Strain dependent attenuation: Observations and a proposed mechanism

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The measured attenuation (Q−1) of a rock is a function of a number of parameters, one of those being the applied strain amplitude. It is important to understand the effect that strain amplitude has on Q−1 for several reasons: different measurement techniques use differing strain amplitudes and may measure a dissimilar Q−1, near source (large strain) wave propagation may behave highly non‐linearly, and the strain amplitude dependence can provide insight into the attenuation mechanism. A physical model based on the contact friction between crack surfaces in the rock has been developed to describe rock deformation and dissipation under large applied strain. The three‐dimensional crack surfaces are characterized by a statistical distribution of asperity heights. The sliding contact of these spherically‐tipped asperities dissipates frictional energy. Hertzian theory is applied to the average asperity contact and predicts that the large strain attenuation is given by Q−1 = kζε/P4/3, where k is a constant consisting of the matrix elastic parameters, ζ is the crack density, ε is the strain amplitude, and P is the confining pressure. The total attenuation measured appears to be the sum of this strain dependent term and a strain independent term. The results of ultrasonic pulse transmission experiments are compared with the model's prediction. Both P and S waves with strain amplitudes from 10−8 to 10−5 were employed. Frequencies from 0.4 to 1.5 MHz were used in conjunction with rock confining pressures of 2 to 580 bars on dry Berea sandstone and lucite samples. The spectral ratio method and rise time technique were applied to deduce the Q−1 values. The observed data and other observations from the literature compare well with the model's prediction for the dependence of Q−1 on large strain amplitude, crack density, and pressure.