In situ test of hydraulic fracturing (HF) provides the only way to observe in situ stress magnitudes directly. The maximum and minimum horizontal stresses, SHmax and Shmin, are determined from critical borehole pressures, i.e., the reopening pressure Pr and the shut-in pressure Ps, etc, observed during the test. However, there is inevitably a discrepancy between actual and measured values of the critical pressures, and this discrepancy is very significant for Pr. For effective measurement of Pr, it is necessary for the fracturing system to have a sufficiently small compliance. A diagnostic procedure to evaluate whether the compliance of the employed fracturing system is appropriate for SHmax determination from Pr was developed. Furthermore, a new method for stress measurement not restricted by the system compliance and Pr is herein proposed. In this method, the magnitudes and orientations of SHmax and Shmin are determined from (i) the cross-sectional shape of a core sample and (ii) Ps obtained by the HF test performed near the core depth. These ideas were applied for stress measurement in a central region of the Kumano fore-arc basin at a water depth of 2054 m using a 1.6 km riser hole drilled in the Integrated Ocean Drilling Program (IODP) Expedition 319. As a result, the stress decoupling through a boundary at 1285 m below seafloor was detected. The boundary separates new upper layers and old lower ones with an age gap of ~1.8 Ma, which is possibly the accretionary prism. The stress state in the lower layers is consistent with that observed in the outer edge of accretionary prism.
 Motion of rocks is so slow in nature that it takes a considerable time for us to realize the motion. Contrary to this, the stress state in rocks allows us to immediately infer crustal dynamics involving the rocks, which is typically represented as Anderson's classification of faulting, i.e., normal, thrust, and strike-slip faulting, and the stress is necessary for safe construction and maintenance of underground man-made structures, including boreholes. The first in situ stress measurement of scientific ocean drilling was carried out at Site C0009 during the Integrated Ocean Drilling Program (IODP) Expedition 319 as part of Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) Stage 2 [Saffer et al., 2010; Moe et al., 2012]. A new borehole, Hole C0009A, was drilled to 1603.7 mbsf (meters below seafloor) from the seafloor at a water depth of 2054 m, and hydraulic fracturing tests for stress measurement were performed using the latest wireline logging tool. A riser system used for the hole drilling made the usage of the tool possible.
 The hydraulic fracturing (HF) test provides the only way to observe stress magnitudes directly. In this test, a section of a borehole is isolated, and the borehole wall is subjected to increasing fluid pressure. With increasing the borehole pressure P, the hoop stress, which includes components caused by P and the maximum and minimum horizontal stresses, SHmax and Shmin, changes from compression to tension first at the two positions aligned with the azimuth of SHmax. When the combined hoop stress exceeds a tensile strength of rock, it induces tensile fractures. The fractures extend in the direction of SHmax in case of vertical boreholes such as Hole C0009A. The fractures close with venting and open with re-pressurization. In situ stress magnitudes are determined from critical borehole pressures observed during the test. The shut-in pressure Ps is used to determine the minimum horizontal stress Shmin, and the reopening pressure Pr is used to determine SHmax. The latter one is defined as the borehole pressure at the moment of fracture opening. However, a discrepancy inevitably occurs between actual and measured values of Pr due to a problem associated with the way of measurement, and sometimes it becomes very significant. For effective measurement of Pr, it is necessary for the fracturing system to have a sufficiently small compliance C [Ito et al., 1999; 2005; 2006]. If not, the measured Pr becomes independent of SHmax to take the same value as Ps, in other words with Shmin. This gives a reasonable explanation for the fact that in the data of field tests so far, there is an obvious tendency for measured values of Pr and Ps to be close to each other [e.g., Evans et al., 1989; Lee and Haimson, 1989; Sano et al., 2005].
 Taking account of the effect of the system compliance C on the measurement of Pr, two strategies for determination of the in situ stresses at C0009A were applied. First, the compliance of the fracturing system composed of the dual packer tool, i.e., the Modular Dynamic Tester (MDT, Schlumberger), was evaluated, and the borehole pressure change with fracture opening upon the theoretical model considering the compliance effect was predicted. As a result, the compliance was confirmed within allowable range in which the measured Pr can be applied for determining SHmax. The SHmax and Shmin at 878.7 mbsf were accordingly determined from the measured values of Pr and Ps. Secondly, as a new idea not restricted by the system compliance and Pr, a core-based method was applied. This method assumes that a core sample retrieved from an anisotropic in situ stress field should expand elliptically in an elastic manner, the maximum expansion occurring in the direction of SHmax. The stress deviation (SHmax − Shmin) can be determined from the difference between the maximum and minimum diameters of the elliptical core. The SHmax can be determined as a sum of the stress deviation (SHmax − Shmin) and the Shmin determined from the shut-in pressure Ps, which is obtained by the in situ test of hydraulic fracturing carried out near the core depth. By this second strategy, the magnitudes of both SHmax and Shmin and the SHmax azimuth at 1532.7 mbsf were successfully determined.
2 Site C0009 and Stress State Observed in Former Expeditions
 The Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) is a coordinated, multiexpedition and multistage project of the Integrated Ocean Drilling Program (IODP). The fundamental scientific objectives of this project include characterization of the nature of fault slips and strain accumulation, fault and wall rock compositions, fault architecture, and state variables throughout the active plate boundary system. As the NanTroSEIZE Stage 1, IODP Expeditions 314, 315, and 316 were carried out in late 2007 through early 2008. These expeditions were followed by IODP Expedition 319 as the first expedition of the NanTroSEIZE Stage 2, and two boreholes were prepared by riser and riserless drilling at Site C0009 and Site C0010, respectively. Details of this expedition have been reported by Saffer et al. . Site C0009 targeted in the present study is located in the central region of the Kumano fore-arc basin and the upper plate above the seismogenic and presumed locked portion of the plate boundary thrust system. A borehole, Hole C0009A, was drilled here to 1603.7 mbsf from seafloor at a water depth of 2054 m using riser drilling technology for the first time in the history of scientific ocean drilling. The upper 700 m was cased, a 12¼ inch hole was drilled from 700 to 1510 mbsf, and cores were cut from 1510 to 1539.9 mbsf using a rotary core barrel. This borehole was designed to (i) determine the composition, physical properties, and stratigraphy of the basin sediments, (ii) conduct downhole measurements to determine stress magnitude and orientation and pore pressure magnitudes, (iii) install casing in preparation for a riser observatory, and (iv) acquire data from a two-ship vertical seismic profile experiment to characterize the rock volume surrounding and below the borehole, including the subduction thrust at a depth of about 10 km.
 For the former stage of the NanTroSEIZE, a transect of eight sites was selected for riserless drilling to target the frontal thrust region, the midslope megasplay fault region, and the Kumano fore-arc basin (Figure 1) [Kinoshita et al., 2008]. At four sites among them, i.e., C0001, C0002, C0004, and C0006 among them, borehole images were taken using the Schlumberger geoVISION LWD tool. As a result, borehole breakouts were observed at all four sites, and their orientations at three sites of C0001, C0004, and C0006 indicate northwest-southeast azimuths of SHmax. This is consistent with trench-normal shortening in the thrust dominated tectonic environment, while the SHmax orientations slightly deviate from the far-field plate motion vectors based on GPS results [Heki, 2007]. In contrast, breakouts suggest that SHmax is rotated by about 90° at Site C0002 relative to Site C0001 located at about 10 km away to the southeast. The reason for this stress rotation is still not clear but it might be caused by factors such as local deformation due to gravitation-driven extension in the fore arc and thrusting and bending within individual geologic domains. The stress analyses on breakouts in this area have been described in detail elsewhere, e.g., Chang et al.  and Lin et al. .
3 Hydraulic Fracturing Tests: Tool and Test Depths
 Borehole breakouts are well recognized as being a reliable indicator of SHmax orientation as used in the NanTroSEIZE. In this case, a breakout azimuth is applied for the stress determination. Further analyses have been made to determine even magnitude of in situ stress from breakout width along the borehole circumference [e.g., Haimson and Herrick, 1985; Brudy and Zoback, 1999; Haimson and Chang, 2002; Chang et al. 2010]. However, recent progress on borehole image logging indicates that there is a possibility of a significant increase in the breakout width with time [Moore et al, 2011; Chang and Moore, 2012]. Such phenomena should lead to a significant error in stress magnitudes estimated from measured breakout width, while breakout azimuth is unchanged with time; therefore, its reliability in the determination of stress orientation remains valid. On the other hand, the hydraulic fracturing method can provide a unique measure for direct determination of in situ stress magnitude, while it requires an in situ test of hydraulic fracturing (HF) in a borehole. Thus, this method was applied for further understanding of the state of stress at Site C0009. The riser system used for drilling a hole there, Hole C0009A, made the measurement possible. The borehole tool for the HF test had a large diameter close to that of a borehole. The riser system provided easy and safe access for such a big tool to enter and exit a borehole at the seafloor far below the drill floor. Moe et al.  reported the operational planning process related to the in situ tests carried out in Hole C0009A.
 The Modular Dynamic Tester (MDT, Schlumberger) wireline logging tool was used to carry out in situ tests in Hole C0009A for measurements of not only stress but also permeability and pore fluid pressure. Its modular design allows it to be customized for such multiple measurements. The configuration for Hole C0009A was set to include the gamma-ray sonde, a pump-out module (MRPO), a single probe module (MRPS), and a dual packer module (MRPA) (Figure 2). The last module is used to isolate a 1 m test interval of the borehole. The packers have a 10 inch diameter prior to inflation and are designed to plug boreholes in a range of diameters from 12¼ to 14¾ inches. The MRPO is used to pump fluid from the mud column to the packers or into the test interval. The MRPO can either withdraw or inject fluid into the test interval. Pressures in the packers and test interval are recorded simultaneously and can be displayed in real time on a monitor placed in the operator's house.
 In situ stress measurements by the HF test were limited to two times at different depths due to allowable cost and time. Those test intervals were selected by examining available core samples and logging data (particularly image and caliper logs). The criteria for choosing a location were (i) freedom from preexisting fractures, (ii) a hole diameter <14¾ inches, (iii) hole ovality, i.e., maximum diameter/minimum diameter, of <130%, and (iv) continuity of the above conditions for more than 3 m along the borehole. Note that the open hole section between 703.9 and 1539.9 mbsf was reamed with a 12¼ inch drilling assembly before the HF tests. Central depths of test intervals at 878.7 and 1532.7 mbsf, which were near top and bottom of the open hole section, were finally selected. The latter is located within the cored section of 1509.7–1593.9 mbsf. The HF tests and the other measurements using the MDT tool were carried out in a single run. The tool was lowered to the bottom of the hole, and the HF test was carried out, first at 1532.7 mbsf and then at 878.7 mbsf as the tool was pulled up.
4 Test Results
4.1 First HF Test at 1532.7 mbsf
 The standard procedure of the HF tests has been summarized by Haimson and Cornet . It involves a process of repeating a cycle of raising and lowering borehole pressure several times for creating (or opening) and closing hydraulically induced tensile fractures. However, the in situ conditions and the time limitation due to concerns over borehole stability did not allow us to follow this procedure. Figure 3 shows time variations of the pump-out rate, packer pressure, and borehole pressure at the test interval actually observed during the HF test at 1532.7 mbsf. The variation of borehole pressure associated with tool operation was carefully examined. The test period can be divided into three parts, i.e., periods I, II, and III. The pressure variation at each period can be interpreted as follows. For period I, pump-out fluid was supplied to inflate the packers. At time “a,” the packer pressure started to increase since the packer inflated sufficiently to fill the cross-sectional area of the borehole, and afterwards the fluid supply could contribute to elevation of the packer pressure. The packer inflated further, not in the radial direction but rather in the axial direction for a while. The axial inflation compressed fluid in the test interval, and the compression led to a pressure increase in the test interval. After termination of the fluid supply at time “b,” the interval pressure decreased not steeply but gradually. These phenomena indicate that the packers worked well to isolate the test interval and that there were no significant flow pathways such as natural fractures or breakouts to cause significant leakage from the test interval. For period II, pump-out fluid was supplied to the test interval, and accordingly, the interval pressure increased. However, the pressurization was stopped at time “c” because the pressure increase was so gradual that it was expected to take a considerably long time until the occurrence of breakdown. For period III, the interval was pressurized again at injection rates greater than those of period II with assistance of an additional pump. As a result, the interval pressure increased more quickly to 41.7 MPa, but the pump suddenly stopped at time “d” due to an electrical problem. After a short break for fixing the problem, the pressurization was restarted at time “e” at the maximum injection rate; however, it led to just a slight pressure increase, not reaching the pressure at time “d,” and afterwards the interval pressure decreased gradually while the fluid injection was continued at the same rate during period II. Such distinctive features which appeared in the pressure record suggest that new tensile fractures were initiated at time “d” or somewhere else between times “c” and “e.” In this case, it is most reasonable to choose the pressure at time “f,” i.e., 41.5 MPa, as the shut-in pressure Ps since Ps should appear as the point of maximum curvature on the pressure decay curve after shut-in [Hayashi and Sakurai, 1989; Hayashi and Hamson, 1991], and the pressure decay curve in the period III of the present test has the maximum curvature obviously at “f.” However, the pressure decay curve is not so typical that the detected value should be recognized to be less accurate. On the other hand, there was no way to detect the reopening pressure since this HF test was stopped at time “g” due to a time limitation related to concern over borehole stability, and the fracture reopening procedure was not applied.
4.2 Second HF Test at 878.7 mbsf
 Observed time variations of pump-out rate, packer pressure, and borehole pressure at the test interval are shown in Figure 4. The test period can be divided into three parts, i.e., periods I, II, and III. Period I was spent for packer inflation. Isolation of the test interval was confirmed from its pressure development in accordance with the packer pressurization. For period II, the pressurization of the test interval was repeated three times. The interval pressure changed typically as expected from the standard model of Haimson and Cornet , indicating that new tensile fractures were initiated in the first cycle and reopened in the subsequent cycles. The test interval was vented to relieve excess pressure completely at the end of period II, and in period III, the last (fourth) pressurization cycle was started from a pressure slightly lower than the initial pressure in the borehole, i.e., the hydrostatic pressure. Note that venting was carried out by withdrawing the fluid in the test interval, which allowed making the interval pressure lower than the initial borehole pressure. In the fourth cycle, after the interval pressure peaked, it once decreased quickly and then increased again until shut-in, while the fluid injection was continued at a constant rate. Similar fluctuation in pressure was also observed in the first cycle. These phenomena may be interpreted as an effect of a mud cake covering the borehole wall. The borehole pressurization of the first cycle broke the mud cake, allowing fluid invasion into the induced fractures; however, it re-formed during the venting process between the third and fourth pressurization cycles. In the fourth pressurization cycle, the re-formed mud cake unexpectedly worked well to maintain the interval pressure at a level even slightly higher than the peak in the first cycle. This HF test was stopped at the end of period III.
 The shut-in pressure Ps and the reopening pressure Pr were obtained from the pressure-time record. To detect Ps from the pressure decay curve after shut-in, the method of Hayashi and Hamson  was applied since the point of the maximum curvature on the pressure decay curve is hard to define directly as Ps unlike the HF test at 1532.7 mbsf. This method is based on regression analysis of the plot of dt/dP versus P, where P is pressure and t is time. Figure 5a shows the plot of dt/dP versus P obtained from the pressure decay curve after shut-in for the case of the second pressurization cycle. A straight line was fitted to the first portion of the dt/dP versus P data. The point of departure of the remainder of the curve from the straight line was taken as Ps. As a result, Ps was determined to be 34.9 MPa. We applied the same analysis to determine Ps for the other pressurization cycles, and the results are summarized in Table 1. The reopening pressure Pr was detected from the pressure ascent curve of both the second and third cycles. This analysis was not applied to the fourth cycle since the pressure ascent curve was considered to be significantly affected by the mud cake as discussed above. Figure 5b shows the plot of P versus Vacc for the second cycle, where Vacc is the accumulated volume which was injected. The curve deviates from the initial linear trend at 34.9 MPa, so that Pr is determined to be 34.9 MPa. Pr of the third cycle was determined in the same way. The results are summarized in Table 1 together with Ps. Thus, the average Ps of four measurements is 35 MPa, exactly the same as the average Pr of two measurements, i.e., Ps = Pr = 35 MPa.
Table 1. Summary of Critical Pressures Detected From the Borehole Pressure and Injection Flow Rate Versus Time Record Obtained at 878.7 mbsf
Shut-in pressure Ps (MPa)
Reopening pressure Pr (MPa)
5 Stress Determination From Shut-in and Reopening Pressures
 When vertical fractures are induced in tension by hydraulic fracturing in a vertical borehole, the shut-in and reopening pressures, Ps and Pr, of the fractures should be related theoretically to the maximum and minimum horizontal stresses, SHmax and Shmin, as follows [Ito et al., 1999]:
 With these two equations, the values of SHmax and Shmin can be both determined from the two measured pressures of Pr and Ps. Accordingly, the measured values of Ps = Pr = 35 [MPa] obtained from the in situ HF test at 878.7 mbsf lead to the determined values of SHmax = Shmin = 35 [MPa]. The stress orientation is not a matter of course in this case. The reliability of Shmin determined from Ps by equation (2) is generally accepted. However, this is not the case for SHmax, and further examination of the in situ test conditions is required to confirm the reliability of SHmax determined from equation (1).
 Equation (1) includes pressure penetration into the fracture prior to fracture opening [Ito et al., 1999]. As a result, the fracture begins to open at a pressure less than or equal to Shmin. The reopening pressure can be measured as a pressure at the deflection point of the borehole pressure P versus the accumulated injected volume, Vacc, curve. However, the effect of the initial fracture opening on the slope of P-Vacc curve is so weak that for measurement of the actual reopening pressure given by equation (1), the compliance of fracturing system should be sufficiently small and close to the compliance of the fracture at the initial stage of fracture opening [Ito et al., 1999; 2005; 2006]. The former and latter compliances refer to the system compliance C0 and the fracture compliance Cf, respectively, where C0 is generally known as wellbore storage and Cf is defined as the increasing rate of fluid volume associated with fracture opening, Vf, driven by the borehole pressure P, i.e., Cf = dVf/dP. If C0 is fairly large compared with Cf, the measured Pr becomes independent of SHmax and has the same value as Ps, in other words with Shmin. Then the SHmax determined from equation (1) is equal to Shmin, i.e., SHmax = Shmin. This result is apparently consistent with that obtained from the in situ HF test at 878.7 mbsf as described above. This consistency suggests the possibility that the C0 for the case of the HF test at 878.7 mbsf was inappropriately large for measurement of Pr. Therefore, the discrepancy between the measured and actual reopening pressures was estimated for the P-Vacc curve simulated theoretically on conditions of the HF test at 878.7 mbsf in Hole C0009A.
5.2 Approximate Model of Borehole-Fracture System
 A borehole-fracture system was assumed here as shown in Figure 6, where a is the borehole radius, c is the total length of the induced tensile fracture with a residual aperture w0, and L is the open fracture length, i.e., the length of the section in which the aperture becomes larger than w0. The simulation of the P-Vacc curve requires that a complicated problem be solved, fully coupling a compressible fluid flow and elastic deformation of a solid structure as described in detail by Ito et al. . However, the results of the coupled simulation show that until the borehole pressure reaches the value of Shmin, the fracture opening proceeds quasi-statically, while keeping almost uniform internal pressure balancing with the borehole pressure [Ito et al., 2006]. Accordingly, if the pressure in the fracture is assumed to change uniformly with the borehole pressure, the simulation of the P-Vacc curve becomes drastically simplified. First, the assumption allows us to determine the open fracture length L uniquely as a function of P, as follows. Fracture mechanics considerations require that the stress intensity factor KI at the tip of the opening portion of the fracture must be zero for L < c. That is,
where KIP is a component associated with P, and KIS is that associated with SHmax and Shmin. From Tada et al. , analytic expressions for both components are given by
where s = L/(a + L) and the functions f1(s) and f2(s) are given by
L can be determined as it satisfies equation (3) for a given value of P.
 Once L is known, the fracture compliance Cf can be estimated. The fracture-opening displacement wm (=w − w0) increases the cross-sectional area of the borehole-fracture system and results in an increase in fluid volume dVf. Areal change occurs not only in the fracture section but also in the borehole section, illustrated as a shaded portion in Figure 7a, i.e., the area of [fracture opening at the borehole wall] by [borehole diameter]. The latter plays an important role in dVf at the initial stage of fracture opening, especially for the case of a small system compliance C0. In order to estimate those areal changes, the fracture-opening displacement wm of a pressurized borehole-fracture system is here approximated by that of the uniformly pressured, 2-D bilateral fracture with length (2 L + 2a), as illustrated in Figure 7b. Then, using the solution for a similar fracture given by Tada et al. , the explicit expression of Cf can be deduced as follows:
where h is the fracture height, ν and G are the Poisson's ratio and the shear modulus of rock, respectively. Note that (i) Cf is a function of P, since it includes L changing with P, and (ii) Cf is defined for P > Pr0, where Pr0 is the borehole pressure given by equation (1), at which the fracture actually opens.
 The assumption of uniform pressure in the fracture enables further simplification of the analytical expression of the increasing rate of P with Vacc and results in
 Prior to fracture opening, Cf is zero and the borehole pressure P increases linearly with Vacc at a rate of 1/C0. This relationship is nothing but the definition of C0. After fracture opening, Cf becomes greater than zero, and the P-Vacc curve deviates from linearity. From equation (8), the relationship between P and Vacc is finally obtained as follows:
where P0 is the initial value of P. Using the above equations, the P-Vacc curve can be easily simulated even by spreadsheet-based computation. The Vacc can be converted into time, t, for a constant injection rate Q by t = Vacc/Q. However, note that equation (3) is not applicable for P > Shmin, since it then becomes indefinite. Figure 8a shows a comparison of the above approximate simulation and the strict simulation presented in Ito et al.  assuming, as an example, that a = 50 [mm], h = 1[m], G = 25 [GPa], ν = 0.2, C0 = 0.5 [cm3/MPa], SHmax = 15 [MPa], Shmin = 10 [MPa], and P0 = 3 [MPa]. The fracture begins to open at 7.5 MPa as estimated from equation (1). Figure 8b shows another example obtained assuming SHmax = 20 [MPa], while the other conditions are the same as the case of Figure 7a, where the fracture begins to open at 5.0 MPa. Both results show that the present model can simulate the P-Vacc curve with sufficient accuracy for detecting the apparent reopening pressure, i.e., the pressure at which the curve deviates from initial linear trend.
5.3 Parameter Setting and Results
 For simulating the P-Vacc curve by the present model, seven parameters, i.e., a, h, G, ν, C0, SHmax and Shmin, must be set in accordance with the in situ test at 878.7 mbsf in Hole C0009A, where the fracture opening is less sensitive to ν and not essentially affected by P0. They were set so that a is 171 mm (6⅛ in.) according to the drilling record, h is 1 m from length of the test interval, ν is 0.3 as generally assumed, and Shmin is 35 MPa from the measured shut-in pressure. Unknown SHmax is assumed here as it satisfies SHmax/Shmin = 1.2, i.e., SHmax = 42 [MPa], as an example. C0 is determined from the in situ test data. Figure 9 shows the plot of P versus Vacc for the pressure ascent portion prior to the breakdown of the first pressurization cycle, in other words, prior to fracture initiation. As can be seen from equation (8), C0 is given as the inverse of the slope of the P-Vacc curve because of zero Cf . The value of C0 = 427 [cm3/MPa] ( = 4.27 × 10−4 m3/MPa) was actually obtained from Figure 9 for use in the simulation. Finally, there remains the shear modulus G. Its value was determined from analysis combining laboratory test data by Boutt et al.  and logging data. Boutt et al.  conducted laboratory permeability tests on a specimen 10 cm long and 5 cm from core 4R-1 recovered at a depth of 1537.47–1537.59 mbsf as a part of cores recovered from 1509.7 to 1593.9 mbsf in Hole C0009A. The tests were carried out at a confining pressure of 10 MPa, and measurements of sample deformation during loading-unloading steps yielded a bulk modulus K of about 3 GPa. This value is converted to the shear modulus of 1.77 GPa assuming a theoretical relationship between K and G.
 On the other hand, G is related to shear wave velocity Vs as follows:
where ρ is rock density. On this relation, the shear modulus at 1537 mbsf estimated from the laboratory tests of Boutt et al.  can be connected with the shear modulus at a depth of 878.7 mbsf as follows:
where the subscripts of “8” and “15” are attached to each one of G, ρ, and Vs of the rocks at 878.7 and 1537 mbsf, respectively. The logging data [Saffer et al., 2010] show that the rock density is almost homogeneous, being 2.1 g/cm3 over the depth range of the open hole, i.e., ρ8/ρ15 = 1, while the shear wave velocity at 878.7 mbsf is smaller than that at 1537 mbsf by a ratio of Vs8/Vs15 = 0.806. Substituting these ratios and the value of G15, i.e., 1.77 GPa, into equation (11), the shear modulus at 878.7 mbsf, G8, of 1.15 GPa is finally obtained for use in the simulation.
 Based on the approximate model, the relationship between P and Vacc was simulated for the parameter values set as above. The relationship is drawn as a curve in Figure 10a. An apparent reopening pressure of 32.3 MPa is detected on the curve, and it is slightly larger than the actual reopening pressure of 31.5 MPa estimated from equation (1). The difference is just 0.8 MPa, which corresponds to an error of less than 3%. From this result, it was concluded that the system compliance C0 for the case of the HF test at 878.7 mbsf was within the allowable range for SHmax determination from Pr. Note that the fracture opening initiates a change in the slope of the P-Vacc curve more clearly for larger boreholes and softer rocks as long as C0 does not change, since the fracture compliance Cf becomes accordingly larger as can be seen from equation (7). In the case of the HF test at 878.7 mbsf, the large borehole and the soft rock contributed well to raise Cf adequately for SHmax to be determined from Pr even though the test system had a relatively large C0 of 427 cm3/MPa. For example, when the shear modulus G is 4 times as large as the case of Figure 10a, the P-Vacc relation becomes so linear, as shown by the dashed line in Figure 10b, that it becomes obviously impossible to detect Pr0 correctly. The effect of the packer deformation constitutes a considerable ratio of the system compliance C0. The effect decreases with increasing inflation pressure in the packer. Thus, by setting the inflation pressure as high as possible, C0 can be reduced even for the same setup of the test system.
6 Stress Determination From Shut-in Pressure and Core Deformation
 The method described in the previous section cannot be applied to the case of the HF test at 1532.7 mbsf since Ps was measured but Pr was not, which is necessary for SHmax determination. Therefore, we determined SHmax by combining with another indicator, i.e., deformation of a core sample.
 Let us consider the coring process. A hollow cylindrical core tube is used to obtain core samples. A core bit is pushed to the exposed surface of rock at the bottom of the borehole with a rotating motion. As a result, a column of rock is carved out and stored in the core tube. A cross-section of the carved column at the moment of drilling should be perfectly circular since the column is carved out by a rotating bit. However, a portion of the column away from the drill bit must expand elastically in response to the relief of in situ stress. The expansion should occur in an asymmetric manner under the relief of anisotropic in situ stress field, as shown in Figure 11a. The core should expand most and least in the directions of SHmax and Shmin, respectively. The stress relief induces strains in the core, which is the same as those induced in the rock mass when it is relieved from the in situ stresses, as shown in Figure 11b. If the rock is homogeneous and isotropic and is elastically deformed, the stress relief induces the tensile strains emax and emin in the directions of SHmax and Shmin, respectively, and they are given by
 These strains can be represented by using the maximum and minimum diameter of the core, dmax and dmin, respectively, as follows:
 From equations (12), (13), and (14), the differential stress in the plane perpendicular to the axis of the core can be related to the difference of diameters of the core as follows:
While the original diameter of the core, d0, is unknown, the core deformation by stress relief is very minute, and d0 in the right side of equation (15) could be replaced by dmin. Thus, the azimuths of SHmax and Shmin can be determined from the azimuths of dmax and dmin. This idea is advantageous in that the SHmax azimuth can be determined without problematic and costly measurements of the induced tensile fracture trace on the borehole wall. Furthermore, the differential stress (SHmax − Shmin) can be determined from the values of dmax and dmin based on equation (15). This is the basic concept of Diametrical Core Deformation Analysis, DCDA, which was originally presented by Funato and Chen  and verified through field data analyses and laboratory experiments by Funato et al. . Combining DCDA with Ps or the other stress indicator of Shmin, we can determine the magnitude of SHmax as a sum of the Shmin and the differential stress (SHmax − Shmin) from DCDA.
6.2 Diameter Measurement and Determined SHmax
 DCDA requires precise measurement of core diameters in all directions. To accomplish this, the measurement tool shown in Figure 12 has been developed by Funato and Chen . Core diameter is measured at a resolution of 0.1 µm using an optical micrometer, while a core sample is rotated on two rollers at constant speed. The rotation rate is normally set at one rotation per 3 min, and as a result, the diameter is measured at every 2° rotation angle for the range 0–360°. As can be easily seen, one rotation, i.e., 0–360°, is redundant as it is twice the requirement for measuring circumferential diameter distribution. The additional data measured for the range 180–360° are used for confirmation of the measurement. Furthermore, the diameter measurements are repeated at different distances from the end of a core sample, and the consistency of those results are examined. If the deformation is not uniform along the core, the core is suspected of being disturbed by some drilling problems. The circumferential distribution of the core diameter is theoretically given by
where θ is the circumferential angle measured from a reference position, dθ is the core diameter at θ, and α is the direction of dmax. This equation is fitted to the average of the observed diameter distribution by least square regression in order to find the best estimations of α, dmax, and dmin.
 We obtained core 4R-4, recovered at a depth of 1539.96–1540.16 mbsf in Hole C0009A. The diameter measurements of the core were carried out at intervals of 2 cm along the axial length between 6 cm and 12 cm from the upper end of the core sample of with a total length of 20 cm and were repeated twice at each location. The results are summarized in Figure 13, where the angle θ is measured in a clockwise fashion from a reference position defined temporarily, since the core was not oriented at drilling. The diameter measured at different distances from the end of the core sample are shown by thin lines. All of the curves are similar in sinusoidal shape. These results show that the core sample was uniformly deformed into a shape with an elliptical cross-section as theoretically expected. The thick black line represents the average of the measured diameter. By least square regression for fitting equation (16) to the average, the optimum values of dmax − dmin = 0.224 [mm], dmin = 58.1 [mm] and α = −15° (or 165°) were obtained. Substituting the determined diameters into equation (16), the differential stress (SHmax − Shmin) is determined to be 13.6 MPa, where for this calculation, the shear modulus of G15 = 1.77 [GPa] estimated from the laboratory tests of Boutt et al.  was used, as described previously. Finally, we have the SHmax magnitude of 55.1 MPa as a sum of the differential stress and the Shmin of 41.5 MPa determined from Ps in the HF test.
 On the other hand, a borehole image log indicates a sedimentary structure with a dip of about 30° and a dip direction of N7 ± 12°W at the depth of the HF test, i.e., 1532.7 mbsf [Saffer et al., 2010]. An inclined sedimentary structure is also found on the surface and interior of core 4R-4, and the structure dips by about 30° in the direction of 180 ± 5° relative to the reference position. This structure in the core should correspond to that found on the borehole image log. From this observation, the absolute orientation of the core can be determined by adjusting each dip direction of the core and the borehole image. As a result, the direction of the reference position is determined to be N173 ± 12°E, which results in the dmax direction, i.e., the SHmax direction, of N157 ± 13°E (or N23 ± 13°W).
 If Pr were to be obtained in addition to Ps by the hydraulic fracturing test, it could lead to another determination of the SHmax magnitude independent of the core deformation, where the system compliance should be, of course, within the range appropriate for measuring Pr, as discussed in the previous section. In this case, the SHmax magnitudes determined in both ways could be cross-checked. This procedure would greatly contribute to enhancement and confirmation of the determined SHmax.
7 Summary and Discussion
 Figure 14a shows the magnitudes of horizontal stresses, SHmax and Shmin. In this figure, hydrostatic pore pressure Pp and vertical stress Sv calculated from overburden are also plotted for comparison, where Pp was confirmed to be a hydrostatic condition by in situ tests using the single-probe module installed in MDT [Saffer et al., 2010]. The SHmax and Shmin were determined assuming hydraulically induced tensile fractures with vertical orientations, as described in previous sections. Although there was unfortunately no borehole imaging logs available to identify the fracture orientation directly, this assumption is supported by the results that in both cases of 878.7 and 1532.7 mbsf, the magnitudes of Shmin determined from the shut-in pressure equilibrating with the fracture-normal stress are obviously smaller than Sv. Other evidence described below was found, which verified the determined stresses as indirect proof for the assumption of fracture orientation.
 Several types of wireline logging runs were performed for the open hole section in Hole C0009A [Saffer et al., 2010; Lin et al., 2010]. Furthermore, the collection and analyses of drill cuttings and mud gas respectively were performed, taking advantage of the riser drilling operations applied to this hole. Many data sets obtained by those operations indicate the existence of a major boundary around 1285 mbsf. Figure 14b shows records of a caliper installed in the Formation Micro-Imager (FMI), which has four arms set at every 90° to measure borehole diameters in orthogonal directions, C1 and C2. The records indicate a significant change at 1285 mbsf. Above that depth, both diameters C1 and C2 have the same value as the bit-size of 12¼ in. This result is harmonic with recorded orientation of the arm for C1 (Figure 14c). The arm orientation shifts continuously with the depth of the logging tool, which should be possible because of the circular and smooth surface of the borehole. Contrary to this, below a depth of 1285 mbsf, the measured diameters indicate borehole enlargement in the direction of N225°E almost down to the bottom of the borehole, where the HF test at 1532.7 mbsf was applied to a short depth window in which the borehole remains in gauge. Such directional and continuous enlargement of the borehole is recognized as the borehole breakout resulting from a compressive failure caused by anisotropic stress concentration around the borehole. Therefore, the observed enlargement of borehole indicates the existence of considerable anisotropy in horizontal stresses, i.e., SHmax ≠ Shmin, at least below 1285 mbsf [Lin et al., 2010]. This observation is consistent with the present horizontal stresses determined by the HF test at 1532.7 mbsf and the core at 1540 mbsf, i.e., SHmax = 55.1 [MPa] and Shmin = 41.5 [MPa]. In addition, the SHmax azimuth of N135 ± 11°E estimated from the breakout orientation by Lin et al.  is close to that determined in the present study, i.e., N157 ± 13°E.
 On the other hand, the boundary at 1285 mbsf was also marked by increased lithification as shown in Figures 14d and 14e, this feature having been interpreted as resulting from secondary consolidation associated with the increased age of the sediment below the boundary by ~1.8 Ma [Saffer et al., 2010]. Thus, new soft formations above 1285 mbsf overlie old hard ones below. The difference in lithification of the new and old formations suggests that the anisotropic horizontal stresses interpreting the borehole breakout observed in the old formations should induce more severe borehole breakouts in the new formations. However, no breakouts at all were actually observed there (see Figures 14b and 14c). In order to explain such inconsistency, it is concluded that there exists stress decoupling associated with the marked change in lithology through the boundary at 1285 mbsf and that the anisotropy of horizontal stresses in the new formations at upside is much smaller than that in the old formations at downside. This conclusion is consistent with the horizontal stresses determined from the HF test at 878.7 mbsf in the present study, i.e., SHmax = Shmin = 35 [MPa]. At that depth, the overburden stress Sv and the pore pressure Pp are estimated to be 37.7 and 30.0 MPa, respectively. Thus, the determined state of in situ stress is categorized into the normal faulting stress regime; however, it is slightly short of the frictional equilibrium on preexisting, optimally oriented faults assuming a friction coefficient of 0.6. Such a stable stress condition may lead to sparse distribution of normal faults in the Kumano basin around Site C0009 [Saffer et al., 2010]. Note here that Lin et al.  detected the drilling-induced tensile fractures (DITF) at several depths between 749 and 980 mbsf. These fractures have a nearly constant orientation at N108 ± 11°E, suggesting there was some differential horizontal stress in the interval contrary to the isotropic stress state, SHmax = Shmin, determined in this study by the HF test at 878.7 mbsf. Considering the DITF and the fact that tensile fractures are generally sensitive to stress state, there might be actually so small difference between SHmax and Shmin that the difference cannot be detected by the HF test. Accuracy of the stress magnitudes determined by the HF test depends on the detected values of Pr and Ps. For the case of the HF test at 878.7 mbsf, if there is a detecting error of ±0.1 MPa in both Pr and Ps as inferred from Figures 5a and 5b, the SHmax could be larger than the Shmin by about 0.3 MPa.
 The SHmax azimuth has been determined so far from the borehole breakout at Sites C0001, C0002, C0004, and C0006 in this area (see Figure 1) [Chang et al., 2010]. The SHmax azimuth is oriented northeast-southwest only at Site C0002, and it is rotated by about 90° to be northwest-southeast at Sites C0001, C0004, and C0006. The latter orientation is similar to the SHmax azimuth in the formation below 1285 mbsf at Site C0009. On the other hand, the lithological analyses show that the drilled holes are fully located within the accretionary prism at Sites C0001, C0004, and C0006 and partially, i.e., below 1285 mbsf, located within it at Site C0009. Thus, the consistency in the SHmax azimuth for those four sites possibly indicates that the SHmax caused by plate motion is conveyed through the accretionary prism landward from its outer wedge. At Site C0009, such a stress state is likely decoupled from the state of isotropic horizontal stresses in the layers lying on the accretionary prism, as described above. The isotropic stress state is reasonably assumed to be formed by sedimentation in a central region of the Kumano basin where Site C0009 is located. These observations support the idea of Saffer et al.  that the strange stress state at Site C0002 located at the seaward edge of the Kumano basin has been formed by some local activities such as northwest-southeast extension approximately perpendicular to the trench, which is currently in progress near the site.
 We presented two practical methods to measure the state of stress within a subsea formation under deep sea water. These methods are based upon findings of hydraulic fracturing tests which provide the only way to obtain the stress magnitude directly. They were applied to an offshore hole of Hole C0009A drilled using a riser system at the Kumano Basin. The hole was drilled to 1603.7 mbsf from seafloor at a water depth of 2054 m passing through an unconformity at 1285 mbsf, which possibly lies at the boundary between the basin structure and the accretionary prism located at shallower and deeper depths, respectively. The stresses were measured at both sides, i.e., 878.7 and 1532.7 mbsf, and the results show that the maximum and minimum horizontal stresses, SHmax and Shmin, are very close at 878.7 mbsf; however, a considerable difference between them exists at 1532.7 mbsf. On the other hand, the caliper log indicates a significant change in the borehole shape at 1285 mbsf. The borehole remains in gauge down to 1285 mbsf; however, directional and continuous enlargement appears suddenly below that depth. These data suggest that the stress decoupling occurs at 1285 mbsf. While the stress state at 1532.7 mbsf is in a condition of the frictional limit for the strike-slip faulting stress regime assuming a friction coefficient of 0.6, the stress state at 878.7 mbsf is short of the frictional limit for the normal faulting stress regime. However, in both of the stress states, the least stress is near the pore pressure as expected for a subsea formation. This implies that the stress condition will be in or out of the frictional limit with a small change in the least stress or the pore pressure due to some geological events. Thus, precise stress data are important, especially for understanding subsea formation from a geophysical point of view. The methods presented in this study make it possible to obtain such precise stress data.
 The data used herein were provided by the IODP. The authors gratefully acknowledge the support provided by Expedition 319 scientists, the D/V Chikyu drilling crew, logging staff, and laboratory technicians. This work was supported by Grants-in-Aid for Scientific Research 21107006 (MEXT) and 24246147 (JSPS), Japan.