Propagation of sound waves in a rock undergoing phase transformations

Abstract

The velocity of compressional waves in a limestone is determined up to 25 kb. Two phase transitions occur in this range of pressure. The first (at about 15 kb) is associated with a pronounced and continuous decrease in velocity and a marked increase in attenuation; the second (at 23 kb) is associated with a discontinuous jump in velocity and no appreciable change in attenuation. The velocity of shear waves is determined up to 15 kb; a decrease in velocity similar to that in the P velocity appears at about this pressure. Poisson's ratio computed from the velocity data drops from 0.29 at 13 kb to 0.19 at 15 kb. A detailed study of strain up to 21.5 kb reveals no discontinuous change in volume and suggests that on a macroscopic scale the first transition is a high‐order phase transition. Using data from the velocity measurement and the strain measurement, we estimated the characteristic time for the first transition to be about 0.05 μsec. Not enough data are available to estimate the characteristic time for the second transition, but it must be very much longer. Inside the earth a phase transition with a characteristic time of about or less than 0.1–1 sec may affect the propagation of seismic waves in much the same way as the first calcite transition affects the propagation of the ultrasonic waves and thus result in a pronounced decrease in velocity and a marked increase in attenuation. The decrease in Poisson's ratio may serve as a criterion for differentiating phase transitions from other possible causes for low‐velocity layers.

Shear and compression waves in shocked calcium carbonate

“…Lacking data on single-crystal CaCO3(II), Grady et al [1978] fit the elastic moduli in the pure phases as well as the one model parameter to Wang and Meltzer's [1973] measurements of the pressure dependence of the ultrasonic longitudinal wave speed in Oak Hall limestone. The resulting good agreement of the calculated, relaxed, longitudinal wave speed with these ultrasonic measurements was incorrectly cited as evidence that Wang's mechanism, which was incorporated into the model, was producing the decrease in wave speeds.…”

“…The new and unique information provided by the shear wave measurements in a shock-induced, high-pressure phase warrants special emphasis. First, the shear wave speeds are a significant extension to the ultrasonic measurements, which were limited to less than 3% compression because the shear wave signal was strongly attenuated [Wang and Meltzer, 1973]. The present data show that after an initial decrease, the shear wave speed becomes nearly constant, and subsequently increases with compression.…”

“…It is noteworthy that, by fitting their model to frozen-composition wave speeds, Grady et al [1978, Figure 12] obtained good agreement between the calculated hydrostatic compression curve, which depends on relaxed bulk modulus values, and that measured by Wang and Meltzer [1973]. An alternative model considered by Aidun [1989] that used available purephase modulus values also achieved good agreement with a hydrostatic compression curve.…”

Compression of calcite to 40 KB

“…we used calcite single crystals, whereas Wang and Meltzer [1973] used Oak Hall quarry limestone, which 'is fine grained.…”

“…The calculation of V•,(P) based on the assumption that both #(P) and B(P) vary with pressure in a similar manner is shown by a solid line. The calculations using the experimental values #(P) [Wang and Meltzer, 1973] are shown by a broken line. It is seen that the V•(P) estimated by using the present values of B(P) rises with rising pressure, reaches a maximum, and drops at the pressure of the calcite 1-calcite 2 transition.…”