Volume 12, Issue 4
Free Access

Acoustic and mechanical properties of Nankai accretionary prism core samples

Hugues Raimbourg

Hugues Raimbourg

JAMSTEC, Natsushima-cho,, Yokosuka, 237-0061 Japan

Now at Institut des Sciences de la Terre d'Orléans, Université d'Orléans, 1a rue de la Ferollerie, F-45071 Orléans, France

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Yozo Hamano

Yozo Hamano

JAMSTEC, Natsushima-cho,, Yokosuka, 237-0061 Japan

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Saneatsu Saito

Saneatsu Saito

JAMSTEC, Natsushima-cho,, Yokosuka, 237-0061 Japan

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Masataka Kinoshita

Masataka Kinoshita

JAMSTEC, Natsushima-cho,, Yokosuka, 237-0061 Japan

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Achim Kopf

Achim Kopf

MARUM, University of Bremen, PO Box 330440, D-28334 Bremen, Germany

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First published: 07 April 2011
Citations: 23


We studied undeformed sediment and accreted strata recently recovered by Ocean Drilling Program/Integrated Ocean Drilling Program (ODP/IODP) drilling in Nankai Trough convergent margin to unravel the changes in physical properties from initial deposition to incipient deformation. We have derived acoustic (Vp) and mechanical (uniaxial poroelastic compliance, compaction amplitude) properties of samples from various drill sites along the Muroto (ODP 1173) and Kii transects (IODP C0001, C0002, C0006, and C0007) from isotropic loading tests where confining and pore pressure were independently applied. We quantified the dependence of Vp on both effective (Peff) and confining (Pc) pressure, which can be used to correct atmospheric pressure measurements of Vp. Experimental Vp obtained on core samples extrapolated to in situ conditions are slightly higher than logging-derived velocities, which can be attributed either to velocity dispersion or to the effect of large-scale faults and weak zones on waves with longer wavelength. In the high-porosity (30%–60%) tested sediments, velocities are controlled at first order by porosity and not by lithology, which is in agreement with our static measurements of drained framework incompressibility, much smaller than fluid incompressibility. Rather than framework incompressibility, shear modulus is probably the second-order control on Vp, accounting for most of the difference between actual Vp and the prediction by Wood's (1941) suspension model. We also quantified the mechanical state of Nankai samples in terms of anisotropy, diagenesis, and consolidation. Both acoustic and mechanical parameters reveal similar values in vertical and horizontal directions, attesting to the very low anisotropy of the tested material. When considering the porous samples of the Upper Shikoku Basin sediments (Site 1173) as examples of diagenetically cemented material, several mechanical and acoustic attributes appeared as reliable experimental indicators of the presence of intergrain cementation. We also detected incipient cementation in samples from IODP Site C0001 (accretionary prism unit). In terms of consolidation, we distinguished two classes of material response (shallow, deformable samples and deep, hardly deformable ones) based on the amount of compaction upon application of a Peff large with respect to the inferred in situ value, with a transition that might be related to a critical porosity.

1. Introduction

In accretionary prisms such as Nankai, overpressures, i.e., pore fluid pressures exceeding hydrostatic values, within the décollement have been paid much attention as they provide an efficient way to reduce the friction and have a large impact on seismic rupture around the updip limit of the seismogenic zone [Bangs et al., 2009; Moore et al., 1995; Tobin and Saffer, 2009]. Unfortunately, direct measurement of pore fluid pressure is difficult to achieve and overpressures are often inferred indirectly, for example from a low Poisson's ratio estimated using seismic velocities Vp and Vs [Dvorkin et al., 1999a], or through the large-scale modeling of prism fluid circulation [Saffer and Bekins, 1998, 2006].

Another method consists in converting seismic velocity into porosity to estimate the state of compaction and to infer possible overpressures [e.g., Tobin and Saffer, 2009]. The Vp porosity relationships are experimentally calibrated with well logs or cm-thick discrete core samples [Erickson and Jarrard, 1998; Hoffman and Tobin, 2004; Hyndman et al., 1993], while the velocities on which such laws are applied are determined during seismic reflection campaigns, i.e., with a resolution of tens of meters at best. In addition to this problem of wave frequency, another problem is restoring velocities measured on core at atmospheric pressure to in situ conditions. Hamilton [1971a] proposed corrections for subseafloor sediments, but the problem remains for deeper samples.

More generally, the interpretation of geophysical profiles of Vp [e.g., Tobin and Saffer, 2009] or seismic impedance [Bangs et al., 1999; Bangs and Gulick, 2005; Park et al., 2002] rely on the knowledge of the evolution of the material during burial, in particular its consolidation, i.e., the reduction in porosity as a result of overburden increase. Although simple compaction curves [Athy, 1930] assume a very simple relationship between depth and porosity, actual consolidation is much more complex and porosity profiles are often ambiguous as they reflect hydrological state and possible overpressures [Screaton et al., 2002] as well as the internal strength of the rocks, which depends on lithology and diagenesis [Morgan and Ask, 2004]. In this respect, the experimental analysis of material strength evolution during consolidation is key to interpreting geophysical data.

In this paper we present the results of mechanical, isotropic experiments carried out on samples collected in the Nankai subduction zone during ODP Leg 190 (Site 1173) and IODP Legs 315/316 (Sites C0001, C0002, C0006, C0007) to characterize their mechanical (poroelastic, plastic) and acoustic properties. The first objective of this experimental study is to provide experimental constraints on simple theoretical poroelastic models of high-porosity (30%–60%) sediments, in order (1) to derive correction factors to restore to in situ conditions velocities measured at atmospheric pressure on discrete core samples (i.e., the standard IODP laboratory routine) and (2) to interpret the relationship between Vp and porosity. Core-scale, experimental Vp are also compared to logging/seismic data for integration of velocity data sets. The second objective of our tests is to further characterize the mechanical state of shallow (≤1000 mbsf) samples from the Nankai Trough area, which includes estimation of anisotropy, distribution of rock-strengthening cement/thermal alteration and response to experimental consolidation. Finally, we discuss the relevance of the concept of critical porosity in the light of our experimental results.

2. Tectonic Setting

The continuous convergence of Philippine Sea and Eurasian plates in Japan is responsible for the growth of a large accretionary prism since the Cretaceous [Taira et al., 1988], whose active portion, the Nankai Trough accretionary prism, is submarine and extends on several hundred kilometers along strike near the southwestern margin of Japan. Successive drilling within the Deep Sea Drilling Program (DSDP Legs 31, 87), the Ocean Drilling Program (ODP Legs 131, 190, 196) and NanTroSEIZE (Nankai Trough Seismogenic Zone Experiment) expeditions of Integrated Ocean Drilling Program (IODP Legs 314, 315, 316, 319, 322) and seismic reflection campaigns [Moore et al., 2005; Shipboard Scientific Party, 1991a; Tobin et al., 2009a] enabled to determine the internal structure of the wedge as decomposed into an outer section with a steep slope and active folding and thrusting and an inner section, more gently inclined and overlain by a fore-arc basin (i.e., the Kumano Basin).

Although the internal structure of the prism varies slightly laterally between transects off Muroto Peninsula (ODP Leg 190) and Kii Peninsula (IODP Legs 314/315/316) (Figure 1), in both settings it can be roughly divided into equivalent tectonostratigraphic units, from which we collected samples for testing (site location between brackets). Incoming sediments, located seaward of the prism, are composed of a lower sequence of hemipelagic sediments of the Shikoku Basin (ODP Site 1173), overlain by a variable thickness of trench turbidites. The wedge is made of frontally accreted and deformed sediments, composed of either hemipelagic material or trench turbidites (IODP Sites C0001, C0006, C0007), overlain by slope sediments and underlain by underthrusted sediments. The fore-arc basin is composed of thick, turbiditic material deposited over the inner wedge (IODP Site C0002).

Details are in the caption following the image
Map of the Nankai Trough, including the Kumano and Muroto transects investigated during ODP Legs 190/196 and IODP Legs 314/315/316 [Moore et al., 2009].

3. Experimental Procedure

3.1. Principle

Tested samples are cylinders with 1.5 in. (≈3.8 cm) diameter and 10–20 mm height, cut by a diamond saw from ODP/IODP cores (Figure 2). Experiments were carried out within an oil high-pressure vessel, where Pc, the confining pressure is fixed, while two independent water lines enable us to control Pp, the pore fluid pressure on both circular faces of the cylinder (the continuity of the fluid film from the pipes to the flat surface of the sample is ensured by the placement of metal filters on sample surfaces). For each set (Pc, Pp) of applied conditions, we measured sample height variations from two diametrically located points (Δh = equation image) as well as the time necessary for a compressional wave to propagate through the sample.

Details are in the caption following the image
(a) Experimental device of isotropic loading, where we measure variations in sample height Δh = equation image following Pc and Pp evolution. (b) Associated typical loading path, decomposed into a first, poroelastic phase, where Peff is kept below Peffin-situ and poroelastic compliance equation image as well as Vp dependence on Peff (i.e., equation image) are estimated, and a second phase where the potential plastic deformation upon application of a large Peff with respect to in situ conditions is assessed. (c) Associated normalized height evolution within the pressure vessel. Apart from an initial and limited decrease in height, partly due to filter shrinkage and holder movement, during the first phase of deformation, applied through cycles of Peff for several Pc increments, deformation appears almost reversible. During the second phase, large shrinkage occurs and persists even upon Peff release. Square (star) is the initial (final) normalized height measured out of the chamber. (d, e) Elementary step of poroelastic phase 1 (indicated on Figure 2c): for a given Pc, several Peff are applied, enabling to derive the compliance equation image (Figure 2d) as well as equation image (Figure 2e) (sample C0001H-5H-vert).

Experiments described here differ from usual consolidation experiments [Johns, 1986; Karig and Ask, 2003; Saffer, 2003] where uniaxial, vertical loading aims at reproducing in situ conditions prevailing during compaction. Our experiments were not meant to simulate in situ loading, but to assess the mechanical and acoustic state of the specimen using variable conditions of isotropic confining and pore pressures in an instrumented autoclave vessel.

3.2. Experimental Devices and Precision

Sample height variations Δh are measured by two Linear Variable Differential Transformers (LVDT), with a precision of ∼1μm, which measure the displacement between the 2 holders on either side of the sample. The precision on sample absolute height h = ho − Δh is in the order of ∼100μm, i.e., of much lower accuracy than the internal parameters, because (1) of possible movement of the holder during the insertion inside the high-pressure vessel and the first application of Pc and (2) the low precision on the sample initial height ho, measured out of the chamber with a caliper. In contrast, the precision in relative height variations is comparable to LVDT accuracy.

Compressional wave velocity Vp is measured using two piezoelectric transducers glued to the sample holder in titanium, which vibrate at a 3 MHz frequency. Travel time is estimated by hand picking of the wave arrival with a precision that depends on the signal quality, but that we estimate to be ∼0.1μs. The precision in relative travel time between two sets of conditions, estimated by the correlation between the two waveforms is much higher (∼0.01μs).

3.3. Mechanical Tests

For each studied samples, the test was decomposed into the three phases described hereafter. For any samples, we defined in situ effective pressure Peffin-situ as
equation image
where σv is the load of the rock column overlying the tested sample z, its thickness, and ρf the fluid density. Note that this value is not the actual in situ effective pressure, as in most cases no direct measurement is available, but a theoretical value calculated for hydrostatic pore fluid pressure. Actual in situ pore fluid pressure is larger than hydrostatic value (for fluid expulsion and compaction to proceed), but we suppose that the difference is small, because all our samples are relatively shallow, with relatively high porosity/permeability and they have not been subjected to rapid loading like material underthrust below the decollement. Furthermore, Site 1173 is used as a reference site where excess pore pressure is considered as negligible [e.g., Screaton et al., 2002] and direct measurements at depths in Kumano fore-arc basin confirm pore fluid close to hydrostatic conditions [Saffer et al., 2009].

3.3.1. Initial Resaturation

After insertion of the specimen into the high-pressure vessel, full rehydration and saturation prior to testing is ensured by raising the confining pressure Pc and pore fluid pressure Pp simultaneously to Pc ∼ 1 MPa and effective pressure Peff of the order of a few tenths of MPa. Upon transmission of the pressure through the pores, two simultaneous phenomena contribute to resaturation; first, the gas initially present is mechanically compressed so that its volume is divided by a factor equal to the pore pressure (when expressed in bars) and second, increase in pressure triggers gas dissolution in the liquid.

The applied effective pressure Peff is fixed to a value well below the in situ effective pressure. The samples are left with these conditions overnight before the mechanical test starts. Height variations during this phase are limited to a few tens of microns, i.e., a few permil, which illustrates that the samples were already close to saturation in their initial state after coring and cool storage.

3.3.2. Poroelastic Phase

Once the experiment has started, the first phase of loading consists in applying incrementally different magnitudes of Peff (Figures 2b and 2c) while Pc is kept at a fixed value. We impose during this phase the effective pressure to be kept below Peffin-situ.

Although Vp and height variations are not linear over a large Peff range [e.g., Tobin and Moore, 1994], in the range 0.5–3 MPa for deep samples (ca. > 300 mbsf) and 0.5–Peffin-situ for shallow samples (<300 mbsf), our samples can be reasonably considered as linear (e.g., Figures 2d and 2e). We can thus use height variations to derive a poroelastic coefficient equivalent to a uniaxial compliance equation image (Figure 2d) and to express similarly the dependence of Vp on Peff by the coefficient equation image (Figure 2e). As the loading is isotropic, one can assume that equation image = 3 equation image, so that the Peff-related, “dry” (drained) framework incompressibility Kdry can be evaluated as
equation image

To check the actual reversibility of deformation, the final step of Peff applied is also the smallest one (e.g., 1, 2, 3 then 0.5 MPa), and only when the sample expands back for this last step are the two linear coefficients estimated. This procedure is repeated for several values of Pc, so that several values of the compliance and Vp sensitivity are derived for varying conditions of Pc on the same specimen.

3.3.3. Plastic Phase

Following the poroelastic response, we increase Peff up to values in the range 1.5 Peffin-situ–2.5 Peffin-situ during a second phase. This increase results in irreversible compaction, which becomes apparent when releasing Peff. For each increment in applied Peff, we wait a time sufficient for both deformation and fluid pressure to tend toward asymptotic values. In addition, in each of our samples, for several steps of applied Peff, including the largest one, we assess the time necessary for pressure to equilibrate through the sample by applying a differential pressure (∼1 MPa) between the sample upper and lower surfaces and letting it decay, similarly to the method for measuring permeability described by Brace et al. [1968]. Depending on the sample and on the applied Peff, durations required for the pressure difference to decrease down to ∼0.2–0.1 MPa ranged from a few seconds to ∼2 h, which led to define the maximum time of our experiments as ∼48h.

The amplitude of the irreversible deformation was highly variable and largely depended on the tested material. Irreversible compaction in a sample such as shown in Figure 2c reached a few percent and was readily apparent in the large change in the slope of the height variations upon application of large Peff, which is a traditional way to diagnose the onset of irreversible compaction in consolidation experiments [Casagrande, 1936]. In contrast, the transition between poroelastic and plastic deformation was undecipherable in other samples and final plastic deformation was limited to less than 1%.

There is a choice of variables to express the amount of irreversible deformation (see Table 1). To separate the effects of sample initial resetup in the machine, poroelastic deformation and compaction, the amount of compaction is best estimated within the high-pressure vessel as the normalized reduction in length when Peff is increased from Peffin-situ to Peffmax (see sample C0001H-5Rvert in 15). On the other hand, for some samples, such as shallow ones in Site C0006, a large irreversible deformation started from the smallest application of Peff, so that the compaction can be estimated from the normalized length reduction from Peff = 0 to Peffmax, or from the ratio of sample height measured outside of the vessel before and after the experiment.

Table 1. List of Samples From the Nankai Trough Accretionary Complex and Incoming Shikoku Basin Sediments Used in This Studya
Sample Depth (mbsf) Porosity (%) Peff in Situ (MPa) T in Situ (°C) Dir. Deposition Settings Lithology Tectonic Settings Mineralogy (%) Uniaxial Compliance Consolidation Acoustic Properties
h v Clay Qtz Pl. Cc. equation image (10−3/MPa) equation image equation image equation image equation image (km/s/MPa) Vp (km/s)
C0006E-20X 132 48.1 1.1 5.5 X Tr. Sandy silt Front. Thr. 40.9 22.2 21.4 1.2 −7.0 0.911 2.664 0.881 0.070 1.932
C0006E-25X 180 - 1.6 7.0 X Silty clay 26.5 25.9 25.3 1.2 −5.5 0.917 1.926 0.911 0.070 2.099
C0006E-30X 221 51.5 2.0 8.0 X Silty clay 47.4 22.6 21.1 0.5 −5.4 0.892 1.487 0.878 1.972
C0006E-35X 270 45.0 2.5 9.5 X Silty clay 47.9 23.7 20.5 1.7 −6.0 0.923 0.829 0.916 0.035 2.040
C0006E-42X 343 40.6 3.2 11.5 X Silty claystone 43.9 18.0 27.2 1.7 −4.5 0.985 1.505 0.963 0.052 2.058
C0006E-47X 386 41.0 3.6 12.5 X Silty claystone 39.0 21.4 24.7 7.2 −1.2 0.986 0.323 0.983 0.040 2.323
C0006F-11R 488 45.8 4.6 15.0 X X Hemipel. Silty claystone 56.4 20.6 15.4 0.7 −1.4 0.997 0.530 0.978 0.023 2.095
C0006F-19R 563 43.0 5.2 17.0 X X Silty claystone 59.7 18.9 10.7 1.5 −3.3 0.998 0.865 0.948 0.035 2.198
C0001H-1R 232 62.1 1.6 12.0 X Out. Tr. -W. Silty clay Accr. Pr. 50-65 15-25 10-20 0-5 −8.5 0.981 9.150 0.895 0.035 1.733
C0001H-5R 270 57.5 1.8 14.0 X X 50-65 15-25 10-20 0-5 −2.4 0.969 7.739 0.914 0.019 1.767
C0001H-12R 336 55.3 2.3 17.0 X 50-65 15-25 10-20 0-5 −1.8 0.962 5.504 0.942 0.008 1.815
C0001H-16R 374 56.1 2.6 18.5 X 50-65 15-25 10-20 0-5 −1.7 0.973 4.008 0.947 0.010 1.912
C0007C-8X 75 56.0 0.7 5.0 X Tr. Silty clay Front. Thr. 30-55 20-30 20-45 0-5 −12.1 0.921 2.420 0.903 0.034 1.712
C0007C-10X 90 42.0 0.8 6.0 X Sandy silt 30-55 20-30 20-45 05 −10.8 0.973 1.820 0.921 0.053 1.812
C0007D-17R 325 43.0 3.1 16.0 X Silty claystone 50-55 22-24 20-25 0-5 −1.2 0.999 0.364 0.977 0.034 1.816
C0007D-24R 390 50.0 3.7 18.0 X Hemipel. Silty claystone 60-70 18-22 12-20 0-5 −2.0 1.000 0.806 0.972 0.019 1.956
C0002B-20R 649 43.0 4.8 25.0 Dis. Bas. Plain Clayey silt Fore-arc Bas. 40-55 25-30 20-30 0-5 −1.1 0.996 0.602 0.976 0.034 2.103
C0002B-44R 875 41.0 6.9 30.0 X X Slope apron Clayey silt 40-55 15-25 10-30 0-30 −1.4 0.991 0.664 0.972 0.047 2.331
C0002B-60R 1014 32.0 8.3 34.0 Out. Tr. -W. Silty clay Accr. Pr. 45-70 15-30 10-30 0-5 −1.1 0.990 1.429 0.970 0.041 2.626
1173-28X 254 65.0 1.5 45.0 X X Hemipel. (USB) Silty clay Oceanward 40-50 30-40 10-20 0-10 −4.5 0.987 4.411 0.947 0.009 1.763
1173-33X 309 63.0 1.8 55.0 X X 40-50 30-40 10-20 0-10 −3.1 0.950 9.078 0.898 0.008 1.744
1173-38X 350 51.0 2.1 62.0 X Hemipel. (LSB) Silty claystone 50-60 30-40 0-10 0-5 −4.5 0.967 3.892 0.939 0.027 1.877
1173-40X 376 50.0 2.3 66.0 X Silty clay 50-60 30-40 0-10 0-5 −4.5 0.984 2.538 0.958 0.033 1.897
1173-44X 408 49.0 2.6 70.0 X Clayey silt 50-60 30-40 0-10 0-5 −4.7 0.975 3.209 0.935 0.021 1.906
1173-49X 455 45.0 3.0 76.0 X Silty claystone 50-60 30-40 0-10 0-5 −4.4 0.970 4.669 0.932 0.024 1.985
1173-51X 479 46.0 3.2 78.0 X 50-60 30-40 0-10 0-5 −3.4 0.958 5.360 0.929 0.022 1.940
1173-53X 494 42.0 3.3 80.0 X 50-60 30-40 0-10 0-5 −3.8 0.977 2.196 0.952 0.029 2.045
1173-55X 519 42.0 3.6 83.0 X 50-60 30-40 0-10 0-5 −3.3 0.985 1.637 0.947 0.028 2.049
1173-59X 550 41.0 3.9 87.0 X 50-60 30-40 0-10 0-5 −2.9 0.988 0.986 0.962 0.027 2.096
1173−64X 600 38.0 4.4 92.0 X 60-70 20-30 0-10 0-5 −2.2 0.989 0.554 0.963 0.026 2.172
1173−70X 657 37.0 5.0 98.0 X X 40-60 20-30 0-10 var. −2.9 0.989 1.306 0.959 0.028 2.220
  • a We estimated porosity ϕ in each of our experimental samples from the combination of our own measurements of loss of weight after drying with shipboard grain density data (moisture and density (MAD) measurements) [Expedition 315 Scientists, 2009a]. Peffin-situ is calculated assuming hydrostatic pore pressure. Dir. refers to the direction along which properties were measured, either vertical (v) or horizontal (h). Depositions settings: Hemipel., hemipelagic; Out. Tr. -W., outer trench wedge; Tr., trench; Dis. Bas. Plain, distal basin plain; U(L)SB, Upper (Lower) Shikoku Basin. Tectonic settings: Front. Thr., frontal thrust; Fore-arc Bas., fore-arc basin; Accr. Pr., accretionary prism; Oceanward, seaward of the trench. Consolidation, i.e., height variations associated to the application of a large Peff (of the order of 1.5 to 2.5 Peffin-situ depending on the site considered) is indicated by several indexes: equation image is the ratio of sample heights measured out of the pressure vessel before and after the whole experiment, equation image is the normalized height reduction measured within the chamber between Peffin-situ and Peffmax, and equation image is the ratio of height for Peffmax (measured in the chamber) over initial height (measured outside).

We does not apply large Peff in a single step, but incrementally through successive cycles of increasing amplitude (i.e., up to maximum Peff, then back to low Peff; see Figure 2c). This procedure allows us to assess the evolution of the poroelastic coefficients through compaction, by estimating them on the portion of each cycle within the yield surface (in particular in the last step after maximum compaction when Peff is released and behavior returns back to the poroelastic field).

3.4. Core Material

Core samples from ODP Site 1173 at the Muroto transect (Figure 1) and IODP Sites C0001, C0002, C0006 and C0007 recovered along the Kii transect were available for our experiments (Table 1). The lithology of the samples varies mostly between silts and clays. All of them are constituted principally of clay minerals, with a proportion between 40% and 60%. Due to the proximity of a fossil spreading ridge, temperature gradient is few times larger at Site 1173 than along the Kii transect [Shipboard Scientific Party, 2001].

In spite of these variations, for each site, the samples examined here were collected within homogeneous units (except for the two deepest samples of C0006 and the deepest one of C0007) to minimize artifacts and allow direct comparison of the test results. We also checked visually the starting material to discard any sample showing macroscopic cracks or other evidence of brittle deformation.

We have tested a total of 31 samples in the isotropic pressure apparatus (Table 1). Most of these specimens were mounted so that properties were measured in a single direction, either “vertical” (longitudinal), i.e., sample long axis is parallel to core axis in ODP/IODP reference frame (C0001, C0002, C0006 and C0007) or “horizontal” (transverse), i.e., sample axis perpendicular to core axis, without further constraint on the direction (Site 1173). For six of them, preparation of two mutually perpendicular cylinders allowed us to estimate the properties in two orthogonal directions (vertical and horizontal). The very low measured anisotropy both in Vp and poroelastic compliance (see 20) led us to conclude that sample state and properties are relatively independent of the orientation of the samples. As a consequence, all our results are intercomparable and are plotted irrespectively of the measurement direction.

4. Results

4.1. Mechanical Properties

4.1.1. Correlation of Mechanical State With Other Variables

In Figures 3 and 4 we present poroelastic compliance (equation image) and plastic deformation (hf/ho) as a function of porosity (Figures 3a and 4a), in situ effective stress (Figures 3b and 4b) and age (Figures 3c and 4c), for all the tested material, irrespective of its lithology or site of origin.

Details are in the caption following the image
Poroelastic uniaxial compliance equation image determined in the different Sites C0001, C0002, C0006, and C0007 of IODP Legs 315 and 316 and Site 1173 of ODP Leg 190, as a function of (a) porosity, (b) in situ Peff calculated assuming hydrostatic pore pressure, and (c) age.
Details are in the caption following the image
Irreversible shrinkage, measured as the final height hf normalized by the initial one ho (both measured out of the pressure vessel) after a test where Peff was applied up to values between 1.5 Peffin-situ and 2.5 Peffin-situ in the different Sites C0001, C0002, C0006, and C0007 of IODP Legs 315 and 316 and Site 1173 of ODP Leg 190, as a function of (a) porosity, (b) in situ Peff calculated assuming hydrostatic pore pressure, and (c) age. Poroelastic Moduli

Over the tested samples tested, poroelastic compressibility varies by more than an order of magnitude. Surprisingly, the expected trend of decreasing compressibility with decreasing porosity is weak and seems to vary strongly between the different sites (Figure 3a). Whereas relation between porosity and age is similarly highly scattered (Figure 3c), the compressibility shows a net exponential trend with effective stress (Figure 3b). Irreversible Deformation

The extent of irreversible compaction (estimated from the ratio of sample height measured outside of the vessel before and after the experiment) in response to a load increase over in situ conditions, i.e., to the application of Peff in the range 1.5∼2.5 Peffin-situ, shows large differences within the tested samples. We observe a wide range of sediment response from virtually no compaction to irreversible shortening larger than 10% (Figure 4). The resistance to compaction is better correlated with Peffin-situ (Figure 4b) than with either age (moderately good agreement, see Figure 4c) or porosity (poor correlation; see Figure 4a), suggesting that the sample plastic behavior and yield strength is closely tied to in situ stress conditions.

4.1.2. Site-by-Site Depth Evolution of the Material Mechanical State

The general strengthening with depth can be further analyzed site by site, i.e., for lithologically homogeneous sediments (Figure 5). Such strengthening is reflected both in a decrease in poroelastic compliance and in a decrease in irreversible deformation (normalized reduction in length from Peffin-situ to Peffmax for Site 1173 and from Peff = 0 to Peffmax for Site C0006, see 7), which are restricted to a rather narrow depth interval, whose precise position varies between sites. For Site C0006 (as well as C0007, see Figures 3 and 4), located at the toe of the prism, the threshold overburden stress causing the change in strengthening occurs between 2.5 and 3 MPa, while at the Shikoku Basin Site 1173, it appears to kick in at ∼4 MPa (see Figure 4b).

Details are in the caption following the image
Variations with depth in physical properties and composition for Sites 1173 (ODP Leg 190) and C0006 (IODP Leg 316): (a) porosity, (b) plastic shrinkage after application of Peff in the range 1.5 Peffin-situ–2.5 Peffin-situ, (c) poroelastic coefficient, and (d) composition determined by XRD. In both sites there is a rapid strengthening around some depth interval (vertical gray band), evidenced by a decrease in poroelastic compliance and plastic deformation. These variations in mechanical strength, not correlated with any sharp change in composition, are rather the result of the combined action of cementation/decrease of the porosity down to some “critical” value corresponding to compact state. (Note for XRD data: (Site 1173) the proportions of the clay minerals are determined only for the particles with a size < 2 microns and are normalized with respect to total clay [Shipboard Scientific Party, 2001; Steurer and Underwood, 2005]. Site C0006: the clay mineral proportions are normalized with respect to the bulk composition. The “smectite” content is in fact smectite + montmorillonite content.)

4.1.3. Consolidation Behavior

The consolidation curves of samples C0001H-5H, C0007C-8X and C0007D-17R (Figure 6) are representative of all the samples we tested. The mechanical response to the experimental consolidation can be schematically divided into two end-members: while shallow samples (C0001H-5H, C0007C-8X) were affected by a large irreversible deformation, deep samples (C0007D-17R) were hardly deformed (Figure 6). In addition, within shallow deformable samples, we observed two contrasted kinds of behavior: sample C0001H-5H was affected by irreversible compaction only when Peff exceeded a threshold of the order of Peffin-situ. In contrast, sample C0007C-8X showed the most intense shrinkage upon the application of the initial step of Peff, i.e., for Peff much lower than in situ value.

Details are in the caption following the image
Typical patterns of mechanical response to an applied effective pressure larger than Peffin-situ: C0001H-5Rvert (green) and C0007C-8X (blue) are affected by a significant amount of irreversible shrinkage, which is virtually absent during C0007D-17R (red) deformation. Such plastic deformation is nevertheless very different between samples C0001H-5Rvert and C0007C-8X; in C0007C-8X, most of irreversible deformation occurs upon the first steps of Peff application, even for values lower than Peffin-situ (vertical bars). In contrast, in sample C0001H-5Rvert, the response to deformation remains mostly poroelastic until Peff reaches values close to Peffin-situ, from where irreversible compaction starts. Stars correspond to final normalized height measured out of the pressure vessel while all other points are measured within the vessel. Note the large variations between the three samples in the elastic rebound, i.e., the change in height (hence porosity) in the last phase of each experiment upon release of the pressures from in situ conditions.

4.2. Vp Controlling Factors

In addition to the direct mechanical response, we also assessed P wave velocity evolution as a function of increasing effective (Figure 7) and confining (Figure 8) stresses. Although P wave arrival time was undecipherable without applying Peff and Pc, for values as low as a few hundred kPa, the signal was sufficiently strong to estimate Vp and its dependence on Peff and Pc.

Details are in the caption following the image
(a) Linear dependence of Vp on effective pressure during poroelastic (reversible) deformation of sample C0006F-11R. (b) Compilation of equation image over several sites (abscissa Peffin-situ estimated for hydrostatic pore pressure).
Details are in the caption following the image
Vp dependence on Pc in core sample C0001H-16R. For each step of Pc (i.e., each elementary step of phase 1, where deformation is reversible), Vp was estimated for a given Peff (arbitrarily chosen to be equal to 3 MPa), using the regression law described in Figure 2e.

4.2.1. Peff Dependence

During poroelastic (reversible) deformation and fluid expulsion (see above and Figure 2), an increase in Peff results in stiffening of the structure expressed by an increase in compressional wave velocity (Figure 7a), which is close to linear in the range 0.5–3 MPa for deep samples (ca. > 300 mbsf) and 0.5–Peffin-situ for shallow samples (<300 mbsf), similarly to poroelastic moduli. This linear approximation breaks down at large Peff (∼10 MPa), where Vp tends asymptotically toward a constant value, as well as at very low Peff (<0.5 MPa), where Vp variations with Peff, hence the coefficient equation image, get larger.

Values of equation image compiled over the drill sites studied are preferentially concentrated in the range 0.02∼0.04 km/s/MPa (Figure 7b). In contrast to poroelastic moduli, equation image does not seem to correlated with depth in the samples analyzed.

4.2.2. Pc Dependence

By interpolating Vp to a constant Peff (arbitrarily chosen to be 3 MPa) for various Pc in the domain of poroelastic deformation, we assessed the possible effect of confining pressure on Vp (Figure 8). The quality of the obtained trend varies between samples, but the slope equation image is in the range 1.2–1.8 10−3 km/s/MPa, yielding a correction to be applied to onboard measurements to restore them to in situ Pc. For samples from the vicinity of the trench such as Site 1173, where almost 5 km of water lie above seafloor, this correction is of the order of 0.1 km/s, i.e., nonnegligible.

4.3. Anisotropy of Acoustic and Mechanical Properties

Both uniaxial compliance and Vp (determined for in situ conditions) show very similar values in the two perpendicular directions for most of the samples (Figures 9a and 9c). When a difference between the pair of experiments is observed, it does not show any systematic pattern. Although the small number of samples tested prevents us from drawing conclusions on a site-by-site basis, our data attest to the very limited anisotropy of the material recovered a few hundred meters below the seafloor regardless of its position in the margin.

Details are in the caption following the image
Anisotropy of (a, b) acoustic and (c) mechanical properties. For each core sample, two cylindrical pieces were prepared, with the axis of the cylinder (hence the direction of measurement) orientated either parallel to core axis (longitudinal samples/properties) or perpendicular to it (transverse samples/properties). Samples with horizontal axis were not orientated in the geographical system.

5. Discussion

5.1. Core/Log/Seismic Integration

5.1.1. Correction Factors to In Situ Conditions

As the majority of Vp measurements on core samples are performed in the laboratory, corrections to restore Vp to in situ conditions are necessary. On the basis of submersible-assisted measurements of Vp, Hamilton et al. [1970] and Hamilton [1971a] derived for subseafloor sediments corrections factors for salinity, temperature and confining pressure. In addition, for deeper sediments, effective pressure is an additional variable likely to play a role on Vp, involving another correction factor [e.g., Hoffman and Tobin, 2004]. Our experiments for various conditions of Pp and Pc provide the opportunity to assess the corrections factors to be applied to sediments down to ∼1000 mbsf. Pc/Pp Dependence

The simplest poroelastic model of our samples consists of an incompressible, fluid-saturated solid skeleton whose geometry is the sole function of Peff. In such a framework, the porosity is independent of Pc for a given Peff, which is in agreement with our measurements of sample height for various Pc. Regardless of porosity variations, an increment of Pc results in an increase in fluid pressure at a given Peff; since the sample is incompressible, this leads to an increase in Vp. The magnitude of such an increase depends on the saturated (“undrained”) moduli Ksat and μsat [Mavko et al., 2009], which can in turn, using Gassmann's [1951] substitution equations, be expressed in terms of dry (“drained”) framework incompressibility Kdry and shear modulus μdry and fluid incompressibility Kf. Saturated shear modulus is simply
equation image
For near-incompressible solid grains, i.e., with incompressibility much larger than framework incompressibility (assumption justified by the values measured in our samples, see 34), incompressibility Ksat can be approximated by
equation image
with ϕ the porosity.
Such saturated poroelastic moduli combine to give the velocity as
equation image
The effect of an increment in fluid pressure Pp on Vp operates through an increase in both Kf and fluid density ρf, yielding
equation image
equation image
equation image
Taking average values of Vp = 1.9 km/s, ϕ = 0.5, ρ = 1850kg/m3, Kf(atm pressure) = 2.34GPa and Kf(100MPa) = 2.98GPa [Knauss, 2005] we obtain
equation image

These values are very similar to the experimental findings (Figure 8), which confirms that our Pc dependence of Vp actually reflects the effect of variations in pore fluid pressure on velocity. For practical purpose, as the actual in situ fluid pressure is not known, in samples such as ours where the effective pressure is limited to low values, one can use, instead of the fluid pressure, the confining pressure Pc to derive the correction, which is not negligible for the deep-sea rocks considered here. Temperature Dependence

Temperature variations between laboratory (23°C) and in situ conditions induce variations in density and elastic moduli, hence a correction on velocity is a priori necessary. We do not have experimental data as regards the effect of temperature, but we can apply the simple model developed above, yielding, for the temperature dependence,
equation image
with equation image ≈ 10 MPa/°C [Knauss, 2005] and equation image ≈ 0.17kg/°C [Fofonoff, 1985]. Taking again as average values Vp = 1.9 km/s, equation image = 0.5 and ρ = 1850 kg/m3 yields a correction for the temperature of equation image ≈ 0.00318 km/s/°C. For example, for subseafloor sediments (ΔT = 1.5 − 23 = −21.5°C), the temperature correction is −0.068 km/s, really close to the correction given by Hamilton [1971a] of −0.074 km/s, which was derived for ocean water. For each of our sample, we estimated the temperature correction using their respective Vp, ϕ and ρ, which we determined in the laboratory, as well as their in situ temperature (values in Table 1, estimated from the gradients given by Shipboard Scientific Party [2001], Expedition 315 Scientists [2009b, 2009c], and Expedition 316 Scientists [2009a, 2009b]). Peff Dependence

We derived experimentally in the range 0.5–3 MPa a linear coefficient equation image to account for the variations in Vp with effective pressure. To restore atmospheric pressure Vp to Peffin-situ, the sole correction equation image X Peffin-situ is insufficient, as Vp decrease for low Peff are larger than predicted by the linear correction [e.g., Tobin and Moore, 1994]. For the sake of simplicity, we defined the additional correction as a constant ΔVp:
equation image
which we roughly estimated in our samples. Similarly to equation image (Figure 7), values of the constant correction ΔVp are quite variable between samples. Nevertheless, if we try to establish general corrections for effective pressure, we can define two distinct categories of samples. “Cemented” samples (see below 37) have very low equation image (≈0.01 km/s/MPa) and ΔVp (≈0–0.05 km/s). “Uncemented” samples have larger equation image (equation image–0.05 km/s/MPa) and ΔVp (≈0.05–0.1 km/s). These values have to be considered with caution, as they are unlikely to be relevant to a large range of lithologies and settings (e.g., the larger correction in carbonate-rich sediments by Urmos and Wilkens [1993]). It is nevertheless certain that the correction to be applied cannot be constant and has to depend on effective pressure. Validity of Our Experimental Measurements

The corrections determined above enable us to check whether our experimental Vp match shipboard core velocities (measured at atmospheric pressure and ambient temperature). For this purpose, we must for each of our sample (1) extrapolate our experimental Vp down to Peff = 0 and (2) apply a correction to reduce Pp down to zero. Among the various holes studied, Site 1173 is the one where the most numerous atmospheric pressure core Vp data are available. Our experimental velocities, restored to atmospheric pressure conditions, are in close agreement with Vp determined at atmospheric pressure (Figure 10), attesting to the validity of our measurements and of the corrections we derived from them. This further shows that the difference in pulse frequency (500kHz for shipboard core velocity [Blum, 1997], 3MHz for our device) does not induce significant velocity dispersion, even if the frequency we used is slightly over 1MHz, the limit usually considered for neglecting velocity dispersion [Kibblewhite, 1989].

Details are in the caption following the image
Comparison of compressional velocities Vp either (1) measured onboard on core samples (diamonds), i.e., for Pc = 0 and Peff = 0, or (2) estimated in our experiments (squares) as the limit for Peff = 0 and corrected to Pc = 0 (see text for description). Measurements from both data sets were performed at ambient temperature (∼20°C–25°C). Matching Laboratory With In Situ Vp

The restoration of compressional wave velocities measured in the laboratory to in situ conditions requires the addition of corrections for temperature, fluid (≈ confining) and effective pressures defined above:
equation image
As noted by Hamilton [1971a], for Pc of the order of 50 MPa, the corrections for temperature and pore fluid pressure, of opposite sign and of similar amplitude, cancel out, so that they can be neglected. For settings with much shallower ocean, e.g., fore-arc basin sediments, this is not the case and the corrections must be carefully assessed.

5.1.2. Comparison of Laboratory-Derived Data With Logging/Seismic Data

Concomitant core sampling and logging while drilling provide an excellent basis to determine (2) Vp for in situ conditions using logging tools and (2) Vp at atmospheric pressure (i.e., null effective pressure) directly on core samples in the same lithology. From the average mismatch between core and logging Vp (based on the comparison of onboard P wave velocities on discrete samples with wireline DSI data in the borehole), Hoffman and Tobin [2004] derived an average correction to be applied to restore core velocities to in situ conditions. This correction relies on the assumption that logging and discrete core Vp, although determined at different frequencies and over different representative volumes, are the same. The problem can be considered the other way round and one can check whether in situ Vp determined by distinct methods (core/logging/check shots/seismic) coincide or not.

The lack of knowledge of Peffin-situ severely hampers a precise estimate of in situ Vp for core samples; a priori, only a range of values, bounded by the two end-member cases (hydrostatic or lithostatic Peff), can be assessed (Figure 11). Nevertheless, indirect arguments as well as direct measurements (see 5) support the idea that the actual effective pressure is close to hydrostatic pressure.

Details are in the caption following the image
Comparison of Vp experimentally determined on core sample with logging data acquired during drilling: (left) Site C0001, (middle) Site C0002, and (right) Site C0006. Experimental Vp were assessed for in situ conditions of temperature and pressure, i.e., Pc equal to the overlying sedimentary load, Pp equal either to hydrostatic (direct measurement), or lithostatic (extrapolation using experimental regression coefficients) conditions. Logging data correspond to logging while drilling (Sites C0001 and C0002) or check shot (Site C0006) [Expedition 314 Scientists, 2009].

Our laboratory-determined data (corrected for the temperature difference) are in average higher than other kinds of velocities, with a difference in the range 0.05∼0.3 km/s for hydrostatic pore fluid conditions (Figure 11). We have no definite explanation for the systematic discrepancy between core and logging velocities. As logging Vp relies on waves with a much larger wavelength than laboratory measurement, one possible cause to this discrepancy is velocity dispersion, although there is no consensus on both its amplitude and underlying microscopic processes [Best et al., 2001; Gorgas et al., 2002; Hamilton, 1971b; Kibblewhite, 1989; Robb et al., 2007]. One can note that our measurements are in agreement with shipboard velocities (Figure 10), so that dispersion, with respect to logging Vp, should also affect shipboard core Vp. A second factor can contribute to lower logging velocities with respect to core velocities; the larger the wavelength, the larger the size of the representative elementary volume, hence the larger the range of size of the defects (faults, zones of weak material) potentially lowering the velocities. This can explain why measurements on cm-scale “strong” samples yields higher velocities than logging measurements that necessarily incorporate faults and weak zones. In this respect, velocity data derived from check shots from the surface (Site C0006), where the seismic source and the receiver are distant by a thousands of meters, are likely to be more affected than logging data acquired with the LWD SonicVisionTool (Sites C0001 and C0002), where source and receiver are ∼3 m apart [Expedition 314 Scientists, 2009].

5.1.3. Vp Versus Porosity Relationship

In order to compare core and logging/check shot Vp over the different sites, we determined Vp versus porosity curves for all data sets for in situ conditions (see Appendix A for a description of the data used). As a result (Figure 12), for ϕ in the range ∼0.3–0.6, Vp versus porosity points from cores of all sites cluster along a single trend. This shows that velocities, for high-porosity material, do not depend at first order on composition/clay fraction, as was already noted by Erickson and Jarrard [1998].

Details are in the caption following the image
Vp as a function of porosity. Color symbols pair resistivity-derived porosity with LWD Vp for Sites C0001, C0002, C0004, and with check shot Vp for C0006 (see Expedition 314 Scientists [2009] for method description). Hollow symbols pair laboratory-measured Vp for Pc equal to the overlying sedimentary load, Pp equal to hydrostatic conditions and ambient T with porosity of our experimental material estimated by combining our own measurements of water loss upon drying with onboard data of solid grain density and adding a correction for rebound (see Appendix A). H&T, Hoffman and Tobin's [2004] empirical law; EJ98 high (normal), Erickson and Jarrard's [1998] empirical law for high (normal) sediment consolidation; Wood, Wood's [1941] suspension model calculated for incompressible solid grains and water rigidity at P = 50 MPa and T = 1.5°C.

Most of the logging data plot along the same trend, but for C0002 and C0004 (unit IV) where velocities are higher and C0001 (unit I) where they are lower. The interpretation of these discrepancies between core and logging data is quite complicated, as they combine potential errors on both velocity and porosity data. Plots of our rebound-corrected sample porosity with resistivity-derived porosity shows significant differences (Appendix A), that may account for most of the discrepancy between logging and core data in Figure 12.

Our experimentally derived Vp versus porosity relationship is close to Erickson and Jarrad's [1998] “high-consolidation” curve, but departs significantly from their “normal consolidation” curve as well as from Hoffman and Tobin's [2004] relationship. One possible reason is that the correction (+0.043 ± 0.029 km/s) applied by Hoffman and Tobin [2004] to restore atmospheric pressure data to in situ conditions is smaller than the correction we derived above to account for the increase in pore fluid and effective pressure. As Vp versus porosity curves are often used to estimate properties at depths larger than drilling depth range, for example pore pressure [e.g., Tobin and Saffer, 2009], the choice of the curve has potentially significant consequence: a shift in Vp versus porosity relationship by +0.1 km/s results in decrease in estimated pore pressure by ∼0.6 MPa (see Appendix B), which is nonnegligible for the relatively shallow rocks (<1000 mbsf) considered here.

5.2. Sensitivity of Vp to Material Physical Changes

5.2.1. Variations in Vp During Consolidation Vp Versus ϕ Evolution During Experimental Consolidation

Following earlier workers' analysis [Karig, 1996; Karig and Ask, 2003], some insights on the consolidation state of Nankai sediments can be gained from the comparison of the characteristics of in situ and experimental compaction. For the sake of simplicity, we consider only small variations around which porosity evolution can be approximated by a linear relationship as
equation image

As detailed in 4, we did not precisely estimate porosity variations and can only infer them from height variations. Taking the isotropic assumption (equation imageequation image) as a maximum estimate, we estimated the porosity variations in sample C0006E-30X (∼220 mbsf) along the experimental consolidation curve. As a result of the application of an increasingly large Peff, irreversible shrinkage occurred, with porosity variations Δequation image = 2% for a variation of Peff of 1 MPa, which can be roughly converted into Δequation image = 2%/100 m (Figure 13a). A similar relationship equation image, or equation image can be deduced from in situ variations of porosity. In situ compaction curve at Site C0006 calculated on core samples (porosity from moisture and density (MAD)) [Expedition 316 Scientists, 2009a] in the depth range 50–250 mbsf yielded a porosity decrease of the order of Δϕ = 4%/100 m. The factor two of difference between experimental and in situ compaction trends suggests that, in addition to instantaneous compaction, a significant proportion of in situ porosity decrease results from time-dependent processes and that the short durations of experimental consolidation did not allow such processes to be active. Although Saffer [2003] obtained for Nankai samples consolidation trends similar for experimental and in situ conditions, one may note, however, that this is not commonly the case, because in many consolidation experiments, coefficients equation image are an order of magnitude lower than for in situ consolidation curves [Karig and Ask, 2003].

Details are in the caption following the image
(a) Determination of experimental compaction curves ϕ = func(Peff) for sample C0006E-30X (∼220 mbsf). The porosity variations are derived from height variations by applying a factor 3, i.e., Δϕ = (1 − ϕ) 3equation image (see text). Porosity decrease at to corresponds to irreversible deformation inherited from sample setup and application of initial Peff. Fitting the compaction curve (dashed line) yields a coefficient Δϕ = 2% for a variation of Peff of 1 MPa, which can be roughly converted into Δϕ = 2%/100m. Natural compaction curves in Site C0006, either from linear trend in the depth range 50–250 mbsf (porosity from MAD measurement) [Expedition 316 Scientists, 2009a] or from the tangent at 220 mbsf (porosity from resistivity data) [Tobin et al., 2009b], yields a porosity decrease of the order of. Δϕ = 4%/100m (b) Associated velocity increase during compaction, which can be estimated as ΔVp ≈ 6.10−2 km/s for ΔPeff = 1 MPa. Combining porosity and velocity variations trends yields the experimental Vp versus ϕ relation as ΔVp = 3 10−2 km/s/%, comparable to the in situ Vp versus equation image shown in Figure 12.
In parallel to the porosity decrease, we observed, associated with the irreversible deformation undergone by this particular sample, an increase in velocity, which can be estimated as ΔVp ≈ 6.10−2 km/s for ΔPeff = 1 MPa (Figure 13b). Combining porosity and velocity variations trends yields the experimental Vp versus ϕ relation as
equation image

This trend, calculated on a single sample experimentally consolidated, is relatively similar to our “in situ” Vp versus ϕ relationship in Figure 13, which is derived by estimating in situ Vp and porosity in many samples from various depths. This good agreement between experimental and in situ compaction trends shows that the increase in Vp with depth is mostly the result of mechanical factors and that diagenesis and cementation play a minor role, at least in the shallow domain considered here. Relative Contribution of Porosity and Peff Variations to Vp

Within mechanical factors, one can distinguish the effect of effective pressure increase and porosity decrease, which both result in an increase in grain-to-grain contact hence on velocity increase. In Vp versus ϕ empirical relationships such as Figure 13, the two effects cannot be easily differentiated, as low porosity samples generally correspond to larger depths/higher Peffin-situ than high-porosity ones.

On the contrary, in our experiments, during the poroelastic phase, we can directly assess the sole effect of Peff on Vp, as porosity variations are in general of an order of magnitude smaller than Vp variations. In such cases, the material stiffening due to Peff increase may be related to the closure of crack-shaped microcavities or intergrain contacts [e.g., Brace et al., 1972], which hardly affects the total pore volume, but strongly influences the elastic moduli and hence P wave velocity.

During the poroelastic deformation of our samples, the effect of Peff increase up to 10 MPa is limited to ∼0.25 km/s. On the other hand, on the Vp versus ϕ relationships shown in Figure 12 (where in all the samples Peffin-situ was smaller than 10 MPa), Vp variations are as large as ∼1.2 km/s. This shows that porosity variations are the primary contribution to Vp increase and Peff only a secondary factor, similarly to the conclusion reached by Erickson and Jarrard [1998] on the basis on multifactor cross-correlation statistical analysis.

5.2.2. Mechanical Poroelastic Model in the 30%–60% Porosity Range and Sensitivity of Vp to Material Stiffening Poroelastic Moduli

When considering the three typical end-members described in 15, in sample C0007D-17R (limited irreversible compaction) uniaxial compliance is −0.0012 MPa−1, in C0001H-5H (large irreversible compaction, presence of cement) it is twice that value, ∼−0.0022 MPa−1, while in sample C0007C-8X (large irreversible compaction, no cement) it is ∼−0.012 MPa−1, i.e., ten times larger than in C0007D-17R. Over the range of tested samples, while poroelastic coefficients are affected by very large variations (by a factor of the order of 10), the associated variations in P wave velocities are limited to ∼50% (Figure 12).

An explanation may be found when regarding the respective values of the distinct terms involved in the Vp expression
equation image
Recalling Gassmann's [1951] equations for near-incompressible solid grains, the saturated (“undrained”) incompressibility Ksat is given by
equation image
where Kf is of the order of 2–3 GPa [Knauss, 2005], ϕ of the order of 0.5, so that equation image is of the order of 4–6 GPa.

In contrast, our measurements of uniaxial compliance are in the range −0.01 ∼ −0.0012 MPa−1, which, when converted into “dry” framework incompressibility (Kdry−1 = − equation image = − equation image, see 6), yields Kdry in the range 30∼300 MPa, which is in agreement with modulus estimated from pore fluid variations for isotropic Peff loading by Bourlange et al. [2004]. Similarly, Kdry derived from uniaxial consolidation of clays and fine sand by Karig and Hou [1992] is at most ∼500 MPa for porosities down to 25%.

Furthermore, such Kdry values, determined from drained static experiments are also in agreement with the “dynamic” Kdry determined from the knowledge of Vp, Vs and ρ in natural samples [see Hamilton, 1971b, Figure 2], within 30%–50% porosity range, where Kdry is plotted under the label “frame bulk modulus”). These low incompressibilities measured in natural samples stand slightly at variance with the much higher moduli estimated by effective modeling in the high-porosity domain by Dvorkin et al. [1999b]. Mechanical Model of High-Porosity (30%–60%) Sediments

In the limit of very small Kdry (assuming incompressible solid grains) and null shear modulus, the Gassmann formulation of Ksat becomes similar to the simpler suspension model of Wood [1941], as they both converge toward equation image [e.g., Wilkens et al., 1992] (see Figure 12, where Wood's [1941] relationship was calculated for Kf(50 MPa) = 2.47GPa) [Knauss, 2005].

Our experimental Vp, as well as Erickson and Jarrard's [1998] relationship, are faster for a given porosity than Wood's [1941] relationship, with a difference that expresses the contribution of solid framework incompressibility Kdry as well as shear modulus μsat. The ratio of actual Vp over Vp from the suspension model is of the order of 1.1 to 1.2, which implies that the combined contribution of Kdry and μsat is of the order of 20%–40% of equation image. As the latter term is in the range 4–6 GPa, Kdry measured in this study accounts only for at most ∼10% of equation image. This implies that the shear modulus μsat, even in the high range (50%–60%) of the tested porosity, is significant, with values of a few hundreds of MPa, i.e., larger than the framework incompressibility.

This conclusion is consistent with logging-derived Vs for Site 1173 in the range 0.35–0.55 km/s [Goldberg, 2003], which convert into values of the shear modulus (Vs = equation image) of several hundreds of MPa. Similarly, shear modulus estimated from Vs measurements in experimentally consolidated samples is of the same order even for porosities as large as 50%–60% [Gettemy and Tobin, 2003].

In conclusion, in the porosity range of our whole sample set (30%–60%), equation image is the controlling factor of Ksat, as was also stressed out by Erickson and Jarrard [1998], with only second-order contributions by the solid framework shear modulus (μsat) and third-order contribution by solid framework incompressibility (Kdry). One consequence of this low values of Kdry and μsat is that Vp variations reflect mostly the variations in porosity ϕ rather than variations in Kdry or μsat, which explains the absence of a clear dependence on lithology (see 28 and Figure 12). This principal dependence of Vp on ϕ results in the fact that the largest errors when interpreting Vp data originate from uncertainties in the determination of in situ porosity, originating from two main factors: (1) a fraction of measured pore water of the sample (up to 40% of total content) does not correspond to pore space, but to smectite interlayers and is released during drying for porosity measurement [Brown and Ransom, 1996], and (2) the amount of elastic rebound, which is required to convert atmospheric pressure measurement of porosity to in situ value, is really ill-constrained (see the large variations between the three samples in Figure 6, and discussion by Karig [1993]).

5.2.3. Detection by Vp of Incipient Cementation Test Material: Upper Shikoku Basin From Site 1173

The development of grain-to-grain bonding leads to a significant strengthening, of which one consequence is delayed compaction (underconsolidation), characterized by a porosity larger than average for a given depth [Leroueil and Vaughan, 1990], as long as the pore volume is not fully filled with authigenic precipitates. Accordingly, the large porosity of the lower section of the Upper Shikoku Basin (USB) measured in Site 1173 was interpreted as the result of cementation [Shipboard Scientific Party, 2001], which was also supported by the observation of a silica phase coating grain contacts as well as the relative evolution of Vp and ϕ with depth [Spinelli et al., 2007]. Other observations of diagenetic alteration include the progressive illitization of the finer-grained, smectite-rich portions of the USB facies [Sunderland and Morgan, 2004]. Both transformations reactions have been related to elevated temperatures in the area of Cape Muroto. As a result of these observations, sediments from the lower section of the USB can be considered as appropriate material in which the mechanical and acoustic effects of cementation can be experimentally characterized. First Indicator: Detection of Cement Destruction

The first experimental evidences of cementation can paradoxically be found when artificially triggering cement destruction, by applying an effective pressure sufficiently large for compaction to resume. In the cemented samples of the USB facies of Site 1173 (254 and 309 mbsf), the state after compaction is characterized by increase, with respect to initial state, in both mechanical compliance equation image and velocity sensitivity on effective pressure equation image (Figure 14a and 14b, right), which may be interpreted as reflecting destruction of intergrain bonds upon compaction onset. It contrasts with the behavior of uncemented samples, where the slopes equation image and equation image in the poroelastic domains are similar before and after compaction (Figure 14b, left).

Details are in the caption following the image
(a) Properties equation image and equation image in samples from Site 1173 before (diamonds) and after (squares) the application of a large Peff, of the order of 2effin-situ. The largest increase (in absolute value) of both mechanical parameters is observed for the two shallowest samples, which are located within the opal-CT cement zone defined by Spinelli et al. [2007]. This particular evolution may be interpreted as the breakage of cement bonds during compaction and constitute by consequence a possible indicator of the presence of incipient cementation. (b) Variations in mechanical/acoustic properties before and after irreversible shrinkage. Star (circle) stands for the state at the beginning (end) of the experiment, the solid (dashed) line indicating the associated slopes equation image and equation image. In sample C0007C-10X, in spite of considerable shrinkage, no significant variation in the slopes is observed, while in sample C0001H-5H, compaction results in a large increase in the modulus of the slopes, i.e., the material becomes more compressible and sensitive to Peff variations. Second Indicator: Low Value of equation image

In contrast to deeper samples, the cemented samples of USB show a sharp difference in acoustic properties, with a very low dependence of seismic velocity on effective pressure (see Figure 14a, left, and discussion by Karig [1993]). This observation may result from the influence of microcracks, shear bands, or microporosity at intergrain contacts. In uncemented samples, such microvoids close upon increase in Peff, resulting in material stiffening, hence Vp increase, while in cemented samples the microvoids may be totally or partially filled by authigenic cement, so that Vp is much less affected by Peff variations. The advantage of the acoustic signature of cementation lies in the fact that Vp dependence on Peff appears relatively constant or, at least, uncorrelated with depth or lithology (Figure 7b). Consequently, the presence of cement can be directly diagnosed from low equation image. In contrast, poroelastic moduli, which can help detecting the presence of cement through material stiffening [Burland, 1990; Karig and Hou, 1992; Karig and Ask, 2003], are quite equivocal indicators as they are also controlled by several other parameters such as porosity, lithological composition or Peffin-situ. As a result, the presence of cement in USB is difficult to infer directly from the compliance profile (Figure 3).

5.3. Mechanical State of Material in Nankai Trough

5.3.1. Anisotropy

The review of available data for accretionary prism samples does not give a clear picture of P wave velocity anisotropy pattern. In Nankai, Bray and Karig [1986] reported a very low degree of anisotropy of Vp (measured at atmospheric pressure) in DSDP samples from Sites 582 (hemipelagic mudstones for USB below the trench fill sediments) and 583 (trench fill sediments above the frontal thrust). In contrast, Vp (measured at atmospheric pressure) in sediments from ODP Site 808 (outer marginal trench wedge to USB and LSB, between 400 and 950 mbsf) is lower in the vertical (i.e., core parallel) direction than in the horizontal direction (irrespectively of azimuth) by up to ∼10% [Brückmann et al., 1993]. In accreted sediments within the Barbados accretionary complex, Brückmann et al. [1997] reported either positive anisotropy (i.e., horizontal Vp faster than vertical one), mostly between 0% and +4%, in hole 948C or no anisotropy in hole 949B (both claystone with total clay content mostly around or above 60%) [Underwood and Deng, 1997), without a clear explanation for the difference between the two sites.

Beside these results on accretionary prisms, the analysis of a larger data set of velocities in silt-clays sediments and sedimentary rocks from various settings shows that Vp are statistically lower in vertical than horizontal direction [Bachman, 1979], with an anisotropy calculated with the regression equation that increases with velocity and is in the range 0%–5% for velocities below 3 km/s. This general pattern, determined from atmospheric pressure Vp measurements, contrasts with the overall very small anisotropy of P wave velocity we measured for in situ conditions in our samples (Figure 9a).

One factor influencing anisotropy is the deposition mode: in fine-grained sediments from the Mississippi fan (DSDP leg 96), vertical to horizontal anisotropy is very limited in current-deposited sediments but larger in normally settled, hemipelagic sediments [Wetzel, 1987]. Anisotropy also increases as a result of compaction [Wetzel, 1986]. These trends show that the geometry of the pores and grain-to-grain contacts is essential to anisotropy, which should therefore be also dependent on effective pressure. This effect can somehow explain the discrepancy between atmospheric pressure (Vp vertical significantly lower than Vp horizontal) and in situ measurements (very small difference): when effective pressure is applied, some of the intergrain voids close and the velocity increases. This increase is not necessarily the same in the vertical and horizontal directions. Indeed, assuming that lower velocity (for atmospheric pressure measurement) of the vertical direction results from the preferred normal orientation of cracks and micropores, it may be affected, upon Peff application, by a velocity increase larger than the horizontal direction, which seems confirmed by our measurements of equation image in the two orthogonal directions (Figure 9b). In other words, lower vertical velocity (for atmospheric pressure measurement) implies, because of preferred orientation of micropores, larger increase upon Peff application, so that significant velocity anisotropy measured at atmospheric pressure nearly vanishes for in situ conditions. This result indicates that anisotropy determined at atmospheric pressure may be overestimated with respect to in situ conditions.

5.3.2. Mechanical State Weak, Unlithified Shallow Material in Sites C0006 and C0007

Although consolidation studies usually focused on the yield point, i.e., the effective stress for which plastic deformation resumes [Feeser et al., 1993; Moran et al., 1993; Morgan and Ask, 2004; Vrolijk et al., 1998], there has been little attention paid to the volume shrinkage when very low stresses, much below yield, are applied, either during resaturation of the sample or during the first steps of the test itself. This deformation was significant only for shallow material in Sites C0006 (samples 20X, 25X, 30X, 35X) and 7 (8X and 10X), i.e., for trench facies sediments, which have a lower clay fraction than other tested samples.

As the shrinkage occurs for an effective pressure much lower than Peffin-situ, in situ sample volume must incorporate this shrinkage, which implies that there was a significant volume expansion in the time lapse between coring and the start of our experiments. Such expansion is some sort of porosity rebound, although the reference curves by Hamilton [1976] show an amount of rebound that increases with depth, i.e., deep samples should be affected by a larger amount of expansion/shrinkage than shallower ones, which is not the case here. It should be noted that the porosity rebound is calculated on the basis of consolidation curves upon pressure release [Lee, 1973; Silva and Hollister, 1973]. On the other hand, the volume shrinkage in our samples was not reversible upon pressure release. This implies that, compared to porosity rebound, which is an immediate and elastic process, the volume expansion affecting our samples is slower. Time-dependent anelastic strain recovery measured in samples from C0002 and C0006 is by a few orders smaller than the volume variations described here [Byrne et al., 2009], but their samples correspond to large depths, where we did not observe any significant sample shrinkage. Independently of the precise mechanism at stake and its timing, this volume shrinkage, which is not correlated with changes in lithology or age gap, attest to the low mechanical cohesion of the affected samples and unravels the presence of a mechanical boundary in Sites C0006 and 7 in the depths range (250–350 mbsf) and (100–300 mbsf), respectively. Cemented Material in Sites 1173 and C0001

We observed a large increase in both poroelastic compliance and equation image after plastic deformation in samples C0001H-5R, C0001H-12R and C0001H-16R, a behavior very similar to the samples of USB of Site 1173 where the deformation led to cement destruction (see 37 and Figure 14b). Such behavior is not observed in other deformable samples, such as C0007C-10, where acoustic and poroelastic moduli are left roughly unchanged by the volume shrinkage.

In addition, our samples from Site C0001 are characterized by a very low equation image, which is also observed in cemented samples from USB. Finally, as a third common attribute, samples from Site C0001 share the same response to consolidation as USB: little deformation down to a critical value of Peff close to the calculated Peffin-situ, then for larger Peff a very large plastic shrinkage.

All these attributes indirectly support the presence of rock-strengthening cement in C0001 (accretionary prism unit). As this unit is probably the proximal equivalent of the USB cored along the Muroto transect [Expedition 315 Scientists, 2009b], the cementing agent may be similar, either authigenic opal [Spinelli et al., 2007] or clay [Ujiie et al., 2003], though our mechanical tests provide no evidence as regards the nature of the cement.

5.4. Critical Porosity

5.4.1. In Terms of Vp Evolution

The concept of critical porosity (ϕcritical) is defined as transition from a fluid-supported to a matrix-supported state [Dvorkin et al., 1999b; Nur et al., 1998]. In such model, in the high-porosity regime (ϕ > ϕcritical), the sediment behave like a suspension, i.e., without rigidity and with incompressibility modulus given by Wood's [1941] equations. It is not completely appropriate, as (1) high-porosity sediment Vp are faster than predicted in the suspension model (Figure 12) [Hamilton, 1971b], (2) they have a small but nonnegligible “dry” framework incompressibility Kdry (Figure 3), and (3) they can transmit shear waves, i.e., they have nonnull rigidity [e.g., Hamilton et al., 1970], which shows that there is a solid particle framework with some strength, even at very high porosity. Because of these shortcomings, in a modified version of the model [e.g., Erickson and Jarrard, 1998], the critical porosity corresponds simply to the sharp increase in the solid framework strength around some porosity, reflected in a sharp increase in Vp. The precise value of this critical porosity is not clearly defined: the value of ∼40% is given for sandstones by Nur et al. [1998], while ϕcritical is in the range 27%–40% for arenites [Vernik, 1998]. For a wider range of sediments, including shales, the critical porosity defined by Erickson and Jarrard [1998] is either 0.31 or 0.39, depending on the degree of consolidation and irrespectively of the lithology, while for Hoffman and Tobin [2004], for various trench facies and hemipelagic sediments from the Nankai Trough, ϕcritical is estimated as 0.295. On the other hand, for clay-supported siliciclastics, Vernik [1998] proposes that on the contrary to grain-supported material, no sharp transition in strength around a given porosity, i.e., no critical porosity, exists.

As Erickson and Jarrard [1998] and Hoffman and Tobin [2004] approaches are empirical and based on curve-fitting, it is not sure whether a critical porosity, i.e., sharp increase in Vp around a given value of the porosity, is actually present or not. Moreover, as the transition from fluid- to matrix-supported state is not a valid model, the physical meaning of the critical porosity is unclear.

As our samples encompass a porosity range over 30% ϕcritical, we cannot rule out the possibility of a sharp increase in material strength around some critical value of the porosity below 30%. Nevertheless, the definition of ϕcritical in terms of Vp, and not poroelastic moduli, introduces a bias, inasmuch as for our high-porosity (30%–60%) material, the tenfold increase in framework incompressibility Kdry (Figure 3) is hardly reflected in Vp, which is principally controlled by water incompressibility. As a consequence, the sharp increase in Vp that may define ϕcritical reflects the point where the strength of the framework becomes of the same order as the fluid strength, while the increase in framework strength occurs actually over a much larger porosity range, for porosity above ϕcritical.

In addition, clays and sand prepared from disaggregated particles that were experimentally consolidated down to large Peff (∼20 MPa) by Karig and Hou [1992] have still relatively low poroelastic moduli (Young's modulus E ≤ 1GPa) with respect to fluid strength, even when porosities reach very low values. (∼25% for sand and 20% for clays). In contrast, natural samples of equivalent lithology and porosity have moduli 10 times larger, reflected in much higher P wave velocities. This shows that rather than porosity, the major control in the sharp increase in Vp for intermediate- to low-porosity sediments is cement. The physical meaning, in terms of poroelastic strength, of the critical porosity, appears therefore questionable, especially in clay-rich material such as the one studied here.

5.4.2. In Terms of Consolidation

While the idea of the critical porosity has been much exploited in determining the relationship between Vp and ϕ, its consequences for consolidation have not been explored. In their physical model, Nur et al. [1998] define the critical porosity as corresponding to a compact arrangement of particles, theoretically around 36% for rigid spheres of a given diameter. If such compact state is relevant, compaction processes above and below such a porosity threshold are fundamentally different: above the critical porosity (ϕ > ϕcritical), sliding at grain-to-grain interfaces enables their redistribution and global porosity reduction, while below (ϕ < ϕcritical), a change in the grain shape itself (from grain fracturing or pressure solution, for example) is required to sustain the porosity reduction. As a result, rates of consolidation should be different in the two domains of porosity.

Our results seem to support these two distinct behavior: in Sites 1173 and C0006, upon application of a large Peff, in the range 1.5–2.5 Peffin-situ (Figure 5b and 5c), there is a relatively sharp transition from shallower samples with a large irreversible shrinkage to deeper ones, where the shrinkage is limited. Semiquantitative XRD analysis of the material (Figure 5d) attests that mineralogy is relatively homogeneous (except for the two deep samples of C0006 pertaining to a different unit) and cannot account for such large differences.

The case of Site 1173 is complicated, as the depth distribution of cement [Spinelli et al., 2007; Sunderland and Morgan, 2004; Ujiie et al., 2003] has a large impact on the mechanical state. On the other hand, in Site C0006, where no evidence for cement was found, porosity is probably the best candidate for the material response to consolidation. The value of the porosity for the transition in mechanical behavior is 38%–42% at Site C0006 (Figure 5, top, horizontal gray band), in good agreement with the value of 40% given by Nur et al. [1998] for the critical porosity in sandstones, even if our material is richer in clay. The relatively low plastic deformation of low-porosity samples can be explained if they are in compact state and if applied stresses were too low to trigger grain cataclasis and experiment duration too small for chemical transport to be efficient. Hence, experimental compaction of samples with ϕ < ϕcritical may be inhibited, or at least very limited in comparison with samples with ϕ > ϕcritical.

Nevertheless literature data on consolidation does not evoke this idea of critical porosity influencing consolidation. For example, profiles of porosity versus depth are usually fitted by a unique law, either exponential [Athy, 1930] or polynomial [Hamilton, 1976], i.e., the existence of two domains of porosity, with distinct consolidation behavior, is not considered. Second, in geotechnical testing, no mention is made of a critical porosity separating two domains of behavior.

In consolidation tests, deformation is often represented by a compressibility factor, which relates the void ratio or the porosity to the log of the effective stress. Between poroelastic deformation and primary consolidation (i.e., equation image similar to in situ conditions), Karig and Ask [2003] define a tertiary consolidation, proper to laboratory high rates of loading, where the plastic deformation occurs with much lower compressibility than primary consolidation phase. This tertiary consolidation is probably what occurs in our deep samples, where the experimental deformation is really limited. In line with the concept of critical porosity, one may wonder whether such low compressibility tertiary consolidation is associated only with low-porosity samples. In the work by Karig and Ask [2003], tertiary consolidation is described for samples with porosity in the range 30%–40%. In the study by Karig [1996], low compressibility consolidation occurs for samples with porosity in the range 30%–35%. In the study by Morgan and Ask [2004], where largest porosity is ∼45%, applied effective stress must be increased to a much higher value than yield stress for a significant deformation to occur, i.e., for effective stresses up to twice in situ effective value (assuming hydrostatic condition), the plastic deformation is very limited. In the study by Feeser et al. [1993], the two deeper samples (porosity in the range 35%–50%) [Shipboard Scientific Party, 1991b] did not reach primary consolidation and were affected by very little deformation, on the contrary to the shallow samples (porosity in the range 50%–65%). These results support the occurrence of tertiary consolidation with low compressibility, hence limited total deformation, only in deep, low-porosity samples, while shallow samples seem to reach primary consolidation, with larger compressibility, without undergoing this phase. If this explanation may explain the variable deformation between shallow and deep samples observed in our samples, it is nevertheless not clear at all whether such transition is associated with critical porosity.

6. Conclusions

The four parameters concomitantly estimated during our experiments (Vp, uniaxial poroelastic compliance equation image, sensitivity of Vp to effective pressure equation image, irreversible shrinkage upon application of a large effective pressure) yielded complementary insights on the state of the various samples tested in the Nankai Trough subduction zone (250–1000 mbsf depth range, hemipelagic to trench facies). The main findings can be summarized as follows.

1. Evidence for incipient cementation is detected by its experimental destruction when compactional force is imposed, which leads to a large increase in compliance and Vp sensitivity to Peff, as well as low equation image. On the basis of such attributes, we inferred the presence of cement in Site C0001 (accretionary prism unit) in addition to USB in Site 1173.

2. The amount of irreversible shrinkage varies strongly through the samples (Figure 4), leading to identify a low porosity domain with limited irreversible deformation and a high-porosity domain where large mechanical compaction occurred. While it is not clear whether such mechanical transition can be related to some critical value of the porosity, the change in response seems to occur around 3–4 MPa effective confining stress.

3. Poroelastic moduli increase continuously and by a large magnitude upon porosity decrease (Figure 3), which is generally not reflected by the subtle, low-magnitude Vp variations (Figure 12).

The latter point, as well as the slight discrepancy between core/log and seismic velocities, point out the need for further experimental calibration of the relationships between acoustic attributes and physical properties, in particular when extrapolated to larger depths via seismic reflection profiling


This research used samples and data provided by the Ocean Drilling Program (ODP) and Integrated Ocean Drilling Program (IODP). Support for the project was provided by the Grant-in-Aid for Creative Scientific Research (19GS0211) by MEXT (Ministry of Education, Culture, Sports, Science and Technology) of Japan. We thank the staff in Kochi Core Center for their help with sampling. The paper benefited greatly from the very detailed comments by three anonymous reviewers.

    Appendix A

    The porosity of the core samples we used in our experiments was determined on trimmings from sample preparation, measuring its relative loss of weight after drying at 105°C overnight and converting it to porosity by using the value for grain density of the closest sample measured on board (MAD measurements, see Table 1). Then we applied on this porosity a correction to restore in situ conditions, calculated from monitored values of equation image as a range comprised between two extreme cases, either no radial deformation (equation imageequation imageequation image) or isotropic deformation (equation imageequation image 3equation image). This correction for rebound is extremely variable between samples (as visible in the size of the range of the porosity correction in Figure 12), making it difficult to derive general porosity rebound laws such as in the work by Hamilton [1976].

    In situ porosity for logging data is derived from resistivity, smoothed by averaging over 20 m thick depth interval, as this is the only physical measurement available for all the holes surveyed by Expedition 314 (Sites C0001, C0002, and C0006). The relatively good agreement (Figure A1) between resistivity-derived porosity and our in situ, laboratory-derived core porosity (with rebound correction) allows for comparison between the different data sets, although in detail there are often slight discrepancies, such as logging porosity either lower (up to ∼5% of porosity) for Site C0001 and higher for Site C0002 (up to ∼5% of porosity).

    Details are in the caption following the image
    Comparison of (1) MAD measurements of the porosity of the core samples used in our experiments (with correction for rebound; see text) and (2) porosity derived from logging data, either resistivity or bulk density [Expedition 314 Scientists, 2009].

    On Figure A1 is also plotted another measurement of porosity, derived from bulk density logging, which is also in good agreement with our laboratory-derived core porosity (with rebound correction). This enables the comparison done in Figure 12 between our core/logging data with Erickson and Jarrard [1998] and Hoffman and Tobin [2004] Vp versus ϕ relationships, where in both cases porosity was derived from density logs.

    Please note also that we do not apply any correction for the water bounded to clay [Conin et al., 2011]. This bounded water significantly affects the porosity of our samples estimated by MAD measurements, but as the density-derived porosity used by Erickson and Jarrard [1998] and Hoffman and Tobin [2004] is calculated with a solid grain density also estimated by MAD measurements, for the consistency of our data with theirs we did not correct for the bounded water. Finally, as the correction for clay content to be applied to resistivity-derived porosity is of the same order as the one to MAD porosity [Conin et al., 2011], we use for the logging data (C0001, C0002, C0004 and C0006) in Figure 12 resistivity-derived porosity uncorrected for the clay content, for a similar reason of data set consistency. The consequence is that the porosity plotted in Figure 12 may be a bit higher than “true” interstitial porosity, but all the data sets are intercomparable.

    Appendix B

    If one tries to determine to which extent a given error on velocity affects the other properties, using Hoffman and Tobin's [2004] relationship, a difference in Vp from 2 to 2.1 km/s leads to a porosity difference of ∼0.03, from 0.357 to 0.327. These two porosities, when expressed as void ratio ϕ/(1 − ϕ)(yielding 0.555 and 0.486, respectively), can be converted into effective stresses using field-based virgin consolidation curves in the work by Saffer [2003]. As a result, the equilibrium stress corresponding to Vp = 2 km/s is 5.1 MPa, while for Vp = 2.1 km/s, stress is 5.7 MPa, i.e., a difference in velocity as small as 0.1 km/s leads to differences in stresses as large as ∼0.6 MPa, which are significant with respect to Peffin-situ for the relatively shallow rocks (<1000 mbsf) considered here.