation of the Biot-Rayleigh (BR) variable is approximated with the Zener mechanical model, which results in a memory-variable viscoelastic equation. These approximations are required to model mesoscopic losses arising from conversion of the fast P-wave energy to slow diffusive modes. The wavefield is obtained with a grid method based on the Fourier differential operator and a second-order time-integration algorithm. Since the presence of two slow quasi-static modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modelling has spectral accuracy in the calculation of the spatial derivatives.