Anomalous waveforms observed in laboratory-formed gas hydrate-bearing and ice-bearing sediments
(Color online) (A) A sample ready to be raised into the main chamber of the GHASTLI. The 140-mm-long sample is jacketed in a flexible latex or viton membrane. (B) Each endcap contains a disc-shaped S-wave transducer crystal surrounded by a doughnut-shaped P-wave transducer crystal, shown schematically as they are positioned behind the wear plate, which contacts the sample. The shear crystal is 6 mm in diameter and the P-wave crystal outer diameter is 9 mm. The endcap and sample diameter is 70 mm.
(Color online) Waveforms measured using shear transducers before and after a brief destabilization of the GHBS; denoted pre- and post-D/R cycle, respectively. (A) Waveforms for Ottawa sand with 20% of the pore space saturated with hydrate. (B) Waveforms for Ottawa sand with 43% pore-space hydrate saturation. The solid circle in each plot represents the first arrival, a P-wave. Arrows indicate the first peak in the normal mode immediately following the P-wave. Normal-mode velocities are calculated from their first arrivals, not the peak positions indicated by the arrows. For 43% pre-D/R GHBS (solid curve), the peaks and troughs ahead of the S-wave are fairly uniform. Because there is no discernible, isolated large-amplitude feature arriving before the S-wave, no normal mode is indicated in Fig. 2(B).
(Color online) Numerical derivation of the theoretical phase velocity when the surrounding medium is air; using parameters for the post-D/R 43% GHBS. Allowable phase velocities are those for which the left side (solid curve) and right side of Eq. (15) (shown at two different frequencies with the dotted and dashed curves) are equal. As the dotted and dashed curves indicate, slight frequency changes significantly alter the location of the intersections of the curves.
(Color online) Waveform and amplitude spectra of normal modes for post-D/R cycle of GHBS. (A). Normal mode waveforms with cosine tapers applied. Stars indicate the P-wave first arrivals in these shear-transducer waveforms. (B) Amplitude spectra of the waveforms shown in A. Both waveforms have a single dominant peak frequency.
(Color online) Theoretical and measured group velocities for GHBS (solid stars) and for IBS (open stars). The curves are group velocities calculated from Eq. (22) for the n = 0 to n = 5 normal modes. The encircled stars are thought to be the nondispersive normal mode (NDNM), rather than the second- (n = 2) or third-order (n = 3) normal modes.
(Color online) Measured waveforms and power spectra for ice-bearing Ottawa sands (IBS). (A) Waveforms measured using a shear-wave transducer. Solid circles indicate the first P-wave arrival, followed by the normal-mode arrival (stars) and the shear-wave arrival (triangles). The dotted curve for the 34% IBS is the waveform measured after the sample equilibrated following the brief destabilization. (B) Power spectra for waveforms shown in Fig. 6(A), showing the brief destabilization of the 34% IBS (thick dashed curve) causes a measurable increase in the dominant frequency.
(Color online) (A) Frequency dependence of the radial displacements predicted at r = 0.6 cm for the nondispersive normal mode using parameters for the 20% IBS (dotted curve) and also with an S-wave velocity reduced by 1% (solid curve). The shaded region shows an uncertainty for the estimation of the dominant frequency from Fig. 6(B). (B) Calculated relative radial displacement of the normal modes shown in Fig. 6(A), summed within the frequency range of the dominant peak frequency (Fig. 6(B)), with respect to the P-wave velocity.
(Color online) Waveforms measured for the 43% GHBS measured in 2006 (dotted curve) and 2007 (solid curve). The P-wave arrival (solid circle) is quite distinct from the normal-mode arrival (star) in the 2006 case, but much less so in the 2007 measurement of a different 43% GHBS sample. The type of normal mode seems to have changed as well. These differences are partly due to a difference in the transducers used and partly due to differences in the internal structure of the sample.
Velocities of GHBS and IBS at a given pore-space saturation of hydrate or ice. α1, β1, G α, are the P-wave, S-wave, and normal-mode group velocities of GHBS and IBS. F d is the dominant frequency of the normal mode. Normal modes are denoted as nondispersive normal modes (NDNM), or second order normal modes (Second). Pre- and post-depressurization/repressurization cycle (D/R) results are given to indicate the impact of a D/R cycle on the observed waveform.
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