A direct comparison between vibrational resonance and pulse transmission data for assessment of seismic attenuation in rock

Abstract

For the same volume of rock, I compare the attenuation obtained by seismic pulse transmission over the frequency range 1–150 kHz with that obtained by vibrational resonance techniques over the frequency range 1–50 kHz. The initial studies were performed on a rectangular block of medium‐grained granite which was large enough to permit the installation of a seismic pulse transmission array over a 1.8 m path length, yet small enough to permit whole‐body resonance. A Q of 82, for the P wave, was derived from the vibrational resonance results, whereas a Q of 15 was derived from the pulse transmission results. In light of models proposed for the viscoelastic, geometric, and elastic scattering attenuation mechanisms, the experimental results suggest that this large discrepancy in Q values is due to elastic scattering by grain clusters (rather than individual grains) within the granite. Scattering is significant in the high‐frequency pulse transmission tests, but is considered insignificant in the lower frequency resonance tests. Furthermore, this scattering is represented approximately by a constant-Q loss mechanism, which makes it difficult to separate unambiguously elastic scattering and viscoelastic losses. Subsequent studies performed on a large block of fine‐grained norite yield a resonance Q of 89 and a pulse Q of approximately 102 and suggest a negligible scattering loss for this material. The experimental results for the norite imply that the constant-Q theory of seismic pulse attenuation provides a reasonable description of wave attenuation in a dry, fine‐grained crystalline rock over the frequency range 1–150 kHz.

Tomographic Imaging of Thermally Induced Fractures in Granite Using Bayesian Inversion

“…(15)). As was mentioned in the previous subsection, the value of c depends on the experimental details and on how the pulse rise time is measured (BLAIR, 1990;KAVETZKY et al, 1990). Equation (17) always remains valid, however, provided the relation between pulse rise time and Q v has the form described by eq.…”

“…The constant c depends on the type of source (BLAIR and SPATHIS, 1984;GLADWIN and STACEY 1974;KAVETZKY et al, 1990) and on how t rt is de®ned. If the standard de®nition of t rt as the time when the pulse amplitude changes from 10% to 90% of the pulse maximum amplitude is used, then c $ 0:5 (BLAIR, 1990;KAVETZKY et al, 1990). The spatial distribution of Q can be derived from eq.…”

“…This accuracy of travel-time picking is acceptable for velocity tomography but must be essentially improved for pulse rise time data to make Q tomography possible. Improvement may be achieved by measuring the pulse rise time, not as the dierence between ®rst arrival and pulse maximum arrival times, but as the time when the pulse amplitude changes from 10% to 90% of the pulse maximum amplitude (BLAIR, 1990;KAVETZKY et al, 1990). This method allowed measurement of the rise time with an accuracy of about 0.02 ls which gave relative errors of about 1±2%.…”

Contact micromechanics in granular media with clay

“…Kiister and Toksoz (1974a), Kiister and Toksoz (1974b), Plona and Johnston (1981), , Winkler and Murphy (1984), Blair (1990), Lucet and Zinszner (1992) Squirt Fluid Flow Mavko and Nur (I979), Palmer and Traviolia (1981), Bulau et. al, (1984), Dvorkin et.…”

Enhanced velocity tomography: Practical method of combining velocity and attenuation parameters

“…This is a sum of the pulse travel time and pulse rise time so that it contains information both about velocity and attenuation structure. Using relations I and 2 one can easily verify that However, care must be taken of using such an approach when very high frequencies (or very short pulses) are used because in the MHz frequency range an apparent value of Q can be of the order of 10 or less due to high scattering attenuation [Blair 1990 ]. In such a situation correction due to small Q have to be taken into account to obtain correct velocity as it follows from equation 3.…”