On the frequency-dependent attenuation in low-frequency mechanical testing of rock samples

Abstract

In forced-oscillation mechanical testing of rock samples, low-frequency attenuation is traditionally measured by the tangent of the strain-stress phase lag, which is interpreted as the frequency-dependent inverse quality factor. However, such phenomenological parameter only refers to harmonic waves in a homogeneous medium, lacking physical meaning in heterogeneous media or for finite bodies. It depends on specific boundary conditions and becomes insufficient for characterizing fluid-saturated porous rock. It is also sensitive to geometrical spreading, which is poorly known but can be significant in forcedoscillation experiments. To overcome these limitations and uncertainties of quality factor, one can use the temporal attenuation coefficient, a more fundamental quantity directly representing the relative mechanical-energy dissipation rate within the medium. Here, frequency-dependent attenuation coefficient is formulated from calibration experiments with Plexiglas and several published forced-oscillation measurements with fluid-containing porous rocks at variable temperatures. The resulting attenuation coefficient, unlike the quality factor, reveals important attenuation attributes: Effective geometrical attenuation, effective attenuation, relaxation time, and effective viscosity. The effective attenuation is related to the presence of pore fluids or melts, increases with temperature, and decreases with static pressure and pore-fluid viscosity. The effective geometrical attenuation is small in experiments with sandstone but becomes significant in high-temperature, torsional-deformation experiments with olivine aggregates. Unlike the inverse quality factor, the peak in the residual attenuation coefficient yields additional quantitative parameters to characterize the elasticity and internal friction within the rock. This work provides a new way for studying seismic attenuation, which shall be helpful to oil and gas exploration.

Document Type: Original article

Cite as: Deng, W., Morozov, I. B., Fu, L.-Y. On the frequency-dependent attenuation in low-frequency mechanical testing of rock samples. Advances in Geo-Energy Research, 2024, 12(3): 223-236. https://doi.org/10.46690/ager.2024.06.06

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