It is commonly assumed that almost all of the microcracks in a core have closed at 200 MPa pressure. This is approximately the pressure that the rock would be under at depth in the lower crust. Ideally, the velocity increase with pressure should be greater for high-porosity samples because there are more voids to close. All of our samples had porosities <1%, but there was no correlation between porosity and the velocity difference between 10 and 200 MPa or between porosity and velocity at 200 MPa (Fig. F1).
The compressional wave velocity at 200 MPa is shown as a function of density in Figure F2. Most of the velocities cluster between 6800 and 7000 m/s, but there are two anomalously high values (>7500 m/s) and one low value near 6660 m/s. The latter was measured in the gabbronorite. Also shown in Figure F2 are lines of constant mean atomic weight (Birch, 1961; Iturrino et al., 1991). All of our measurements fall between the lines for mean atomic weights (M) of 20 and 22 with most values near M = 21, which is predicted by Birch's law for common rocks.
The relationship between
compressional and average shear wave velocity is shown in Figure F3
with lines of constant Poisson's ratio (
).
Half of our (12) samples have Poisson's ratios >0.30. This contrasts with the
Leg 118 results from shallower depths in Hole 735B for which none of the (13)
minicores measured had Poisson's ratios >0.3. Rocks with higher Poisson's
ratios are less rigid. It is not clear why gabbros of essentially the same
composition but from greater depth should be less rigid.
The mean compressional wave velocity of our Leg 176 cores at 200 MPa is 7007 ± 266 m/s compared to 7100 ± 200 m/s for the Leg 118 olivine gabbros. The mean density of our Leg 176 cores is 2.95 ± 0.11 g/cm3 compared to 2.95 ± 0.5 g/cm3 for the Leg 118 olivine gabbros. The mean shear wave velocity of our Leg 176 cores is 3780 ± 188 m/s compared to 3900 ± 100 m/s for the Leg 118 olivine gabbros. The mean Vp/Vs ratio of our Leg 176 cores is 1.855 ± 0.064 compared to 1.81 for the Leg 118 olivine gabbros. The mean Poisson's ratio of our Leg 176 cores is 0.294 ± 0.020 compared to 0.28 for the Leg 118 olivine gabbros. None of the Leg 176 cores measured in this study had porosities >1%, but in the Leg 118 study ~20% of the cores had porosities >1%. Clearly, the Leg 176 olivine gabbros acquired over depths from 450 to 1500 mbsf have very similar physical properties to the olivine gabbros from Leg 118 acquired at depths of <450 mbsf.
Compressional and shear wave attenuations were measured in the same cores by New England Research, Inc., using the spectral ratio method (Toksöz et al., 1979). The results are summarized in "Appendix B." The method compares the waveforms of a rock sample with attenuation and a reference sample, usually aluminum, with very little attenuation. It relies on the assumption that the received waveform will be modified slightly by the decrease in higher-frequency energy due to attenuation. If there is scattering caused by heterogeneities within the sample or there are multiple paths of arrivals from the sides of the sample, the waveforms will be dramatically altered and the method breaks down. Figures F4 and F5 summarize the steps in the method for a good waveform (P) and a bad waveform (S), respectively. The compressional wave attenuation values are reasonably good but the shear wave values may be questionable. This method was also used by Goldberg et al. (1991) to study compressional wave attenuation in the Leg 118 cores.
The quality factor, Q, has an inverse relationship to attenuation. Often attenuation is quoted as the quantity 1000/Q. When 1000/Q is large, the attenuation is large. The mean compressional wave 1000/Q value for our Leg 176 cores at 200 MPa is 33.8 ± 21.2. This compares to a mean 1000/Q for the Leg 118 cores made at atmospheric pressure of 49.14 ± 32.03. Again there is little difference between cores from 450 to 1500 mbsf and cores from above 450 mbsf. The shear attenuation, which was not measured on the Leg 118 cores, is 65.1 ± 30.9 for the Leg 176 cores. There is about twice as much shear wave attenuation as compressional wave attenuation.
We investigated anisotropy by considering three sets of three orthogonal minicores selected from large macroscopically homogeneous sections of olivine gabbro. The directional velocity measurements are summarized in Table T2. The plus or minus "raw" or "measured" data from "Appendix A" have been "corrected" to a density datum of 2.95 g/cm3 using Birch's Law, with a molecular weight of 21 (see below) and a Vp/Vs ratio of 1.85. Sections 176-735B-165R-5 and 193R-1 are essentially isotropic. Their compressional velocities are all within 117 m/s, compared to a standard deviation for P-wave velocities of 266 m/s. Similarly, their shear velocities are all within 147 m/s, compared to a standard deviation for S-wave velocities of 188 m/s.
For Section 176-735B-146R-2, however, there does appear to be significant variations in velocity with direction. After correction for density, the z-axis is dramatically slower for both compressional and shear waves. Anisotropy of the Leg 118 olivine gabbros was also discussed by Iturrino et al. (1991).
It is often necessary in
numerical modeling of seismic wave propagation in the oceanic crust to have
simple empirical relationships between compressional wave velocity, shear wave
velocity, and density. For example, a common relationship between compressional
wave velocity (Vp, in kilometers per second) and density (
,
in grams per cubic centimeter) for crustal rocks is as follows (from Ludwig et
al., 1970):
= 0.252 + 0.3788 x Vp.
These are often arbitrary linearizations of complex phenomena. Based on the Leg 118 and 176 core measurements, we recommend the following guidelines. In the absence of other information, a good approximation for oceanic gabbros is to assume a Poisson's ratio of 0.30 to compute Vs from Vp and to use Birch's Law with a molecular weight of 21 at a pressure of 200 MPa to compute density from Vp as follows (Birch, 1961; Iturrino et al., 1991):
= 0.335 + 0.5689 x Vp.
