A multiple relaxation interpretation of the extended Biot model

Abstract

The biphasic extended Biot poroviscoelastic model takes into account the squirt flow in grain-grain contacts and introduces the bulk and shear relaxation modes associated with it. This model has been criticized for its empirical approach, but here the constitutive equations and the time domain wave equations of the model are derived. This also makes it possible to find single phase viscoelastic equivalents for all three wave solutions of the extended Biot model. Particularly, the viscoelastic equivalents for shear wave propagation can be obtained with considerably fewer parameters than the original model. These equivalents are linear viscoelastic models with springs and dampers for the low frequencies and contain half-order spring-pots for high frequencies. For high frequencies, the non-physicality of the shear relaxation mode is highlighted. The relaxation modes of the extended Biot model are interpreted in the framework of multiple relaxation mechanisms showing that the P- and S-wave modes of the model are not much more complex than that for seawater. The model's near linear frequency dependent attenuation in the intermediate frequency range is the result of weighting each relaxation mechanism appropriately.