The propagation of waves in porous media has crucial implications in many areas such as the characterization of industrial foams, spongious bones or petroleum rocks for example. We have developed original numerical methods from the last 10 years to perform high accurate simulations.

Depending on the frequency regime, two models are considered in PROSPERO:  

  • the low-frequency Biot model where the diffusion mechanism is linear 
  • the high-frequency Johnson-Koplik-Dashen (JKD) model where attenuation is governed by fractional time derivative

In both case, isotropic or transversely isotropic materials can be handled.

In porous media, the presence of two compressional waves and one shear waves makes numerical simulations tricky. In particular the accurate representation of the slow compressional waves requires special attention. In heterogeneous media, this wave is generated during the interaction between the propagative waves and the scatterers, but remains localized around the interfaces since it is rapidly attenuated. Consequently, this slow wave has a major influence on the balance equations at the interfaces, modifying crucially the behavior of fast compressional and shear diffracted waves.  

Many tests have been made to validate carefully our numerical approach, by comparison with analytical or semi-analytical solutions. 

As example, we perform comparison with a semi-analytic method developped by A. Mesgouez and G. Lefeuve-Mesgouez for layered media:

Fluid layer over a multilayered porous medium

Snapshot of the wave field

Numerical and analytical comparison of the
recorded pressure at a receiver located
in the fluid


We also perform simulations of multiple scattering in porous media at high frequency. The matrix is transversely isotropic and the scatterers are ellipsoidal and randomly distributed. Using such simulations, phase velocity and attenuation of an equivalent homegeneous media can be evaluated. Comparison with theoretical models like Inverse Scattering Approximation or Waterman-Truell are then possible.


Initial pressure plane wave

Difracted pressure field by ellipsoidal porous scatterers

Initial recorded pressure sismogram




Coherent pressure sismogram after treatment

Effective phase velocity for various scatterer concentrations


Effective attenuation for various scatterer concentrations