Effect of strain amplitude on relaxation spectra of attenuation in dry and saturated sandstone under pressure

Laboratory experiments have been carried out to investigate the amplitude–frequency dependence of compressional- and shear-wave attenuation in samples of dry and saturated sandstone. The measurements were performed using the reflection method on a pulse frequency of 1 MHz in the strain range ∼(0.3–2.0) × 10-6 under a confining pressure of 20 MPa. In general, the attenuation decreases monotonically with increasing strain amplitude as ⁠, where n∼ = 0.003–0.045. The decrease in P-wave attenuation, Q-1p, for dry sandstone is 5%, but for saturated sandstone there is no change. The analogous decrease for Q-1s in the dry and the saturated sandstone is 8% and 4%, respectively. The P-wave relaxation spectra, Q-1p(f), in the dry and saturated sandstone are slightly different from each other but the S-wave relaxation spectra, Q-1s(f), are very different. The amplitude variation causes the change in the value of the relaxation strength Δ that leads to the displacement of the curve Q-1(f) in the Y-direction. The value of Δs in the saturated rock is four times more than the value Δp in the dry rock, and the curves Q-1s(f) are shifted relative to Q-1p(f) towards higher frequencies. The upward–downward amplitude dependence Δp(ε1–6–1) both in the dry and the saturated rock is represented by the descending curve. The Δs(ε1–6–1) curve for the saturated rock shows hysteresis, but for the dry rock hysteresis is absent. The increase in the strain amplitude gives rise to a small change in peak frequency, but stimulates considerable (up to 40%) decrease in the S-wave relaxation peak width. The unusual behaviour of attenuation is explained by a feature of the joint action of viscoelastic and microplastic mechanisms. These results can be used to improve methods of geological interpretation of acoustical and seismic data.