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Acoustic velocity is a complex result of several parameters that together control range and absolute values of velocity in sedimentary rocks. In the next sections we discuss the controlling factors and compare their significance in controlling the acoustic properties.

Mineralogic composition

Pure carbonates are characterized by the lack of clay or siliciclastic content and are mostly produced and deposited on the top or on the slope of isolated or detached carbonate platforms, which have no hinterland as a source of terrigenous material (Wilson, 1975; Eberli, 1991). They consist of >95% of the carbonate minerals calcite (low- and high-Mg), dolomite, and aragonite. The Tahiti reef system is unusual because a large part of the framework is not only made up by in situ coral colonies and skeletal sand but also, and in fact volumetrically most abundant, by microbialite. These reefal microbialites correspond to a late stage of encrustation of the dead parts of coral colonies or, more commonly, of related encrusting organisms (red algae and foraminifers), thus forming surface crusts (Camoin et al., 1999). The microbialites consist of laminated crusts and clotted micritic masses and are characterized by a suite of characteristic fabrics. Their growth forms, great variations in thickness, lateral persistence, and small-scale internal structures allow them to be interpreted as bioaccretionary features (Camoin et al., 1999). They form crusts on average a few centimeters thick, locally up to 10 cm thick, that comprise stacked generations of accretions displaying a wide range of growth forms ranging from irregular domes and bulbs to columnar.

Significant in Tahiti is that the carbonate reefs are contaminated with terrigeneous input (volcaniclastic in origin) from the island. The microbialites in particular are capable of withstanding terrigeneous influx during accumulation and trapped extraneous particles within the microbially mediated precipitation of micrite (Camoin et al., 1999). The abundance of volcaniclastic material probably reflects a depositional input signal which was influenced by (1) the discharge of the Tiarei river supplying the Tiarei site carbonate samples with dispersed fine to medium sand–sized volcaniclastic grains through the matrix, versus a “clean” reefal system at Maraa with very little insoluble residue; and (2) well-rounded sand- to small pebble–sized volcaniclastic grains found throughout the Pleistocene sequence. This last may point to a different carbonate platform geometry compared to the Holocene sequence, with different hydrodynamic and sediment supply conditions that favored the transport and abrasion of coarse volcaniclastic grains, which were subsequently incorporated in the bioclastic grainstone.

Figure F7A and F7B are cross-plots illustrating the clear relationship between insoluble residue and sonic velocity. Samples high in carbonate content plot toward the higher velocity values. At values <8% noncarbonate content, velocities are >4500 m/s. Minor amounts of noncarbonate material, clay, and/or quartz silt/sand can dramatically change acoustic velocities (Kenter et al., 1997b). Clay minerals and organic material have a negative effect on acoustic velocity (Stafleu et al., 1994). In the Tahiti samples the fraction of clay minerals and organic material present may be as high as 8.6 wt% and as such affect the acoustic velocity, causing negative deviations from the general trends. For Unit I, Site Maraa mean noncarbonate content is 5%, whereas for Site Tiarei mean noncarbonate content is 17%. This results in an overall average decrease in P-wave velocity of 130 m/s.

Rock texture, diagenesis, and Poisson’s ratios

Diagenetic overprint is one of the most prominent factors during maturation of carbonate rocks. Carbonate minerals are metastable and prone to rapid and intense modifications that alter the elastic properties of the rock and, therefore, the acoustic velocity. In particular, cementation and dissolution processes continuously modify the pore structure to create or destroy porosity. Unit II samples are different from Unit I samples in two respects. The first is the texture of the sediment. Whereas Unit I samples consist of coralgal-microbialite framework which forms one massive structure, Unit II samples are dominantly arenitic in nature. The granular texture may have originated with wave abrasion of the Unit II reef system, and samples are relatively mature with dominant subrounded grains. The texture would be classified as granular following Kenter et al. (2007). Secondly, grains in Unit II samples are lined by isopachous rims of early marine cement. Touching cement is known to have a positive effect on acoustic velocity. For example, Kenter et al. (1997a) discuss a data set of immature skeletal grainstones and show that a 12% increase in cement (12% decrease in porosity, no change in grain size) correlates to an increase of P-wave velocity of 790 m/s (33%), S-wave velocity of 525 m/s (45%), and decrease in Poisson’s ratio of 0.025 (7.5%).

Figure F8 is a cross-plot of P-wave velocity versus Poisson’s ratio with a number of mixed carbonate-clastic literature data sets (Limburg Quarry, Kenter et al., 1997a; Florida Keys, Anselmetti et al., 1997; Last Chance Canyon, Kenter et al., 1997b) plotted along with the Tahiti sample set. The individual sample sets data are discriminated for carbonate content. Poisson’s ratio, which is a specific ratio of P-wave over S-wave velocity, is defined as the ratio of transverse contraction over longitudinal stretching in a stretched bar and is defined as minus to compensate for normal materials. Poisson’s ratio influences the speed of propagation and reflection of stress waves and is important in predicting the nature of rocks (Rafavich et al., 1984). Poisson’s ratio (v) is easily deduced from VP and VS directly through the following equation (Domenico, 1995; Mavko et al., 1998, p. 52):

v = (VP2 – 2VS2)/2(VP2VS2).

In this application, Poisson’s ratio can be interpreted to represent a measure of the material response to applied stress, which is directly related to the nature of the mineral and texture makeup of a rock. This procedure has been used in the past by various authors (Ostrander, 1984; Rafavich et al., 1984; Shuey, 1985; Verm and Hilterman, 1995; Berg, 1997; Ozel et al., 1999) as a method to express the dependency of pore type and mineralogy.

From the cross-plot (Fig. F8) a number of observations can be made. The Limburg Quarry and Florida Keys (>0.92% CaCO3) data groups are situated in the upper left quadrant of the plot, corresponding to high Poisson’s ratios at relatively low P-wave velocities, typical for clean, immature carbonate samples. The Tahiti sample group is situated at ~4500 m/s P-wave velocity with the samples with >92% carbonate content toward the higher velocity values. The samples with >8% noncarbonate material are found toward velocities of <4500 m/s. Poisson’s ratios are relatively high, ~0.32 on average. The Last Chance Canyon data set displays a similar separation at ~5500 m/s. In addition, samples rich in clay are discriminated and correspond to P-wave velocity values dominantly <4500 m/s. The Last Chance Canyon sample set, however, shows much lower Poisson’s ratios, grouped around 0.25. These rock samples have undergone significantly more diagenetic alteration (cf. Kenter et al., 1997b). Quartz graywackes and quartz-rich wackestones exhibit sutured grain contacts formed as a result of pressure solution during burial. In addition, biomoldic porosity is partially occluded by columnar and blocky calcite cements that postdate the pressure solution and are therefore a product of burial diagenesis. After burial diagenesis, selective vuggy dissolution created the present-day porosity as a result of dissolution and precipitation in oxygenated meteoric near-surface groundwaters. During burial diagenesis S-wave properties profit significantly more than P-wave properties from compaction and cementation. The frame stiffens, with higher S-wave velocities as a result, hence the lower Poisson’s ratios. From the cross-plot one can conclude that the main parameter affecting the acoustic behavior of the samples is the burial diagenesis and presence of noncarbonate material.

Velocity transforms

Popular velocity transforms for density to velocity and porosity to velocity transformations are the Gardner transform (Gardner et al., 1974); the Wyllie et al. (1956) equation, or time-average equation; and the modification of the time-average equation of Raymer et al. (1980). All are empirical relationships. In general, experimental data sets rarely follow these models in great detail, and therefore the equations are used for comparison. Figure F6 shows cross-plots of porosity versus P-wave velocity derived from core-log data from all sites. Discrete laboratory measurements are superimposed. Time-average equations for solid-phase velocities of 6.5 km/s (calcite) and Raymer equations are indicated by a solid line and a dashed line, respectively. Whereas the velocity transforms describe a slightly concave-upward shape, the measured core logging data follow a linear equation and deviate as much as 1000 m/s at a given porosity (Fig. F6). Figure F9 shows cross-plots of acoustic velocity versus porosity (A) and versus density (B), along with velocity-porosity transforms of Wyllie et al. (1956) for various matrix velocities, and (B) Gardner’s equation (1974) for limestone and Anselmetti and Eberli equation (1993) undifferentiated for mineralogy. Discrete measurements for the Tahiti data set are positively offset with respect to the Gardner limestone equation. The data set follows the Anselmetti and Eberli (1993) equation more closely (Fig. F9B). The Wyllie time-average equation gives a good approximation for samples with up to 18% porosity; however, above this it is clear that with increasing porosity the velocity of the discrete measurements shows a positive deviation from the velocity transforms. The same holds for decreasing density. One possible explanation may be the presence of the volcaniclastic minerals of olivine, pyroxene, and plagioclase with respective matrix velocities of 8480, 7850, and 6300 m/s (Carmichael, 1989), which are higher than the matrix velocity of calcite (6530 m/s).

A linear regression was used to calculate velocity-porosity transforms that predict sonic acoustic from porosity and carbonate content or at different levels of volcaniclastic contamination. Similar to the velocity-porosity transforms calculated for siliciclastics by Vernik and Nur (1992), the velocity-porosity relation for a given mineralogic composition is a linear equation. At a fixed porosity, the velocity-mineralogy relation is also a linear function and has a similar variation as the velocity-porosity equation for the range in porosity between 0% and 30% (Fig. F7A). Subsequently, in this porosity range and for this limited data set the effect of carbonate content on acoustic behavior is comparable to that of porosity. At zero porosity, the clean carbonates (Site Maraa) have P-wave velocities of 4.9 km/s and are as much as 130 m/s higher than those for the volcaniclastic-rich samples (Site Tiarei). With increasing porosity, this difference remains fairly constant as the slopes of the velocity-porosity relation are similar (200 m/s higher diversion at 35% porosity). The intersection point of the velocity-porosity transform with the zero-porosity axis decreases with decreasing carbonate content, which may be explained by the presence of clay minerals and organic content. The slope of the velocity-porosity transform for lithologic Unit II samples (cemented mixed carbonate-volcaniclastic specimens) is steeper than that for high Unit I samples. For P-wave velocities this gradient is 5.14 km/s per porosity unit. This is a more common value for mature carbonate rocks and has been documented in previously published data (e.g., Kenter and Ivanov, 1995; Kenter et al., 1997b).

Comparison with core measurements and downhole logging data

Figure F5 shows the comparison between downhole logging velocity, core logging velocity, and P-wave velocity in minicores under confining pressure. Sonic velocities are slower than the discrete measurements with the larger excursions toward the lower velocities. For the Tiarei samples there is a poor correlation between log velocity and discrete velocity measured under effective pressure. Log velocities have corresponding laboratory velocities from 5% to 15% higher. Similar observations can be made from the correlation of log velocity with discrete velocity in lithologic Unit I at Site Maraa. Unit II samples from Maraa, however, show much closer agreement between downhole data and laboratory measurements (Fig. F5A at 21R). Discrete measurements of Unit I experience larger differences than Unit II samples (cf. Fig. F5A–F5C).

The progressive deviation of discrete velocity from log velocity toward higher values is probably primarily related to the “selective” sampling of more competent (and therefore “faster”) rock fabrics during coring operations. In addition, there is a ±2 m uncertainty between the methods used to calculate “log depth” and “core (pipe) depth.” Second, one of the most important effects is the introduction of velocity dispersion: seismic velocities increase with increasing frequency (Paillet and Cheng, 1991; Mavko et al., 1998). Discrete measurements of velocity are performed using ultrasonic frequencies (1 MHz), whereas the sonic log uses 10 kHz frequencies. Third, the quality of the sonic log is closely related to the borehole’s diameter and shape. Abundant cycle skipping in the sonic log raw data and poor hole quality (i.e., presence of coring-induced fractures or other damage to the wall of the borehole; see caliper log in the “Expedition 310 summary” chapter) reduce the quality of the sonic log (Bourbié et al., 1987). Fourth, the scale of lithologic, and therefore petrophysical, alternations within the core is critical compared to the sampling interval of the sonic log. Where discrete measures of velocity are only on matrix sediments, the sonic log provides an average over an interval of 1 ft (~31 cm) in which velocity is averaged over large primary pores containing seawater (~1535 m/s) and rock. These effects should be considered when comparing acoustic data sets from a variety of sources.