A multiple relaxation interpretation of the extended Biot model

Area of Science:

• Geophysics
• Earth Sciences
• Materials Science

Background:

• The biphasic extended Biot poroviscoelastic model incorporates squirt flow and associated relaxation modes.
• This model has faced criticism for its empirical nature.

Purpose of the Study:

• Derive constitutive equations and time-domain wave equations for the extended Biot model.
• Establish single-phase viscoelastic equivalents for the model's wave solutions.
• Simplify parameterization for shear wave propagation equivalents.

Main Methods:

• Derivation of constitutive and time-domain wave equations.
• Development of single-phase viscoelastic equivalents.
• Analysis of relaxation modes and frequency-dependent attenuation.

Main Results:

• Successfully derived model equations and identified single-phase viscoelastic equivalents.
• Achieved significant parameter reduction for shear wave equivalents using linear models and half-order spring-pots.
• Highlighted non-physicality of high-frequency shear relaxation modes.
• Interpreted relaxation modes, showing P- and S-wave complexity comparable to seawater.
• Explained linear frequency-dependent attenuation through appropriate weighting of relaxation mechanisms.

Conclusions:

• The derived viscoelastic equivalents offer a more parsimonious representation of wave propagation within the extended Biot model.
• The study clarifies the physical underpinnings of the model's relaxation mechanisms and attenuation behavior.
• The findings contribute to a better understanding of wave propagation in porous media.