 Article
 Open Access
Comparison of stress state around the Atera fault, central Japan, estimated using boring core samples and by improved hydraulic fracture tests
 Yasuo Yabe^{13},
 Kiyohiko Yamamoto^{13},
 Namiko Sato^{23} and
 Kentaro Omura^{33}
https://doi.org/10.5047/eps.2009.12.002
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2010
 Received: 3 July 2009
 Accepted: 9 December 2009
 Published: 4 March 2010
Abstract
An often disputed subject is whether the stress memory of rocks can be reproduced by deformation rate analysis (DRA). Doubt has also been expressed on whether a rock can memorize its stress history. We compared the stress state around the Atera fault system, central Japan, using the hydraulic fracture test (HFT) and DRA at the same boreholes. The quality of the HFT results at these holes, especially that of the magnitude of maximum horizontal compression (S_{H}_{max}), was recently improved by considering the tensile strength of the borehole wall. The S_{Hmax} azimuth determined by the DRA was about NS. Although this is inconsistent with the geological presumption, it agrees well with the S_{Hmax} azimuth estimated by the HFT and the drillinginduced tensile fracture (DITF). The magnitudes of horizontal principal stresses obtained by DRA were generally consistent with the improved HFT results, and the consistency between stress states estimated by the DRA and the HFT indicates the existence of stress memory. Based on our results, we conclude that the DRA can be one option for measuring the stress state of the earth’s crust.
Key words
 Stress state
 Atera fault system
 stress memory of rocks
 hydraulic fracture test
 deformation rate analysis
1. Introduction
Investigations on the stress state in the earth’s crust provide important information on its deformation process because such information obtained from the stress state is independent of that from the strain or the strain rate determined by geodetic and/or geological methods. A variety of methods have been proposed to measure the stress state at a depth using a borehole. These include the stress relief method and the hydraulic fracture test (HFT) that are sometimes regarded as standard methods even though they are associated with a number of specific defects. For example, it is difficult to apply the stress relief method to a large depth because this method requires precisely coaxial drilling of the hole as well as knowledge of the elastic property of rocks under the in situ stress condition. For the HFT, Ito et al. (1999) pointed out that the reopening pressure which is used to estimate the maximum horizontal compression (S_{Hmax}) cannot be read correctly by the ordinal HFT using a hydraulic system with large compliance.
The stress measurement techniques using core samples recovered from boreholes are yet another option to estimate the in situ stress state at a depth. These techniques are called core methods and are based on the principle of the stress memory of rocks, which is the ability of rocks to accumulate, retain and, under certain conditions, reproduce information on the stress history (Lavrov, 2003). A typical representation of the stress memory is the Kisser effect, which can be described as follows: when a cyclic loading is applied to a rock and the maximum stress in the succeeding loading cycle is larger than that in the preceding loading cycle, the acoustic emission activity in the succeeding loading cycle is very low or not observed until the applied stress reaches the maximum stress in the preceding loading cycle. Kanagawa et al. (1977) proposed the AE method, which is an application of the Kisser effect, and Yamamoto et al. (1990) developed the deformation rate analysis (DRA), the details of which will be described later in this article. All of these methods have the principle advantage that the crustal stress can be estimated with relatively less expense and time. Further, the fullcomponent stress tensor can be estimated using a single borehole, while only stresses in a plane normal to the borehole axis can be measured by the HFT. Stress measurement at a large depth is also difficult with the HFT and the stress relief method, although the core methods are applicable so long as core samples are recovered.
The mechanism of stress memory of rocks has been discussed by Holcomb (1993) and Yamamoto (2009). In practical terms, Villaescusa et al. (2002) demonstrated that the stress states estimated by the DRA under various geological environments were in good agreement with those obtained by the stress relief method. However, despite these efforts, the reliability of the core methods are still in dispute (e.g., Ljunggren et al., 2003).
List of sites.

The Atera fault system is located in central Japan. It extends 60–70 km along the strike in an approximately NWSE direction, as shown in Fig. 1. The bending of rivers and the accumulated displacement observed in the terrace of the Kiso River imply that the predominant slip of the fault system is the leftlateral strikeslip (Sugimura and Matsuda, 1965; Tsukuda et al., 1993). The slip rate is estimated to be about 2.8 mm/year based on the accumulated dislocation (Tsukuda et al., 1993). Toda and Inoue (1995) and Toda et al. (1996) conducted a trenching survey to investigate the paleoseismicity of the Atera fault system. Based on their results, they suggested that the latest activity on the Atera fault system is the 1586 Tensho earthquake (M 7.8) and estimated the recurrence interval to be about 1800 years. The present seismicity of small earthquakes around the Atera fault system is very low, in particular along the southern part of the fault system.
The National Research Institute for Earth Science and Disaster Prevention (NIED) drilled holes at UEN, FKO, HTJ, and HGW (Fig. 1, Table 1) to determine the stress state around the Atera fault system. The UEN, FKO, and HTJ boreholes are aligned perpendicular to the strike of the Atera fault, a southern segment of the Atera fault system, on SW side of the fault. The distance from the fault to UEN, FKO, and HTJ is about 1.5, 4, and 6.7 km, respectively. The HGW borehole is located about 350 m east of the Hagiwara fault, a northern segment of the Atera fault system. Ikeda et al. (2002) carried out the HFT at these sites. However, because they used an ordinal hydraulic system with large compliance, it is possible that the reopening pressure was not measured correctly. Yamashita et al. (2009) performed the tensile fracturing test in the laboratory using rock samples retrieved from the holes where the HFT was carried out. They reevaluated the stress magnitude by calibrating the measurements made by Ikeda et al. (2002) to improve quality of stress estimation.
In this paper, we estimate the state of stress around the Atera fault system by applying the DRA to boring core samples recovered from boreholes in which the HFT was performed. Because the HFT is sometimes regarded as a standard technique to measure the crustal stress at a depth, we compare the stress state obtained by the DRA with that obtained by the HFT in order to assess the reliability of the DRA. The main purpose of this paper is to show that the DRA as well as the HFT can be used as standard stress measurement techniques.
2. Method
2.1 Outline of the techniques
Deformation rate analysis is a technique used to reproduce the stress memory of rocks from their nonlinear relationship between applied stress and strain under a cyclic uniaxial loading (Yamamoto et al., 1990, 1993; Yamamoto, 2009). Yamamoto (2009) assumed as a principle of the DRA that the nonuniformity in stress distribution in a rock is minimized at a site. He theoretically showed that the magnitude of the in situ stress can be reproduced from the inelastic behavior of rocks using the uniaxial compression test.
2.2 Preparation of specimens
We estimated the stress state of six crystalline rock samples recovered from depths (300–400 m) at four sites (Table 1). The temperature in the boreholes was less than 30°C and, therefore, the effects of thermal stress on the measurements due to differences in temperature at the site and in the laboratory should be minor. The stress measurement by the DRA was performed within 4 years of the samples being recovered from depths.
The horizontal stresses in four azimuths at 45° intervals were estimated to determine the horizontal principal stresses, which were measured by the HFT. We also estimated the vertical stress. Three specimens in each horizontal direction and six specimens in the vertical direction were prepared. Each specimen was assigned an identification number for convenience in the form of pppdddVs for a vertical specimen or pppdddaaas for a horizontal specimen, where ppp, ddd, s, and aaa indicate the site name, the sample recovering depth, the identification number of the specimen, and the azimuth, respectively. For example, the first specimen cut from a core recovered from a depth of 379 m at the FKO site to estimate the vertical stress was denoted FKO379V1.
2.3 Reading of the stress memory
The bending of the strain difference function is sometimes unclear. One possible explanation for the unclear bending can be that the magnitude of maximum applied stress is either too large or too small. The former causes an accumulation of extra damage, which degrades the stress memory. The latter results in a short linear segment after the bending that is related to stress memory. This is associated with a difficulty in recognizing the stress memory. Therefore, at least two specimens in each direction must be tested under different magnitudes of the maximum stress.
To summarize, in this section we emphasize that we cannot determine the stress memory of rocks from the individual strain difference functions as described in the following section; rather, they must be surveyed in combination. We applied the following rules in determining the stress memory: (1) the bending stress representing stress memory does not depend on the maximum applied stress; (2) the bending stress representing stress memory does not depend on the combinations of loading cycles; (3) the magnitude of vertical stress does not significantly differ from the overburden pressure; (4) the dependence of axial stress on azimuth obeys a sinusoidal function; σ(θ) = σ_{m} +σ_{d} cos(2(θθ_{0})), where θ is the azimuth, θ_{0} is the azimuth of maximum horizontal compression, and σ_{m} and σ_{d} represent the magnitudes of isotropic and deviatoric components of horizontal stress, respectively.
3. Results
A typical loading history and the stressstrain relationship obtained from a specimen of FKO379V1 is shown in Fig. 4. The loading rate was servocontrolled to be 0.05 MPa/s. Depending on the quality of the data, there could be as many as six loading cycles.
As it is expected that the stress state in the crust tends to be the lithostatic state, we assumed that the magnitudes of horizontal stress do not significantly differ from the vertical stress. Therefore, we did not perform tests with a maximum stress that was greater than threefold the vertical stress in order to restrain pollution by extra damage.
3.1 Reading the stress memory in practice
Here, we explain how to read the stress memory in practice by showing the strain difference functions obtained for specimens of FKO379 as typical examples.
3.1.1 Vertical stress
Figure 5(a)–(e) show examples of the strain difference function for the vertical specimens recovered from a depth of 379 m from the FKO borehole. Because the average density of rocks measured by logging at this site was 2600 kg/m^{3}, the overburden pressure expected for this depth is 9.7 MPa. Figure 5(f)–(j) shows the significance of the bending measured by a technique proposed by Kato et al. (1991) in which two lines are fitted to the neighboring data windows before and after a target stress, and the significance of the difference between the slopes of the two lines is tested using Student’s t statistics. The window length before a target stress in this study is 2 MPa. Because the strain difference functions tend to be less linear after a bending, a shorter window length of 1.4 MPa is used for line fitting after the target stress. The target stress is shifted from point to point to obtain variations in the t value with respect to the applied stress. In this plot, the t value reaches a peak at a bending stress. It should be noted that the largest peak does not necessarily occur at the bending representing the stress memory—the peak in the tvalue function simply indicates the existence of a bending. The bending representing the stress memory must be identified according to the rules stated in the preceding section.
In addition to the strain difference functions in Fig. 5, we can find clear bendings at the applied stress between 8 and 10 MPa in ten strain difference functions, including those of FKO379V5 (not shown here). The estimated vertical stress was 8.9±0.5 MPa.
3.1.2 Axial stress in the reference azimuth (R000)
The bending stresses in the range between 12 MPa and 14 MPa are, therefore, the most commonly observed bendings among all of the strain difference functions for specimens of FKO379000, while the bending stress of about 10 MPa is also found in some functions. We therefore consider the stress of 12.8±0.3 MPa to be the most suitable for axial stress in this azimuth. The stress of 9.8±0.8 MPa is the second candidate.
3.1.3 Axial stress in the azimuth of R045
Figure 7 shows examples of the functions for specimens in an azimuth of 45° clockwise from the reference direction (R045 in Fig. 2). The bending of function of FKO379045135 (Fig. 7(a)) at about 10.5 MPa is relatively clear, but the function slightly bends at about 6.5 MPa. While the function of FKO379045145 (Fig. 7(b)) is contaminated by noises, probably due to fluctuations in the stress rate, it clearly bends at about 11 MPa. The function of FKO379045146 (Fig. 7(c)) has two bendings at about 10 and 15 MPa, respectively, with the former being clearer. The function of FKO379045245 (Fig. 7(d)) bends four times at about 6.5, 9.5, 11, and 14 MPa, respectively. It should be apparent that the bending at about 14 MPa is caused by a significant fluctuation of stress rate under an applied stress of more than 14 MPa. The left three bendings are similar in terms of clearness. The function of FKO379045334 (Fig. 7(e)) has two bendings at about 8 and 12 MPa, respectively.
As is shown by the shaded zone in Fig. 7, all of the functions have bendings at axial stresses between 10 and 12 MPa. We therefore estimated the magnitude of axial stress in this azimuth to be 11.6±0.6 MPa.
3.1.4 Axial stress in the azimuth of R090
All of the functions have bending points between 15 and 17 MPa. Therefore, the axial stress in this azimuth should be 15.5±0.3 MPa. On the other hand, because some functions commonly show bending at about 10 MPa, the stress of 10.0±0.7 MPa is the second candidate for the axial stress in this azimuth.
3.1.5 Axial stress in azimuth of R135
Figure 9 shows examples of the functions for specimens of FKO379135, whose azimuth is 135° clockwise from the reference direction (R135 in Fig. 2). The function of FKO379135136 (Fig. 9(a)) bends at about 13 and 15.5 MPa. The function of FKO379135235 (Fig. 9(b)) has two bendings at about 13 and 16 MPa, respectively, with that at about 13 MPa being more recognizable. The gradient of function of FKO379135256 (Fig. 9(c)) changes at about 15 and 19 MPa, and it appears that there are a few bending (no arrows are attached) at stresses between 5 and 10 MPa. Because these latter stresses are a combination of convex and concave, they should be results of stress rate fluctuation. The function of FKO379135246 (Fig. 9(d)) has a bending at about 15 MPa. The gradient changes in this function at about 6 and 19 MPa, respectively, are too gradual to call them bendings. The function of FKO379135324 (Fig. 9(e)) has a minor bending at about 14.5 MPa.
Bending stresses between 14 and 16 MPa are commonly observed, while clear bending at about 13 MPa can be found in a few functions. The axial stress in this azimuth is therefore estimated to be 16.0±0.6 MPa.
3.1.6 Evaluation of azimuthal dependence of axial stresses
The sinusoidal function in rule (4) is fitted to the azimuthal variation in estimated stress magnitude (Fig. 10). Note that the azimuth in Fig. 10 is not measured from the reference direction but from the geographic north. The core sample recovered from a depth of 379 m at the site of the FKO borehole was oriented by comparing fractures on the core with those on the borehole wall delineated by the borehole televiewer. The reference direction (R000) of this core is N53E.
The bestfit sinusoidal function for the most suitable combination (primary data set) of estimated axial stresses are shown in Fig. 10(a). The S_{Hmax} azimuth is N172E, and the isotropic and the deviatoric stress are 14.0±0.2 MPa and 2.6±0.2 MPa, respectively.
3.2 Stress states at other sites
The stress states at other sites are shown in Fig. 11. The estimated magnitudes of the vertical, isotropic, and deviatoric stresses are summarized in Table 2. Because we could not orient the core sample of HTJ400 (Fig. 11(d)), the azimuthal variation in magnitude of the axial stress at this site is represented relative to the arbitral reference direction. The bendings of strain difference functions for specimens of HGW392 were unclear in most cases. We therefore performed stress measurements in eight azimuths to increase the reliability of estimation (Fig. 11(e)).
4. Discussion
4.1 Reliability of S_{Hmax} azimuth
The spatial variation in the S_{Hmax}azimuth is shown in Fig. 12. The S_{Hmax} azimuth at UEN340 is about EW, which is consistent with the fault motion expected from the geological information. Because, however, the magnitude of the deviatoric stress at this site is not larger than the estimation error of axial stresses in the individual azimuth, the estimated S_{Hmax} azimuth is not expected to be reliable. The S_{Hmax}azimuths at other sites close to the Atera fault (UEN399, FKO296, and FKO379) are almost NS. The S_{Hmax} azimuth of HGW392 is about NESW. These results mean that a rightlateral strikeslip should occur along the Atera fault system, They are not in agreement with the geological presumption that the Atera fault system consists of leftlateral strikeslip faults.
Because the dip of faults in the Atera fault system is nearly vertical, fault slip induced by the present state of crustal stress should be a rightlateral strikeslip, which is in contrast to the expectation based on the geological information. A possible reason for this inconsistency is a temporal change in the stress state, as discussed by Yamashita et al. (2009). However, any further discussion on this inconsistency is beyond the scope of this study.
4.2 Reliability of stress magnitude
The magnitudes of S_{Hmax} and S_{hmin} (the minimum horizontal compression) estimated by the DRA and the HFT are compared in Fig. 13. The error bars attached to the HFT results in this figure represent only errors originating from the tensile strength measurement.
4.2.1 Stress magnitude at UEN
The stress magnitudes at the site of UEN were estimated by the HFT at only one depth, 347 m, while they are determined at two depths (340 and 399 m) by the DRA in this study. The magnitude of S_{hmin} at UEN340 estimated by the DRA is equal to that estimated by the HFT at a depth of 347 m, while the S_{Hmax} determined by the respective techniques differs by 4 MPa. This difference in S_{Hmax}magnitude is significantly larger than the errors in the axial stress estimation by the DRA (0.5–0.7 MPa, Fig. 11(a)).
In the case of the HFT, the magnitude of S_{Hmax} is calculated from the following equation: S_{Hmax} = 3S_{ h }_{min}  P_{b}  T  P_{p}, where P_{p}, T , and P_{p} are breakdown pressure, tensile strength of the borehole wall, and pore pressure, respectively. Therefore, the error in S_{Hmax} estimation is threefold larger than that of S_{hmin}, being about 2.4 MPa at this site. The remainder of the discrepancy may be explained by errors in the measurements of shutin pressure, breakdown pressure, and pore pressure. However, they are not well understood at the present time.
The magnitudes of horizontal principal stresses at UEN399 determined by the DRA are 1–2 MPa smaller than those determined by the HFT. Although the error in fitting the sinusoidal function to the azimuthal dependence of axial stress in the DRA is negligibly small (Table 2), the estimation error of axial stress in each azimuth is relatively large (0.6–0.8 MPa). The estimation error in tensile strength by Yamashita et al. (2009) was 0.8 MPa at this site. The differences between estimations by the DRA at UEN399 and the HFT at UEN347 should not be significant.
4.2.2 Stress magnitude at FKO The HFT were performed at four depths between 243 and 276 m at FKO. The estimated magnitudes of S_{hmin} by the HFT are in a range between 8.0 and 10.0 MPa. On the other hand, the DRA was applied to cores recovered from two depths of 296 and 379 m. The S_{hmin} magnitude estimated by the DRA at FKO296 was 9.3 MPa, which is in the range of S_{hmin} magnitudes determined by the HFT. The S_{hmin} magnitude at FKO379 by the DRA is 11.4 MPa, which is slightly larger than the estimation by the HFT. The errors in sinusoidal function fitting, estimation of axial stresses in individual azimuth, and measurement of tensile strength are 0.4, 0.3–0.6 and 0.6–0.7 MPa, respectively. Considering these errors, the difference between S_{hmin} magnitude at FKO379 and that by the HFT should be negligible.
The magnitude of S_{Hmax} at FKO estimated by the HFT shows a large scatter from 13.7 to 18.9 MPa; in comparison, the magnitude at FKO296 and FKO379 by the DRA is 12.7 and 16.6 MPa, respectively. The estimation atFKO379 by the DRA is within the range of the HFT estimations. Because the estimation error in the fitting of sinusoidal function in the former case is as large as 1.2 MPa, it can also be said that the S_{Hmax} at FKO296 agrees with estimations by the HFT.
4.2.3 Stress magnitude at HTJ
Summary of estimated stresses.

The S_{Hmax}magnitudes by the HFT were close to threefold greater than the vertical stress, while that by the DRA was about twice the vertical stress. The difference between the S_{Hmax}magnitudes by the respective techniques is more than 7 MPa. This difference cannot be explained by estimation errors.
On the other hand, while the HFT was performed at depths of 249–266 m, Yamashita et al. (2009) estimated the tensile strength of cores recovered from a depth of about 325 m because they could obtain only one test piece for tensile stress measurement from cores recovered from depths of 249–266 m. Although they carefully selected cores having similar physical properties as rocks at depths of the HFT based on the logging data to estimate appropriate tensile strength of borehole wall at depths of the HFT, it is possible that the tensile strength of rocks at depths of 249–266 m significantly differs from that at a depth of 325 m. Actually, the tensile strength of a core sample recovered from a depth of about 245 m was about 3 MPa smaller than that from 325 m (Yamashita, personal communication), although its reliability is low. Because the tensile strength affects only the S_{Hmax} magnitude, the inconsistency of the S_{Hmax}estimation can be reduced to 4 MPa if the tensile strength of the core from 245 m is assumed. This is, however, still larger than the sum of estimation errors (by about 2 MPa).
The errors in pressure measurements in the HFT may explain the discrepancy. However, current knowledge on the errors associated with pressure measurement in the HFT is limited, as stated above. Further studies on this subject are desired.
5. Conclusions
The crustal stress around the Atera fault system was measured by the DRA. Because the HFT is sometimes regarded as a standard technique to estimate the state of crustal stress, we compared the estimation by the DRA with that by the HFT. The S_{Hmax} azimuths obtained by the DRA agree well with those by the HFT and the DITF. The stress magnitudes determined by the DRA are also consistent with those by the HFT, as long as the difference in measurement depths of two methods is small. These results imply that quality of stress measurement by the DRA using core samples up to 4 years old is never worse than that by the HFT. As such, the DRA can be one option for carrying out stress measurements at less expense and time.
Declarations
Acknowledgments
Comments and information provided by Dr. F. Yamashita, NIED, were useful for improving the quality of this article. The authors thank Prof. O. Sano, Earthquake Research Institute, University of Tokyo, and Prof. A. Mukai, Nara Sangyo University, for their critical and constructive comments.
Authors’ Affiliations
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