Average profiles of sound speed with depth below the sea floor have been determined for various sediment types by Hamilton (1985). These velocity-depth functions are based mostly on wide-angle seismic reflection methods (Le Pichon et al., 1968; Houtz et al., 1968; Bachman et al., 1983). Seismic velocity-depth measurements from surface ships could not be independently verified until subsurface logging methods were adapted to Deep Sea Drilling Project (DSDP) and Ocean Drilling Project (ODP) drill holes.
Figure A-1 compares the seismic measurements of Bachman and Hamilton from the Ontong Java Plateau (Johnson et al., 1978) with down-hole logging in the same area (Fulthorpe et al., 1989). These results validate seismic sound speed determinations. Figure A-2 compares logging results from the Labrador Sea (Jarrard et al., 1989) with Hamilton's (1979a) prediction for the same sediment type (deep-sea terrigenous turbidites; similar to the fill in Catalina Basin). Figure A-2 shows that Hamilton's methods (based on seismic measurements) reliably predict the average trend of in situ sound speed profiles. Figures A-1 and A-2 also show variations about the trend, which are probably acoustically significant. These might be best modeled statistically as in Gilbert (1980) or Holthusen and Vidmar (1982).
Density-depth functions were discussed by Hamilton (1976). This work was based on laboratory measurements, which were then corrected to in situ conditions using theory and consolidation test results from the geotechnical literature. As with sound speed profiles, confirmation of Hamilton's approach had to await down-hole logging. Figure A-2 shows a sediment density log from ODP hole 646 in the Labrador Sea (Jarrard et al., 1989, figure 1), along with Hamilton's prediction for that sediment type. The average trend is accurately predicted. Again, high-frequency variations are seen.
Figure A-1. In situ and seismic measurements of sound speed. Down-hole log-
ging results from the Ontong Java Plateau compared with the seismic measure-
ments of Bachman and Hamilton (Johnson et al., 1978). From Fulthorpe et al.,
1989, figure 6.
Figure A-2. In situ measurements of sound speed and density compared with
predictions. Down-hole logging results from the Labrador Sea compared with
Hamilton's average relationships for sound speed (1979a) and density (1976) in
the same sediment type. From Jarrard et al., 1989, figures 1 and 12. Logging
began at 206 m sub-bottom. Note different depth scales.
Figure A-3 is a compilation from Kibblewhite (1989, figure 8) for silts and clays. On the basis of this figure and other considerations discussed in the text, Kibblewhite makes a case for an f1 attenuation-frequency relationship above about 10 kHz and below about 1 kHz (p. 729); between these frequency regimes a nonlinear region is postulated. However, a line through the middle of the "silts and clays" region with a slope of 1 passes through the mid-frequency data cluster. An eye-fitted line has a slope of 1.2 over the range 1 to 10,000 Hz. Therefore, the details of the variation of attenuation with frequency is ignored, and an approximate f1 relationship is used in this report.
The attenuation-depth curves of Mitchell and Focke (1980, figure 11) were used to establish a mean attenuation profile. Kibblewhite (1989, p. 720-721) criticizes these measurements because an f1 dependence was assumed in the data reduction. However, Kibblewhite includes them in his figure 8, and they fall within his mid-frequency cluster of data. Because the values are reasonable when compared with other data, because they are based on in situ seismic measurements, and because they include depth dependence, the results of Mitchell and Focke are used in this report. In situ seismic measurements are especially useful because they include all energy loss mechanisms: intrinsic attenuation, scattering, multiple reflection, shear-conversion, etc.
Figure A-3. Compilation of sound attenuation versus frequency measurements.
Compressional wave attenuation measurements in silt-clay sediment and sedi-
mentary rock compiled by Kibblewhite (1989, figure 8). The few mid-frequency
measurements available suggest to Kibblewhite that the relationship between
frequency and attenuation is nonlinear, as required by theory. To a first approx-
imation, however, a line with a slope of 1 provides a reasonable fit to the
existing data.
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