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Methods and materials
A basis for most rock resistivity studies was provided by Archie (1942), who examined the relation between resistivity and porosity in sandstone cores from the U.S. Gulf Coast region. We assume that this relation is an adequate approximation in all of our analyses. He empirically established that the resistivity of a fully water-saturated sediment (Ro) is closely proportional to the resistivity of the pore fluid (Rw):
where the proportionality constant F is called the formation factor. Furthermore, by examining core samples from different formations, Archie established an exponential empirical relationship between F and the porosity (φ):
where the exponent m was determined to be formation specific. Winsauer and Shearin (1952) modified Archie's original equation by including a coefficient a in the relation:
From a physical standpoint, a should be unity, because when φ = 1, F = 1; however, because Equations 2 and 3 are empirical relations, allowing a to vary generally improves the fit between F and φ, as it provides an additional degree of freedom. From a physical perspective, the values of parameters a and m depend on the interconnectivity of the pore spaces, which in turn depends on lithology, cementation, and grain size distribution (Hearst et al., 2000). Smaller values of a and m are qualitatively indicative of well-interconnected pore spaces (i.e., lower Ro for a given φ and Rw).
Many subsequent studies using downhole log data, core data, and laboratory measurements have confirmed the exponential relation to be a good approximation for relating resistivity to porosity (e.g., Jackson et al., 1978; Swanson, 1979; Hilfer, 1991; Ioannidis et al., 1997) and adequate for the purpose of this study.
When gas hydrate is formed from pore fluid, the salts in solution are largely excluded. The result is that the electrical resistivity of gas hydrate is much greater than that of saline pore fluid, and gas hydrate occurrence can significantly increase bulk sediment resistivity (e.g., Collett, 2001; Riedel et al., 2005). To first order, gas hydrate may be taken to be nonconductive (like the sediment grains) as compared to the pore fluid. An empirical relationship describes the effect of nonconductive material in the pore space on resistivity:
where Rt is the true or measured bulk resistivity, Sw is the water saturation (defined as the fraction of the pore space occupied by water), and n is the saturation exponent (Hearst et al., 2000). In the case of partial gas hydrate pore space saturation, the gas hydrate saturation (Sh) is defined as Sh = 1 – Sw. The value of n in Equation 4 is a measure of how the occurrence of gas hydrate affects Ro (i.e., the grain-hydrate-fluid structure). If n is relatively large, gas hydrate forms in a way that strongly impedes current flow and increases bulk sediment resistivity (e.g., gas hydrate located in the pore throats), whereas if n is relatively small, gas hydrate forms in a way that has a lesser effect on sediment resistivity (e.g., gas hydrate occurrence in the pore space, making minimal contact with sediment grains). Pearson et al. (1983) calculated an estimate for n of 1.94; however, modeling by Spangenberg (2001) has shown that n depends somewhat on grain size distribution and the gas hydrate saturation itself. Combining Equations 3 and 4 gives Archie's relation for gas hydrate–bearing sediments (e.g., Collett and Ladd, 2000) as
In practice, for many marine sediments, the pore fluid resistivity Rw usually can be adequately estimated from the equation of state of seawater (Fofonoff, 1985), if in situ pressure, temperature, and salinity are known. Parameters a and m can be estimated empirically by curve fitting F φ versus data from fully water-saturated samples using Equation 3. Gas hydrate saturation can then be estimated for sediment with φ and Rt if Equation 5 is rearranged as
Equation provides a relationship between gas hydrate saturation and resistivity, that empirically accounts for the sediment porosity, the interconnectivity of the pore space, and the effect of gas hydrate occurrence on the interconnectivity of pore space. To estimate gas hydrate concentration from this relation requires measurements of Rt, φ, and Rw, as well as the estimation of empirical Archie parameters a, m, and n. The most important difficulty is estimating the in situ pore fluid salinity (i.e., pore fluid resistivity). The salinity measured in recovered cores could include an unknown amount of pore fluid freshening if in situ gas hydrate dissociates upon core recovery. One method, proposed by Hyndman et al. (1999), allows for in situ salinity and gas hydrate concentration to be calculated simultaneously but introduces additional uncertainties.
The approach taken in this study is to solve Archie's equation (Equation 6) to determine a gas hydrate saturation profile at each site of the drilling transect while quantifying the uncertainties in (1) the empirical Archie parameters, (2) the in situ salinity, and (3) the appropriate choice of porosity measurement, as well as their effect on gas hydrate saturation estimates.
Expedition 311 provided a suite of logging-while-drilling (LWD) logs, including resistivity, density, and neutron porosity, in addition to several types of core measurements, including porosity, grain density, and interstitial water salinity (see the "Expedition 311 summary" chapter), along a transect of sites across the northern Cascadia accretionary prism. These data can be used jointly to solve Equation 6 for gas hydrate saturation. The use of LWD logs recorded by tools immediately behind the drill bit provides measurements as close as possible to in situ conditions. This is paramount in gas hydrate studies, because changes in pressure and temperature caused by drilling can affect gas hydrate stability locally around the borehole.
Downhole formation electrical resistivity data have been obtained from both Expedition 311 and Leg 146 using both conventional wireline and LWD logging tools. The most reliable downhole resistivity measurement is obtained from the LWD geoVISION resistivity-at-the-bit (RAB) tool. The RAB tool is connected directly above the drill bit and uses two transmitter coils and several electrodes to obtain different measurements of resistivity. Resistivity is measured using a focusing technique: the upper and lower transmitter coils produce currents in the drill collar that meet at the ring electrode. In a homogeneous medium, a net current flow perpendicular to the tool would occur at the ring electrode. This radial current flow becomes distorted in heterogeneous formations, and the current required through the ring electrode to focus current flow into the formation is related to the formation resistivity (see the "Expedition 311 summary" chapter). This focusing technique is also used to measure resistivity at three button electrodes (corresponding to three depths of investigation: shallow [~0.3–0.4 m], medium [~0.4–0.5 m], and deep [~0.4–0.6 m]). As the tool rotates in the borehole, the button resistivity is measured every ~6°. The button deep average (BDAV) resistivity, used here as Rt in the Archie analysis, is obtained by averaging the deep button resistivity at a given vertical depth over the range of azimuthally varying measurements. The BDAV resistivity has a vertical resolution of 5–8 cm and provides the most accurate measurement of in situ resistivity.
Figure F2A shows the BDAV resistivity profiles at the four Expedition 311 sites well transect. At each site, the seismically and log inferred base of gas hydrate stability zone or BSR depth is shown. Used alone, these resistivity logs qualitatively indicate certain zones of gas hydrate occurrence. High-porosity unconsolidated marine sediments in the study area generally have resistivities on the order of 1 Ωm. Certain zones above the inferred BSR exhibit much higher resistivities and are therefore interpreted to be gas hydrate bearing, notably at Site U1326 at 73–94 meters below seafloor (mbsf) and 252–261 mbsf, at Site U1325 in thin layers between 195 and 240 mbsf, and at Site U1327 at 120–138 mbsf. The presence of gas hydrate near the BSR is inferred by a slight decrease in resistivity from 1.6 to 1.3 Ωm at Site U1325 and from 2.4 to 2.0 Ωm at Site U1327 across the BSR. Free gas immediately beneath the BSR might slightly increase the resistivity, explaining why no obvious decrease in resistivity at the BSR is observed at Sites U1326 and U1329. However, these two sites both exhibit thin high-resistivity zones immediately above the BSR (255–261 mbsf at Site U1326 and 120–124 mbsf at Site U1329), probably also related to gas hydrate occurrence. Therefore, all four sites probably exhibit at least a small amount of gas hydrate immediately above the BSR. The high-resistivity zone below 176 mbsf at Site U1329 is interpreted not to be gas hydrate but rather an unconformity, below which much older, low-porosity, lithified Miocene (>6.7 Ma) sediments occur (see the "Site U1329" chapter).
Figure F3 shows the suite of downhole resistivity data collected at Sites 889 and U1327. Holes 889A, 889B, and U1327E were logged with wireline induction tools, whereas Hole U1327A used LWD, with the BDAV resistivity shown here. The distance between Holes 889A, 889B, and Site U1327 is on the order of 500 m, whereas the distance between Holes U1327A and U1327E is only ~70 m. The general trend observed in all holes at this site is an increase in resistivity from ~1 Ωm at the seafloor to ~2 Ωm at ~120 mbsf; background resistivities of ~2 Ωm are observed below that depth, with thin higher resistivity zones at different depths at each site. The most dramatic variability between holes is actually between the two most spatially proximal holes (U1327A and U1327E), where consistently higher resistivities (by ~0.3 Ωm) were measured below ~120 m in Hole U1327A, and a high resistivity interval (>5 Ωm, between 120 and 138 mbsf) was measured only in Hole U1327A. The slight resistivity bias can possibly be explained by the use of different tools to log the hole or the different time lags between drilling and logging in LWD versus wireline. However, the observation of the high-resistivity zone (120–138 mbsf) only in Hole U1327A can only be explained by abrupt lateral lithologic variations, such as a confined turbidite deposit, and/or variations in gas hydrate occurrence, such as a steep vein or lens.
To first order, log and core porosity measurements generally account for gas hydrate as part of the pore space because properties that are measured to determine porosity are usually similar for gas hydrate and pore water. The available porosity measurements are from the density and neutron logs and from IODP shipboard core moisture and density (MAD) analyses after any gas hydrate has dissociated (Fig. F2B).
MAD-based core porosity was measured as one of the "index" properties on retrieved sediment cores by the Expedition 311 Scientists (see the "Expedition 311 summary" chapter). Wet mass, dry mass, and dry volume were measured on push-core samples of ~10 cm3 to calculate porosity, as described in Blum (1997) and the "Methods" chapter. Wet mass was measured immediately after the sample was collected, whereas dry mass and volume were measured after the sample was heated at 105° ± 5°C (without vacuum) for 24 h and allowed to cool in a desiccator. Several biases in free water core porosity measurements must be corrected. There is a bias toward higher porosities because dry mass and volume were measured on sediments that had been heated to 105°C, a temperature high enough to release some of the bound water in smectite clay (Winters, 2000). Although clays may be somewhat less resistive than the granular component of the sediment matrix, they are usually sufficiently resistive relative to the pore fluid to be included as part of the matrix in electrical resistivity analyses. Other corrections applied were for porosity rebound (Hamilton, 1976; Goldberg et al., 1986) and for residual salt left behind by the evaporated pore water (Blum, 1997). There is also a potential sampling bias toward lower porosities because porosity could be measured more frequently from more competent (generally less porous) core samples, which have a higher probability of recovery. Because gas hydrate dissociates into water and gas upon core recovery, porosity measurements from core MAD analysis measure in situ gas hydrate as part of the subsequent core pore volume.
Log density–derived porosities are obtained from the LWD density log by linear interpolation of the formation bulk density (ρb) between the density of water (ρw) , taken to be 1.03 g/cm3, and the average grain density (ρg) measured in the core MAD analysis:
An average grain density trend was estimated from core at each site, and values ranged from 2680 to 2780 kg/m3. The variance in grain density measurements gave standard deviation estimates of 30 to 100 kg/m3 that varied from site to site. Note that for the porosity estimate to exclude bound water, the average grain density must include the clay component of the sediment matrix. A log measurement of formation electron density is obtained based on the reduction in gamma ray flux between a source and a detector on the sonde. The source (127Cs) emits gamma rays into the formation, which are then Compton-scattered by electrons in the formation. A fraction of the emitted gamma rays are scattered toward a gamma ray counter on the logging tool. The ratio of received to emitted gamma rays depends on the formation electron density, which is closely proportional to the formation bulk density because of the well-known relation between atomic number and atomic mass. High concentration of certain elements with unusual electron density responses can result in error (Hearst et al., 2000); however, this is not expected to be a problem given the composition of the sediments studied. The measurements are calibrated by empirically relating gamma ray count (i.e., formation bulk density) to core bulk density in a known reference.
The vertical resolution of the density tool used during Expedition 311 was ~15 cm, and the depth of investigation was ~10 cm. Even for LWD measurements, the density log must be excluded or used with caution in zones with poor hole conditions, especially where the hole radius is greater than the depth of investigation of the tool. These washout zones can be identified with the caliper tool. The main sources of uncertainty in a high-quality density porosity measurement are the statistical uncertainty in the gamma ray count used to calculate the density and the uncertainty in the grain density (discussed above). This combined uncertainty is estimated as ±0.03 porosity units (A. Malinverno, pers. comm., 2006). Because the density of pure gas hydrate (ρh = 0.92) is similar to that of pore water (ρw = 1.03) with near seawater salinity, the density porosity calculated from Equation 7 measures gas hydrate nearly as part of the pore volume. Even at high gas hydrate concentrations, the assumption that water (instead of gas hydrate) fills the pore space has only a small effect on the calculated porosity (e.g., see the "Expedition 311 summary" chapter).
The neutron porosity tool emits a high-energy neutron beam into the formation. As the neutrons pass through the formation, they interact with the ambient atoms, slow down, and are eventually captured. A lower energy neutron detector on the tool detects the neutrons that have been slowed by the formation (epithermal neutrons). Neutrons lose the most energy when they collide with atoms of similar mass, so the neutron tool is most sensitive to formation hydrogen concentration (Hearst et al., 2000) and therefore, to a first order, to water content. The ratio of emitted to detected neutrons is empirically related to porosity through calibration to a known reference, ideally with a similar response to that of the formation studied. Two factors known to cause significant errors in the neutron porosity measurement are fluid chlorinity and hydrocarbon content. The chlorine atom has an unusually large (neutron) capture cross section, but its effect can be accounted for if the chlorinity is known. In high enough concentrations, the presence of hydrocarbons can cause a positive bias in neutron porosity: because hydrocarbons represent a large amount of hydrogen, they can significantly increase the formation bulk hydrogen concentration if the other main hydrogen component is from the formation water content.
Clay minerals, when present in large enough concentration, can contain a significant amount of bound water that is measured by the neutron porosity tool as pore space, rather than sediment matrix. For this reason, in clay-rich sediments, porosity estimates from neutron logs are generally greater than those from density porosity (given a choice of average grain density in Equation 7 that includes clay). With knowledge of the clay content from cores, a correction for bound water content can be applied to the neutron log. The neutron porosity logs shown in Figure F2B have been corrected for bound water content by the Expedition 311 Scientists (see the "Expedition 311 summary" chapter) but still have a bias of ~0.06–0.08 greater porosity than the density porosity, probably caused by an incomplete correction for bound water content or other biases that were not adequately accounted for.
Core porosities generally are greater than log density porosities and less than log neutron porosities, but much closer to the density porosity than to the neutron. However, both the density and neutron porosity logs show similar structure, with more scatter in the neutron porosity. Because gas hydrate is mainly composed of (solid) water, it has a similar hydrogen concentration to that of water, so, to first order, the neutron porosity measures gas hydrate as part of the pore volume. However, both the methane in gas hydrate and the free gas below the BSR act to slightly increase the measured neutron porosity because methane has a greater hydrogen concentration than the pore water.
The vertical resolution of the neutron porosity tool used during Expedition 311 was ~30 cm. The depth of investigation into the borehole wall is highly dependent on the hydrogen concentration and is probably <20 cm, given the high-porosity sediments studied here. For both wireline and LWD measurements, neutron porosity is very sensitive to hole conditions.
Archie's law for purely (saline) water-saturated sediments is given in Equation 3, where Rw can be calculated from the equation of state of seawater (Fofonoff, 1985) or other saline fluid compositions if the in situ pressure, temperature, and salinity are known. Pressure is taken to be nearly hydrostatic, temperature is estimated from the seafloor temperature and the thermal gradient, and salinity is taken from a smoothed fit through core salinity measurements at the same site (Fig. F4). In zones inferred to be gas hydrate–free (i.e., fully water saturated), the measured core salinity can be assumed to be equal to the in situ salinity. Empirical Archie parameters a and m can then be estimated from a crossplot of F and φ (Pickett plot) for sediments containing no gas hydrate in areas with good log quality. Gas hydrate–free zones are chosen from the undeformed slope basin sediments of Holes U1327A and U1329A, where little or no gas hydrate was interpreted (i.e., no evidence in core and no large spikes in resistivity are observed). Also, slope basin sediments have less time to accumulate gas hydrate in the pore space because they were deposited more recently than the accreted sediments. Sediments below the inferred BSR in Holes U1325A, U1326A, and U1327A (Fig. F5) were also used. Although the sub-BSR zones probably contain a small amount of free gas, which could affect Rt and φ, these zones plot along the same trend in the Pickett plot as the assumed gas hydrate–free slope basin sediments, so the effect of free gas (in small concentrations) on Archie parameter estimates is small. Also, Hyndman et al. (1999) showed that porosity-resistivity relations in slope basin and accreted sediments are not significantly different.
Using all density porosity data and formation factor values from gas hydrate–free zones yields a cementation factor m of 1.751 and a is determined as 1.394, very close to the earlier estimates by Westbrook, Carson, Musgrave, et al. (1994) and Hyndman et al. (1999). The R2 value of the statistical fit to the data points is 0.82. We therefore fix in this study the cementation factor m to the original value of 1.76 determined for this part of the Cascadia margin for all calculations involving density porosity.
A best fit to the F versus φ data with the fixed m-value for the gas hydrate–free zones (Fig. F5) gives an estimate for a of 1.38 ± 0.18 (one standard deviation), which is similar to the value obtained by Hyndman et al. (1999) from core porosity and resistivity at Site 889/890. Others (e.g., see the "Expedition 311 summary" chapter) have estimated Archie parameters by fixing a to unity so that at 100% porosity Rw = Rt. Although this approach has a valid physical basis, fixing m = 1.76 and searching for the best a gives a better fit for these data. The uncertainty in the Archie relation arises mainly from the uncertainty in the Archie coefficient a. This uncertainty reflects the effect of data noise on the correlation between the porosity and resistivity measurements. Here, this includes random scatter (measurement error) in the density and resistivity logs, as well as error related to the average grain density in the porosity calculation (Equation 7). An estimate of n = 1.94, calculated by Pearson et al. (1983), is used here for the Archie saturation exponent. A sensitivity analysis of the saturation exponent shows that varying n by ±0.20 changes the gas hydrate saturation estimate by only ±0.01, on average. However, inspection of Equation 5 or 6 shows that gas hydrate saturation estimates themselves are more sensitive to n at higher gas hydrate saturations. From a physical perspective, choosing a value for n similar to that of m implies the assumption that the effect of gas hydrate formation on the electrical resistivity is similar to that of simple effective porosity reduction.