Poro-acoustoelastic constants based on Padé approximation

Area of Science:

• Geophysics
• Materials Science
• Acoustics

Background:

• Stress significantly impacts elastic wave velocities in porous rocks, showing complex nonlinear behavior.
• Classical poro-acoustoelasticity theories face divergence and limitless velocity issues at high effective stresses.
• High-order elastic constants in classical theories can lead to unrealistic decreasing moduli with increasing effective pressure.

Purpose of the Study:

• To extend poro-acoustoelasticity using Padé approximation for the strain energy function.
• To develop acoustoelastic constants that provide theoretical limits for elastic wave velocities.
• To address limitations of high-order elastic constants in describing stress-associated velocity variations.

Main Methods:

• Applied Padé approximation to the strain energy function beyond high-order elastic constants.
• Derived new nonlinear acoustoelastic constants.
• Compared theoretical predictions with ultrasonic measurements on topaz and porous rock.

Main Results:

• Padé approximation yields acoustoelastic constants with reasonable theoretical limits for wave velocities.
• This approach avoids divergence and unrealistic modulus behavior at high effective stresses.
• Padé-based acoustoelasticity accurately describes stress-associated velocity variations, validated by experimental data.

Conclusions:

• Padé approximation offers a more robust theoretical framework for acoustoelasticity in porous materials.
• The method accurately models stress-dependent elastic wave velocities, particularly under high effective stress conditions.
• This approach provides insights into microstructural dependence of elastic constants under varying stress.