Volume 127, Issue 2 e2021JB023290
Research Article
Free Access

Lithology and Fault-Related Stress Variations Along the TCDP Boreholes: The Stress State Before and After the 1999 Chi-Chi Earthquake

Mayukh Talukdar

Corresponding Author

Mayukh Talukdar

Department of Civil and Environmental Engineering, Geological Engineering Program, University of Wisconsin-Madison, Madison, WI, USA

Correspondence to:

M. Talukdar,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Writing - original draft, Writing - review & editing, Visualization

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Hiroki Sone

Hiroki Sone

Department of Civil and Environmental Engineering, Geological Engineering Program, University of Wisconsin-Madison, Madison, WI, USA

Contribution: Conceptualization, Methodology, Software, ​Investigation, Writing - original draft, Writing - review & editing, Supervision, Project administration, Funding acquisition

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Li-Wei Kuo

Li-Wei Kuo

Department of Earth Sciences, National Central University, Taoyuan, Taiwan

Contribution: Data curation, Supervision

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First published: 29 January 2022
Citations: 2

Abstract

Understanding the stress state before and after an earthquake is essential to study how stress on faults evolves during the seismic cycle. This study integrates wellbore failure analysis, laboratory experiments, and edge dislocation model to study the stress state before and after the Chi-Chi earthquake. The post-earthquake in-situ stress state observed along boreholes of the Taiwan Chelungpu-fault Drilling Project (TCDP) is heterogeneous due to lithological variations. Along the borehole, we observe that drilling-induced tensile fractures are only present in sandstones, whereas breakouts are mostly present in silt-rich rocks. Laboratory experiments on TCDP cores also show that tensile and compressive strength are weaker in sandstones than in silt-rich rocks. These observations imply that both maximum and minimum horizontal principal stresses are higher in silt-rich intervals. Extended leak-off tests in the TCDP borehole also show lower minimum horizontal stress in sand-rich intervals, consistent with the above observations. We combine these observations to estimate a profile of stress magnitudes along the well which explains the variability of stress states found in previous studies. The stress heterogeneity we observed underlines the importance of acknowledging the spatial scale that the stress data represent. We then use an edge dislocation model constrained by GPS surface displacements obtained during Chi-Chi earthquake to calculate the coseismic stress changes. Our inferred pre-earthquake stress magnitudes, obtained by subtracting the coseismic stress change from the post-earthquake stress, suggest subcritical stress state before the earthquake despite the large displacements observed during the Chi-Chi earthquake in the region where TCDP encountered the fault.

Key Points

  • We obtain a near-continuous stress profile which captures the lithology-dependent and fault-related stress variation along the boreholes

  • Variability in stress states reported from previous studies is explained by stress variations caused by lithological variations

  • The estimated pre-earthquake stress profile indicates subcritical stress state within the Chelungpu fault zone prior to the earthquake

Plain Language Summary

Stress in the Earth’s crust defines the forces acting on faults which drive earthquakes. Therefore, tracking how stress accumulates due to plate motion and is released due to fault slip have been a central topic in the study of earthquake mechanics and associated seismic hazard. Previous studies which analyzed data collected from Taiwan Chelungpu-fault Drilling Project (TCDP), drilled after the 1999 Chi-Chi earthquake, show that the post-earthquake stress inferred from those studies is inconsistent with each other. This study reviewed previous measurements, conducted laboratory experiments, and analyzed borehole data to revisit the stress state after the Chi-Chi earthquake. We show that stress state varies along the TCDP borehole due to lithology and fault-related changes in mechanical properties, which explains why past studies indicated significant variability. We also estimated the pre-earthquake stress before the Chi-Chi earthquake to understand stress conditions leading to the rupture. We calculated the stress change caused by the Chi-Chi earthquake and subtract it from the post-earthquake stress to obtain the pre-earthquake stress. Our pre-earthquake stress estimate suggests that the stress before the Chi-Chi earthquake was low in magnitude compared to the frictional strength of rocks.

1 Introduction

Stress in the Earth’s crust drives earthquakes; therefore, characterizing the state of stress in the crust is essential for mechanistic assessments of seismic risk and hazard. Not only do stresses drive earthquakes, but earthquakes also modify the stress state in the crust by releasing and redistributing the stress in the surrounding crust. This feedback between earthquake and stress occurs over a variety of length and time scales, highlighting the importance of understanding stress before, after, and between earthquakes.

Scientific drilling in fault zones provide unique opportunities to study the magnitude of stress around faults and physical properties of rocks in the fault zone. Stress around boreholes induces wellbore failures like breakouts and drilling-induced tensile fractures (DITFs), which allow us to infer the direction and magnitude of the principal stresses along the borehole. These stress-induced wellbore failures, in combination with hydraulic fracturing tests and strength measurement on drilled core samples, provide opportunities to estimate the in-situ stress state (Moos & Zoback, 1990; Zoback et al., 2003). In the last two decades, major scientific drilling projects like San Andreas Fault Observatory at Depth (SAFOD), Japan Trench Fast Drilling Project (JFAST), and Taiwan Chelungpu-fault Drilling Project (TCDP) have provided key insights into the stress states after Parkfield, Tohoku, and Chi-Chi earthquakes, respectively. Hickman and Zoback (2004) analyzed the well log acquired from SAFOD to suggest a transitional strike-slip to reverse faulting stress regime with high horizontal differential stress. Geophysical image logs acquired from JFAST suggest a stress state change from reverse faulting regime before the earthquake to normal faulting regime postrupture due to coseismic stress release (Lin et al., 2013). This study further suggested a near complete shear stress release, down to ∼0.3 MPa, after the Tohoku-Oki earthquake.

The TCDP, an International Continental Scientific Drilling Program (ICDP) project, penetrated the slip plane of the 1999 Chi-Chi earthquake. In TCDP, previous estimates of in-situ stress calculated from well logs and core measurements do not provide a coherent understanding. Lin et al. (2007) first conducted anelastic strain recovery measurements on TCDP cores, interpreting that the state of stress in the Chelungpu fault system after the earthquake is normal faulting. Subsequent studies used extended leak-off tests, rock strength measurements, and wellbore failure analysis to infer that the post-earthquake state of stress is normal fault to strike-slip fault (Lin et al., 2007), strike-slip fault (Hung et al., 2009), reverse fault (Haimson et al., 2010), and transitional strike-slip to reverse fault (Haimson et al., 2010). The relative magnitude of the principal stresses in these studies is shown in Figure 1 together with the frictional limit for optimally oriented faults drawn with a friction coefficient of 0.85 (Byerlee, 1978). Since there is significant variability in the stress states inferred from these studies, it leaves a question about which stress state represents the correct stress state along the TCDP boreholes or whether the results reflect a heterogeneous stress state.

Details are in the caption following the image

In-situ state of stress in the Taiwan Chelungpu-fault Drilling Project (TCDP) borehole reported in previous literature compared with frictional limits on horizontal stress magnitudes imposed by coefficient of friction of 0.85. The effective horizontal stress magnitudes are normalized with effective vertical stress urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0001 to compare data from different depths.

There are multiple causes of stress heterogeneities in the crust. While some studies suggest difference in strength and physical properties as the major cause of stress heterogeneity indicating an apparent lithology control (Bourne, 2003; Gunzburger & Cornet, 2007; Gunzburger & Magnenet, 2014; Sone & Zoback, 2013; Y. Zhang & Zhang, 2017), other studies have also indicated that slip along secondary faults and fractures can lead to stress perturbation as observed in boreholes (Barton et al., 1988; Day-Lewis et al., 2010; Shamir & Zoback, 1992). Furthermore, geometry of faults and presence of asperities on fault planes control slip distributions (Segall & Pollard, 1980; Sibson, 1985), which determines where and how stress redistributes due to slip along faults. There are rapid lithological variations in the Chelungpu fault system and many secondary faults observed in the TCDP cores (Hung et al., 2009). Therefore, we revisit the TCDP data to understand the potential cause of the in-situ stress variability.

Borehole log data and cores acquired from active fault zones after earthquakes provide information about the post-earthquake in-situ stress state. On the other hand, it is not the post-earthquake but the pre-earthquake crustal stress field that drives earthquakes. It is possible to infer pre-earthquake stress if we can estimate the coseismic stress changes from geophysical data and subtract from the post-earthquake stress observed in boreholes. Such knowledge about the pre-earthquake stress state can provide insights into whether the strength of the brittle crust is weak or strong relative to laboratory measured rock strengths.

In this study, we combined information of lithological variations, previous hydraulic fracturing data, new laboratory strength measurements of TCDP cores, and a comprehensive analysis of borehole data to infer the post-earthquake in-situ state of stress. We also evaluated the coseismic stress change using an edge dislocation model constrained by coseismic surface displacements, which is subtracted from the post-earthquake stress to infer the pre-earthquake stress state. We finally discuss the criticality of the inferred pre-earthquake stress in the region where TCDP encountered the fault.

2 Geological Setting

The Taiwan mountain belt is geographically divided into the Coastal Plains, the Western Foothills, the Hsuehshan Range, the Coastal Ridge, the Longitudinal Valley, and the Coastal Range (Ho, 1986). The boundary between the Coastal Plain and the Western Foothills is the converging margin of the northwesterly subducting Philippine plate under the Eurasian plate, which ruptured the Chelungpu fault and produced the 1999 Chi-Chi earthquake (Figure 2a).

Details are in the caption following the image

(a) Geologic map of Central Taiwan showing the Chelungpu fault which ruptured during the 1999 Chi-Chi earthquake. The epicenter is shown by the location of the beach ball focal mechanism. (b) Taiwan Chelungpu-fault Drilling Project drilled two boreholes across the fault system Holes A and B (image modified after Hung et al., 2009, distance between Holes A and B is not to scale).

The 21 September 1999 Chi-Chi earthquake (Mw = 7.6) had an extensive surface rupture of 85 km along the Chelungpu fault, as shown by the dark red line in Figure 2a. The primary sense of slip was reverse faulting (Ma et al., 1999). The rupture process started at the epicenter, 8 km below surface in the southern region of the fault (as shown by the beach ball in Figure 2a) and propagated to the north within a total time span of 30 s. Surface displacements of over 10 m were observed in the northern portion of the fault and 1–4 m in the southern portion. Studies on the collected seismic records have revealed the rupture process of the fault during the earthquake (Ji et al., 20012003; Ma et al., 2001), and a remarkable contrast in the slip behavior between the northern and southern portion was found. Slip velocity was much faster in the northern portion (2–4 m/s) than the southern portion (less than 1 m/s), and seismic radiation was dominated by low frequency waves in the north, whereas in the south, higher frequency radiation was observed.

2.1 Taiwan Chelungpu-Fault Drilling Project

TCDP drilled two scientific research boreholes (Holes A and B) in the northern part of the Chelungpu fault, about 2 km east of the surface rupture near the town of Da-Keng, shown by the star in Figure 2a. The boreholes were drilled from 2004 to 2005, that is, about 5–6 years after the earthquake. The boreholes intersected the primary slip plane which ruptured during the Chi-Chi earthquake at 1,111 m (Hole A) and 1,133 m (Hole B), respectively. The boreholes encountered lithological units and other faults, both dipping 30° to the east. Because Hole B is 40 m further east from Hole A, it penetrated similar lithological units and fault interfaces, but at slightly different depths from the surface (Figure 2b).

The drilling coring operation extended from 500 to 2,000 m in Hole A and 950 to 1,300 m in Hole B, as shown by the vertical cross section in Figure 2b. Geophysical logging data acquired during the drilling project include high-resolution electrical resistivity image data recorded using the Formation Micro Scanner™ (FMS) and Formation Micro Imager™ (FMI). FMS collected resistivity image data in the upper portion of Hole A (500–1,300 m), whereas FMI was used for the lower portion of Hole A (1,200–1,870 m) and the entire section of Hole B. Because the FMS tool contains only 64 sensor buttons compared to the 192 sensor buttons of the FMI tool, the FMS tool has less coverage of the borehole wall. We studied these FMI and FMS logs in detail to characterize structures and lithological boundaries along the borehole. We also utilized the gamma ray and sonic log to draw inference on stress magnitude along the borehole.

2.2 Lithological Variations

The Chelungpu fault system mainly comprises of shallow dipping thrust faults, parallel to the bedding in the area (Sone, Yeh, et al., 2007; Yeh et al., 2007). The primary geological units in the upper 2 km are the Cholan Formation, Chinshui Shale, and Kueichulin Formation in the hanging-wall block (Song et al., 2007), and then the Cholan Formation again in the footwall below the reverse fault (Figure 2b). Lithology in this area is characterized by alternating sandstone, siltstone, and shale with the presence of intermediate stratigraphic units like silty sandstone, sandy siltstone, and interlayered sandstone and siltstone (Song et al., 2007).

The natural gamma ray log is a measure to differentiate lithologies. Higher gamma ray is associated with higher potassium, uranium, and thorium, usually present in clay minerals and organic materials present in the rock (Hassan et al., 1976). In TCDP rocks, the primary clay minerals present are illite, kaolinite, chlorite, and smectite (Kuo et al., 2009). TCDP core observations confirm that the silt-rich layers correspond to higher gamma ray intervals than sand-rich cores (Figure 3). Thus, we used gamma ray count as a proxy for lithological variations along the boreholes, setting gamma ray threshold values to classify the lithologies (Figures 3a and 3b). The litho-stratigraphic column obtained as such is consistent with those obtained from Song et al. (2007) based on direct core observations.

Details are in the caption following the image

Gamma ray log in (a) Hole A and (b) Hole B logs used to define the lithology in the area. An upward shift of Hole B gamma ray log by 22 m matches the Hole A gamma ray.

From the comparison of gamma ray logs from two boreholes, we observe that a 22 m upward shift of Hole B data matches the Hole A gamma ray log, consistent with the local bedding dip of about 30° seen in drilled cores (Figure 3). Therefore, it is possible to combine observations from Holes A and B, allowing comparison of repeated but independent observations collected on the same lithological units and structures.

3 Wellbore Failure

Drilling of boreholes in the Earth perturbs the local stresses around the borehole. This perturbed stress on the borehole wall varies in magnitude as a function of azimuth according to the Kirsch equations (Kirsch, 1898). In a vertical wellbore, the effective circumferential stress, σθθ = Sθθ − Pp, at the borehole wall varies azimuthally as (Moos & Zoback, 1990)
urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0002(1)
where Sθθ is the circumferential stress at the borehole wall, SHmax and Shmin are maximum and minimum horizontal principal stresses, respectively, θ is the angle from the azimuth of SHmax, PP is the formation pore pressure, ΔP is the difference between the drilling mud pressure and the formation pore pressure, and σΔT is the circumferential thermal stress induced by cooling of the wellbore. This equation assumes that the stresses are Andersonian, thus the vertical stress is a principal stress acting parallel to the borehole axis and that the rock is isotropic. We use a sign convention where compression is positive and extension is negative.

In a vertical borehole, maximum effective circumferential stress, urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0003, occurs in the direction of Shmin (θ = 90°) and minimum effective circumferential stress, urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0004, occurs in the direction of SHmax (θ = 0°; Figure 6a). When these values exceed the compressive and tensile strength of the rock, wellbore failure occurs, namely breakouts and DITFs, respectively. Therefore, occurrence and azimuth of breakouts and DITFs inform us about the direction and magnitude of horizontal principal stresses when combined with knowledge of the rock strengths.

3.1 Borehole Breakouts

We observed that breakouts are ubiquitous features along the TCDP wells, both in the FMS and FMI image logs. In these resistivity image logs, rescaled to enhance the contrast, the image section is lighter when sensing higher resistivity material and vice versa. In the TCDP borehole, the color variation is subtle between different lithologies because the higher porosity in the sand-rich formation and the higher clay-mineral content in the silt-rich formation both contribute to lowering resistivity. Nonetheless, silt-rich layers appear relatively darker than sand-rich layers (Figure 4).

Details are in the caption following the image

Occurrence of wellbore failures observed in the resistivity image logs. Lighter colors indicate higher resistivity (sand-rich), whereas darker colors indicate lower resistivity (silt-rich, shaley) rocks. (a) Drilling-induced tensile fractures (DITFs) are present until 1032 m in sandstone with lighter shade, whereas breakouts are only present in sandy siltstone below 1,032 m with a comparatively darker shade. (b) Presence of DITFs in sandstone. (c) Transition from darker silt-rich layer to sand-rich layer at 1,009 m shows disappearance of breakouts and occurrence of DITFs in sandstone. (d) Breakouts are only observed in the darker siltstone at the top and bottom of the figure. (a–c) FMI images from Hole B, whereas (d) is an FMI image from Hole A.

Breakouts appear as dark out-of-focus zones with unclear boundaries that occur 180° apart from each other, reflecting the conductive mud present between the imaging tool and the formation. In Hole A and Hole B, breakout width is on average ∼30°, mostly ranging between 15° and 45° (Figure 5b). Resistivity images at certain depths show disappearance of breakouts when there is a transition from a silt-rich stratigraphic unit to pure sand layers (Figures 4a, 4c, and 4d). Breakouts are primarily present in siltstones and rarely present in sandstones. However, when present in sandstones, breakouts in sandstones are narrower in width compared to those in silt-rich layers. Comparison of breakout widths with lithological variation in Hole A shows how the breakout width is greater in siltstone compared to sandstones.

Details are in the caption following the image

(a) An overlay of breakout and DITF azimuths of Hole A and Hole B. (b) Breakout width of Hole A and B combined. (c, d) P and S wave velocity log data.

Utilizing the depth shift between Holes A and B determined from the natural gamma ray logs, we overlay the breakout azimuths information from Holes A and B (Figure 5a). Results show that the breakout azimuths are consistent between the two boreholes and the mean breakout azimuth is around N20°E. This suggests that the direction of SHmax is N110°E (Figure 5a). We find no significant change in breakout azimuth down to 1,300 m as Hung et al. (2009) also observed.

Note that the deviation of the borehole is only 3° until 1,600 m and increases to 12° at 1,830 m where the deepest breakout is observed. Previous studies have shown that deviation below 12° does not influence the stress analysis using breakouts (Peska & Zoback, 1995), therefore the effect of deviation is neglected in this study.

3.2 Drilling-Induced Tensile Fractures

We identify DITFs as thin conductive fractures that occur parallel to or subparallel to the borehole axis. As in breakouts, the dark color reflects the conductive mud filling the fractures, but DITFs appear sharper because the borehole wall is not rugose. The azimuth of DITFs in Hole A and B is approximately N110°E (Figure 5a), consistent with the breakout azimuth. Contrary to suppression of breakouts in sandstone layers, DITFs are primarily present in sandstone layers and absent in other lithologies (Figure 4b). A similar observation was made by Sone and Zoback (2014b) where they observed absence of DITFs in high gamma ray layers within the Barnett shale, Fort Worth Basin. Figure 5a also shows DITF presence in sandstone layers and absence in siltstone layers, as shown by black circles in the plot of breakout azimuth with depth. The upper part of Hole A image log, studied using the FMS tool, does not show DITFs because of the poor coverage and quality of the FMS data. In an FMS image log, the vertical white strips (or no data region) observed in Figure 4 are wider and could coincide with the azimuth where DITFs are observed in FMI images, potentially hiding DITF occurrences.

4 Strength of Rocks

The uniaxial compressive strength (UCS) of TCDP cores has been measured by various authors, and the results demonstrate a high degree of variability. UCS of rocks cored at 1,120 m (Hole B) depth was found to be 32.9 and 44 MPa under water saturated and dry conditions, respectively (Chen, 2005; Lin et al., 2007). However, UCS of TCDP cores from 889 to 892 m (Hole A) was found to be almost twice at 79.5 ± 2.2 MPa (Oku et al., 2007; Table 1). This variability in strength of TCDP cores is explained by the lithological variation as Hung et al. (2009) reported UCS of porous sandstone (Hole B) to be 8–11 MPa but that of homogeneous shale (Hole B) to be ∼70 MPa. We also conducted UCS tests, which also suggests an increase in compressive strength with increasing silt content (for details of UCS tests, see Text S1 in Supporting Information S1). Higher UCS of siltstones can be attributed to the porosity contrast of sandstone and siltstone of TCDP cores. We found from helium porosimeter measurements that the porosity of sandstone (∼20%) was higher than the siltstone variety (∼6%).

Table 1. List of Compressive and Tensile Strength Measurements From the Literature and This Study
Rock type Hole, depth UCS (MPa) Tensile strength (MPa) Reference
Siltstone A, 890 m 79.5 ± 2.2 N/A Oku et al. (2007)
Siltstone B, 1,031 m 76.4 N/A This study
Siltstone B, 1,033 m N/A 7.5 ± 0.5 This study
Siltstone A/B 70 7.4 Hung et al. (2009)
Sandy siltstone B, 746.5 m 58.3 ± 11 4.4 ± 0.4 This study
Silty sandstone B, 1,120 m 32.9 (wet), 44 (dry) N/A Chen (2005); Lin et al. (2007)
Silty sandstone B, 1,183 m 28.5 ± 3.2 1.9 ± 0.6 This study
Sandstone A/B 9.5 ± 1.5 0.5 Hung et al. (2009)
Sandstone B (811.6 m) N/A 0.5 ± 0.05 This study

We conducted Brazilian tensile tests on cores to find that the tensile strength also increases with increasing silt content (Table 1). The average tensile strength of sandstone (∼0.5 MPa) was found to be significantly lower than siltstone (∼7.5 MPa), with intermediate compositions such as silty sandstone and sandy siltstone showing 1.9 and 4.4 MPa, respectively. Our results are consistent with tensile strength inferred from extended leak-off tests by subtracting reopening pressure from breakdown pressure (Hung et al., 2009), where the inferred tensile strengths of sandstone and shale were 0.5 and 7.4 MPa, respectively (Table 1).

5 Constraining Principal Stress Magnitudes

The rock strength data together with the occurrences of breakouts and DITFs suggest that horizontal stress magnitudes are generally higher in silt-rich rocks. The preferential occurrence of breakouts in silt-rich rocks, despite their higher UCS, suggests that urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0005 is greater in silt-rich rocks (Figure 6b). Since urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0006 is a function of 3SHmax − Shmin according to the Kirsch equations, presence of breakouts in the stronger silt-rich rocks is indicative of higher SHmax in silt-rich layers. Similarly, the DITFs, preferentially observed in sandstones, suggest that urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0007 in sandstone is lower than −0.5 MPa, whereas DITF absences in silt-rich rocks suggest that the urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0008 in siltstone is higher than −7.5 MPa (Figure 6b). In other words, the absolute value of tensile circumferential stress in sandstone is higher than its tensile strength and the absolute tensile circumferential stress in siltstone is lower than its tensile strength. Given that urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0009 is a function of 3Shmin − SHmax, this is indicative of higher Shmin in silt-rich layers than in sandstones. Therefore, horizontal stress magnitudes are overall more compressive in silt-rich rocks than in sandstones.

Details are in the caption following the image

(a) Cross section of a borehole showing expected location of wellbore failures. Compressive failures occur as breakouts in the Shmin direction where circumferential stress is most compressive urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0010. Tensile failures occur as drilling-induced tensile fractures (DITFs) in the SHmax direction where circumferential stress is most tensile urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0011. (b) Azimuthal variation of circumferential stress at the borehole wall with angle from direction of SHmax (vertical axis not drawn to scale). The green and yellow sinusoids are circumferential stresses within siltstone and sandstone, respectively. Presence of breakouts in siltstone and absence in sandstone implies higher compressive circumferential stress in siltstones than in sandstones. Tensile failures in sandstone imply lower minimum circumferential stress (urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0012) than its tensile strength.

If we assume that breakouts span over the azimuthal range where σθθ exceeds the UCS, the SHmax magnitude is uniquely related to the breakout width.
urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0013(2)
where Wbo is the angular width of the breakout, UCS is the uniaxial compressive strength, and remaining variables are the same as Equation 1. Thus, if we know the pore pressure, mud pressure, thermal stress, UCS, and Shmin, we can find the magnitude of SHmax. Note that this equation assumes an isotropic failure criterion, that is, we do not consider the effects of bedding plane and bedding dip on the stress concentration and anisotropic strength of rocks (Lee et al., 2012). Equation 2 is also based on a Mohr–Coulomb failure criteria (friction angle is ignored because ΔP is zero) which does not consider the effect of the intermediate principal stress magnitude on rock strength, and thus also on the estimate of SHmax (Chang et al., 2010; Valley & Evans, 2019). We chose to use this relatively simple approach because not enough samples were available to characterize the polyaxial strength criteria for each rock type and our emphasis is on the effect of lithological variation which is reasonably captured by the variation in UCS.

The borehole is drilled at a constant overbalanced mud pressure suggesting that the borehole failures are caused by circumferential stress on the borehole wall. The mud pressure gradient used during TCDP drilling was 10.8 MPa/km, whereas the hydrostatic pore pressure was measured to be 9.8 MPa/km (Hung et al., 2009). Some temporary variability in mud pressure at the bottom of the borehole could occur periodically, in depth, due to the push and pull of the bottom-hole assembly when connecting or disconnecting drill pipes. However its effect is neglected in this study as we do not see any periodic occurrences of wellbore failures and it is not impacting our calculation to the first order. Therefore, ΔP in the TCDP boreholes are taken to be 1 MPa/km. The vertical stress is calculated by integrating the density log.

Thermal stress is induced in the borehole wall due to cooling caused by the mud circulation, altering the stress magnitude at the borehole wall. To evaluate the magnitude of thermal stress caused by borehole cooling, we refer to temperature measurement conducted every 3 m in TCDP Hole A after drilling (Kano et al., 2006). Kano et al. (2006) observed a linear thermal gradient of 22°C/km, whereas in a typical borehole, drilling mud temperature gradient is ∼10–15°C/km (McDonald, 1976). Therefore, maximum temperature difference between mud and the formation at 2 km depth is less than 24°C. Given typical elastic and thermoelastic properties of sedimentary rocks, ΔT of 25°C only cause small changes in the estimate of stress magnitudes, on the order of several MPa (Zoback et al., 2003). We also note that this cooling-induced thermal stress promotes DITFs, but not breakout occurrence. If there is ample time for the borehole wall temperature to reequilibrate with the surroundings before image logs are acquired, the thermal stress effect will diminish over time and its influence on the SHmax estimate derived from breakout width will become further insignificant. Therefore, we proceed with the analysis neglecting the thermal stress term.

5.1 Constraining Shmin Magnitude

Extended leak-off tests were conducted in TCDP Hole B at four different depths: 1,019.5, 1,085, 1,179.0, and 1,279.6 m (Hung et al., 2009). Using the leak-off test data, Hung et al. (2009) inferred Shmin from instantaneous shut-in pressure of the first two injection cycles as 16.3, 23.8, 16.2, and 19.6 MPa for the four depths indicated above, respectively. We note that the shut-in pressures of the first two injection and shut-in cycles were nearly the same for all tests except for the one at 1,279.6 m. Haimson et al. (2010) reanalyzed the extended leak-off tests and interpreted that shut-in pressures from the leak-off test at 1,279.6 m is 29.8 MPa instead of 19.6 MPa, due to a leak in the second cycle. All of these measurements suggest that the Shmin is smaller than the vertical stress, Sv, thus a normal or strike-slip faulting environment.

We expect the magnitude of Shmin to increase with depth along the borehole (i.e., horizontal stress gradient). We observe an increase in Shmin readings with depth from 1,019.5 to 1,085 m. However, the next Shmin measurement at 1,179.0 m is 16.2 MPa, lower than the shallower reading of 23.8 MPa at 1,085 m. The leak-off tests suggest that there are heterogeneities in the Shmin gradient along the borehole. Stress memory experiments by Yabe et al. (2008) and anelastic strain recovery data by Lin et al. (2007) also show heterogeneity in the Shmin gradient. Previous Shmin measurements are summarized in Text S3 in Supporting Information S1.

Heterogeneity in Shmin gradient around the Chelungpu fault system could be a result of differential response of the lithological units to tectonic loading. Such lithology-dependent change in Shmin magnitude was attributed to variation in elastic properties of intercalated Devonian shale, sandstone, and limestone layers by Evans, Engelder, and Plumb (1989). Hydraulic fracturing observations by Evans, Oertel, and Engelder (1989) showed that stiffer beds have higher Shmin compared to compliant beds. In TCDP, we observed similar correspondence between formation stiffness and Shmin. Such correlation can be understood to be a result of uniform horizontal tectonic strain applied to formations of varying stiffness (e.g., Bourne, 2003). Under uniform tectonic strain, larger horizontal stress arises in the stiffer siltstone layers and lower horizontal stress in the compliant sandy layers.

To evaluate the variation in Shmin caused by tectonic deformation, we consider a layered rectangular media deformed uniformly by horizontal tectonic contraction (ΔeHmax; Thiercelin & Plumb, 1994). We can calculate the stress change induced in the direction perpendicular to the tectonic contraction, corresponding to Shmin, using the Hooke’s law of elasticity and invoking two boundary conditions: (a) traction-free top surface and (b) plane strain condition in the vertical plane parallel to the tectonic loading direction (i.e., infinite horizontal extent in the load perpendicular direction; see Text S2 in Supporting Information S1 for derivation):
urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0014(3)

Thus, the change in Shmin is a function of the applied uniform strain, Young’s modulus E, and Poisson ratio v. We calculate E and v from velocity and density logs to obtain a profile of vE/(1 − v2) with depth. vE/(1 − v2) and Shmin gradient show a positive correlation with R2 value of 0.19 (Figure 7a). The correlation is indicative of how the elastic properties variation is controlling the Shmin variation, but the weak correlation may also suggest the possibility of additional causes for the Shmin variation.

Details are in the caption following the image

Correlations between Shmin gradient, elastic properties, and gamma ray. (a, b) Crossplot between Shmin gradient (from previous literature) with vE/(1 − v2) and gamma ray. (c) Crossplot between vE/(1 − v2) and gamma ray.

Silt-rich layers are also rich in clay, which are more ductile and exhibit visco-plastic behavior (Sone & Zoback, 2014a2014b). Ductile deformation leads to long-term viscous relaxation of differential stress leading to increase in Shmin in a normal or strike-slip faulting environment. Such Shmin variation has been observed in shale-bearing basins (Gunzburger & Cornet, 2007; Gunzburger & Magnenet, 2014; Sone & Zoback, 2014a). Extensive hydraulic fracturing stress measurements in Piceance basin, Colorado, USA, showed that minimum horizontal stress is lower in sandstone than in shale or clay-rich rocks (Warpinski & Teufel, 1989; Y. Zhang & Zhang, 2017). Plumb et al. (1991) also suggests that Shmin variations in shale-bearing basins are a result of not only elastic stiffness but also the presence of clay. In TCDP, we see a strong positive correlation between Shmin gradient and gamma ray, which is a proxy for clay-content (Figure 7b), consistent with the idea that Shmin is relatively high in clay-rich formations because of viscous relaxation. Such a strong correlation may not apply in other wells.

The better correlation of gamma ray with Shmin gradient compared to the elastic properties (Figures 7a and 7b) may suggest viscous relaxation as a more probable explanation for the Shmin variation. However, because clay-rich rocks are also stiffer in TCDP rocks (Figure 7c), it is possible that gamma ray is also simultaneously serving as a proxy for stiffness and reflecting the influence of elastic constant, vE/(1 − v2), on Shmin. Distinguishing the elastic and visco-plastic effects on Shmin is not possible with available data and current technology, but it is plausible that both effects yield the current Shmin variation.

In this study, we estimate the Shmin profiles along the TCDP borehole using the linear empirical relations from Figures 7a and 7b. Profiles of Shmin gradient are obtained utilizing the vE/(1 − v2) and gamma ray profiles and applying the empirical relations. Then, the depth is multiplied to the Shmin gradients to obtain the profiles of Shmin based on the elastic properties and gamma ray. We only discuss the results obtained from the gamma ray-based approach here because its correlation with Shmin gradient was better and it potentially encompasses the consequences of both elastic and viscous effects. The result obtained from the empirical relation with vE/(1 − v2) is shown in the supplementary material for comparison (Text S4 in Supporting Information S1), but the conclusions of the subsequent analysis do not change depending on which empirical relation is used.

5.2 Constraining SHmax Magnitude

We can infer the magnitude of SHmax from the estimated Shmin values and breakout width measurements using Equation 2, if we have an estimate of compressive rock strengths. As a practical approach to estimating the UCS profile along the entire section of the TCDP borehole, we used the sonic log to estimate a profile of rock strength (Figures 5c and 5d). In Figure 8, UCS values are plotted against Vp corresponding to the depths of core samples tested in the lab. The vertical error bars indicate the range of UCS values within a sample group. The horizontal error bars indicate the range of Vp values within a ±0.5 m interval around the sample depth. The robust positive correlation between Vp and UCS is evident, thus we establish an empirical relationship between the two parameters to capture the variability in UCS along the borehole. We note that this empirical relationship is qualitatively consistent with the strength reduction expected in fault zones. Although strength measurements of fault zone rocks were not possible due to the lack of intact samples, increase in fracture density generally causes reduction in both UCS and Vp (Fan et al., 2018; Hoek & Brown, 1980).

Details are in the caption following the image

Uniaxial compressive strength (UCS) of TCDP rocks plotted against P wave velocity from the sonic log.

Combining information from the estimated UCS profile, breakout width (Figure 5b), and estimated Shmin profile (Section 5.1) into Equation 2, we can determine the magnitude of SHmax at those depths where the breakout width data are available (Figure 9a). Where no breakouts are observed in the image log, we provided bounds on the SHmax value, unless the lack of breakout data was due to poor image quality. Based on Equation 2, absence of breakouts provides an upper limit to the magnitude of SHmax given a Shmin magnitude.

Details are in the caption following the image

(a) Profile of three principal stress magnitudes with depth. Estimates of Shmin and SHmax are low for sand-rich layers and high for silt-rich layers. (b) Upper limit of SHmax from absence of breakouts given a Shmin magnitude is overlaid on stress magnitudes obtained in regions of breakout occurrence.

Figure 9 shows the resulting near-continuous profiles of the lithology-dependent stress state as inferred quantitatively from breakout analysis and laboratory experiments (Figures 5, 7, and 8). We see that the SHmax magnitudes constrained by breakout width (solid green symbols in Figure 9b) generally plot at higher magnitudes compared to the upper limit of SHmax determined by the breakout absence (open green symbols in Figure 9b). Breakouts primarily occur in silt-rich layers and are rare in sand-rich layers, signifying the generally higher SHmax magnitude in silt-rich layers and vice versa. If breakouts selectively appear in siltstones that have higher UCS, urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0015 must be higher in siltstones (as also observed in Figure 6). Because urn:x-wiley:21699313:media:jgrb55464:jgrb55464-math-0016 is a function of 3SHmax − Shmin and Shmin is found to be higher in siltstones, SHmax must also be higher in siltstones.

We note that the FMS image logs recovered from the upper section of TCDP Hole A, in general, have poor azimuthal coverage due to the smaller number of sensor buttons on the tool. Caliper logs also showed that borehole enlargement occurred at some depths, likely due to the longer time between drilling and logging, further reducing the azimuthal coverage and degrading the image quality due to rough borehole walls. Thus, breakout width is not always measured with high accuracy. We expect a maximum error in breakout width to be approximately 15°. For a 35° width breakout found at 10 MPa pore pressure, 50 MPa UCS, and 20 MPa Shmin, uncertainty of 15° in breakout width translates to SHmax uncertainty of ±1.4 MPa. Thus, the uncertainty of SHmax due to error in breakout width is relatively small compared to its magnitude. Therefore, the error bars are not shown in Figure 9 for clarity.

6 Pre-Earthquake Stress

To be able to understand the stress conditions leading to failure, we attempt to estimate the pre-earthquake stress state before the Chi-Chi earthquake. We can infer the pre-earthquake stress field if we can calculate the coseismic stress changes. In this section, we use dislocation theory to model the displacement field caused by slip on the Chelungpu fault and use Hooke’s law to obtain corresponding stress changes.

We compute displacements in a two-dimensional vertical cross section due to a uniform slip along a reverse fault using solutions derived in Segall (2010). The solution combines the Volterra’s formula with the Melan’s Green function (Melan, 1932) to obtain displacements due to an edge dislocation (see Text S5 in Supporting Information S1 for details). The cross section on which we calculate the solution extends in the vertical direction (x2 direction) and the horizontal direction (x1 direction) perpendicular to the strike of the Chelungpu fault, that is, East-West (Figure 10a). There is no displacement along the x3 axis parallel to the strike of the fault (i.e., plane strain). This assumption holds to the first order because the geological structure continues along the strike of the Chelungpu fault (Figure 2). The fault is considered to be a combination of two edge dislocations in a homogeneous, isotropic, linear elastic half space. Two edge dislocations with opposite slip sense are superposed, one at the free surface on the fault trace and the other at the downdip limit of the fault. The reverse fault we consider dips at 30° and extends 15 km in the downdip direction along the fault. Although simplistic, this two-dimensional model has been found to capture the essential first-order feature of the observed displacement field of the Chi-Chi earthquake (Segall, 2010).

Details are in the caption following the image

(a) Displacement field induced by a reverse fault dipping at 30° with 8 m fault slip. The edge of the fault is 13 km east of the fault trace on the surface. The red line shows the location of the TCDP borehole, which is ∼1.92 m east of the fault intersecting the fault plane at 1,111 m; (b) the eastward and vertical surface displacement. The red line shows the location of TCDP 1.92 km east of the fault; (c–e) strain tensor components derived from the displacement field solution; (f) strain component profiles along the TCDP boreholes 1.92 km east of the fault; (g) deviation of σ22 from vertical is below 15°; and (h) corresponding stress component changes obtained from the strain profile, elastic properties based on the sonic log data, and plane strain boundary condition.

In order to constrain the 2D coseismic displacement field near the TCDP borehole, we referred to the strike-normal horizontal and vertical surface displacements (u1 and u2) obtained from GPS data (Ji et al., 2001; Johnson et al., 2001; Yu et al., 20012003; see Text S6 in Supporting Information S1). Here, fault strike is almost North-South (Figure 2a), thus the horizontal and vertical axis in the fault dislocation model corresponds to the eastward and upward directions, respectively (Figure 10a). GPS displacement in the region where the TCDP boreholes were drilled shows that the coseismic horizontal displacement perpendicular to the fault strike was ∼4.5 m and vertical displacement was ∼2.9 m (Yu et al., 2001). We find that a slip amount of 8 m on the fault plane reproduces these vertical and horizontal surface displacements to a reasonable degree as shown in Figure 10b.

Differentiating the displacement field constrained above, we calculate the corresponding normal (ε11ε22) and shear strain fields (ε12) in the x1x2 coordinate system (Figures 10c–10e). We obtained a vertical transect of strain measurement at a distance of 1.92 km east of the fault trace, corresponding to the TCDP borehole location intersecting the Chelungpu fault at 1,111 m depth (Figure 10f). Then, the 2D strain tensor components are used to calculate the coseismic stress change along the TCDP borehole by applying the Hooke’s law with plane strain boundary condition. To acknowledge the large variability of the elastic properties in the TCDP region, we use elastic constants recovered from the sonic log data (Figures 5c and 5d), although the dislocation model is computed using uniform elastic properties (Table S4 in Supporting Information S1). Since we assumed plane strain condition with no changes in strain along the strike of the fault (ε33 = 0), Δσ33 is calculated as Δσ33 = vσ11 + Δσ22) (Figure 10h).

Coseismic stress change calculated along the TCDP borehole shows that the change in shear stress component is nonzero, Δσ12 ≠ 0 (Figure 10h). This indicates that the principal directions of the coseismic stress change are not necessarily aligned with the x1 and x2 axes. The deviation of the most vertical principal direction (of the stress change) from the x2 axis is shown in Figure 10g, which reaches 13° at deeper depth. 13° is less than the uncertainty of the principal stress directions inferred from the wellbore failure observations. Therefore, for simplicity, we directly subtract the magnitudes of coseismic stress change Δσ11, Δσ22, and Δσ33 from the post-earthquake principal stress magnitudes SHmax, Sv, and Shmin, respectively, to obtain the pre-earthquake principal stress magnitudes (Figure 11).

Details are in the caption following the image

Pre-earthquake stress magnitudes plotted with the post-earthquake stress magnitudes. Increase in Shmin and SHmax magnitudes pre-earthquake and insignificant difference in Sv magnitude.

In Figure 11, the darker colors show pre-earthquake principal stress magnitudes, whereas the lighter colors represent post-earthquake principal stress magnitudes. Since Δσ11 component of the stress change tensor has the highest magnitude (Figure 10h), SHmax shows the highest increase in its magnitude from post- to pre-earthquake. Increase in Shmin from post- to pre-earthquake is less significant than SHmax. The pre-earthquake Sv is not distinguishable from post-earthquake Sv in Figure 9 because coseismic changes in vertical stress is close to zero (Figure 10h). Because the vertical stress is almost the same before and after the earthquake but coseismic Shmin decrease was substantial, there are certain depths where the faulting environment transitioned from strike slip before the earthquake to the current normal faulting environment after the earthquake. Similarly, substantial Shmin change close to the fault zone suggests that the pre-earthquake faulting environment was reverse faulting stress state instead of the current strike-slip environment.

7 Discussion

7.1 Lithology-Dependent Stress Change

The superposition of previous stress magnitude calculations obtained by various methods on our results suggests that our estimated stress profile acknowledging the layer-by-layer rock property changes is able to capture the stress heterogeneity (Figures 9a and 12a). The inconsistency in previous stress estimates was primarily because these studies analyzed stress at different depths where a wide range of lithology was encountered. In Figure 12a, we observe that the most sand-rich layers plot toward the normal faulting environment, whereas the most silt-rich layers plot in the strike-slip/reverse faulting regime. The intermediate compositions fall in the strike-slip regime. Thus, stress is generally more compressive (i.e., higher SHmax and Shmin) in silt-rich layers compared to sand-rich layers, as was also seen in Figure 9.

Details are in the caption following the image

Calculated post- and pre-earthquake effective horizontal stress magnitudes compared with the frictional limits (i.e., stress polygon) and previous stress measurements. (a) Comparison with previous observations. (b, c) Post-earthquake and pre-earthquake stresses color coded with depth and compared with the stress polygon.

As described in Section 5, the predicted stress magnitude variation closely follows the variation in the data used for the stress calculations. Since we calculate Shmin from gamma ray log (Figure 7), increase in Shmin between 1,050 and 1,280 m is predominantly due to the presence of silt-rich facies in the Chinshui Shale (Figure 9a). On the other hand, from Equation 2, we see that SHmax magnitude is influenced by various parameters. Given the negligible variation in thermal stress, mud pressure, and pore pressure, we find that SHmax magnitude is mostly influenced by the UCS and Shmin variation. For breakout width below 60°, Equation 2 shows that the estimated SHmax magnitude has a positive correlation with UCS and Shmin. Therefore, calculated SHmax is higher in silt-rich layers reflecting both the higher UCS inferred from the higher Vp and the higher Shmin magnitude inferred from the higher gamma ray values. Higher SHmax in silt-rich layers can also be understood by the elastic layered media model discussed in Section 5.1 and Text S2 in Supporting Information S1. On applying layer parallel strain to a layered formation with stiff silt layers and compliant sand layers, stress accumulation will be greater in the stiff silt layers leading to higher stress magnitude in the SHmax direction parallel to the direction of loading.

Both the pre- and post-earthquake stress profiles we obtained show a transition in stress state below 1,300 m depth upon entry into the Kueichulin Formation, which is a sand-rich layer. At depth range 1,300–1,450 m, the stress state is primarily normal faulting environment, and the stress state is less compressive below 1,450 m compared to the shallower sections. In this sandstone-rich formation from 1,300 to 1,450 m, breakout azimuth deviates from the general trend of 20° to almost 80° (Figure 5a). Because the empirical relationships used in the stress calculation are primarily based on hydraulic fracturing and rock strength data collected from the shallower sections, it is somewhat questionable whether these observations do reflect true changes in stress state in the deeper section of the TCDP borehole.

This formation-scale changes in stress magnitude in sandstone-rich Kueichulin Formation are consistent with inference from other studies. For example, an analysis of optimally oriented planes, determined from stress change in combination with earthquake focal mechanism showed that the stress state changes at 1,300 m around the top of the Kueichulin Formation (Chan et al., 2012). Chan et al. (2012) suggest that the state of stress in TCDP is strike-slip to reverse fault between 900 and 1,300 m, but the faulting environment switches to normal faulting at 1,300 m. Yabe et al. (2008) conducted stress memory experiments through analysis of deformation rate and acoustic emission rate on TCDP cores. Above 1,150 m, results showed strike-slip faulting, whereas one core from 1,316 m showed SHmax = Sv, denoting a normal fault to strike-slip faulting environment. These results are consistent with the less compressive stress states in sandstone inferred from our stress profile. The consistency of our observations with previous studies suggests that our stress measurements are relevant to some degree below 1,300 m, even though empirical relationships used in this study are derived from data in the shallower section.

7.2 Fault-Related Changes in Stress

We also observe formation-scale stress changes that occur in the Chinshui Shale. Stress gradient lines in Figure 9b show that SHmax magnitude below 1,050 m depth, entering the Chinshui Shale, becomes consistently lower than the 45 MPa/km gradient line. On the other hand, the Shmin magnitude between 1,050 and 1,280 m in the Chinshui Shale is higher than the surrounding formations, as can be seen by the comparison with the 10 MPa/km gradient line. Shmin increase in Chinshui Shale is a direct consequence of lithology dependence, for which gamma ray log is a proxy. However, the decrease in SHmax is not caused by lithology. As discussed above, for breakout widths narrower than 60°, the higher Shmin and UCS within silt-rich rocks should generally lead to higher SHmax estimates if stress is solely controlled by lithology. The decrease in SHmax magnitude estimate is a consequence of the low material strength as inferred from the decrease in velocity of damaged rocks in the vicinity of the Chelungpu fault (Yeh et al., 2007). Thus, in the Chinshui Shale, SHmax magnitude is influenced by both lithology and fault-related damage.

The decrease in SHmax magnitude and the increase in Shmin magnitude close to the fault lead to a relatively isotropic stress state. Figure 12b shows that the stress states corresponding to depth range 1,100–1,250 m around the Chelungpu fault zone plots close to the point where Sv = SHmax = Shmin. Faulkner et al. (2006) suggest that reduced stiffness and increased Poisson ratio of damage rocks can lead to a decrease in differential stress close to the fault core. While the cause of such isotropic stress state is unknown, Ma et al. (2012) analyzed micro-earthquakes observed by borehole seismometers installed in TCDP and also suggested that isotropic events with no identifiable shear wave components were dominant in the vicinity of the fault, indicative of isotropic stress states near the fault zone.

Plot of breakout azimuth with depth shows that the breakout azimuth until 1,300 m is fairly continuous (∼30°) with no major azimuthal change going through the Chelungpu fault zone (Figure 5b). This indicates that there are no major changes in the azimuth of the horizontal principal stresses (or stress rotation) caused by fault slip within the volume investigated by the TCDP borehole. Our observation is contrary to some previous studies which suggest 90° rotation of SHmax across the primary slip plane (Lin et al., 2007; Wu et al., 2007) but is consistent with Hung et al. (2009) that also suggests no stress rotation.

In general, local stress perturbation caused by fault slips occur due to the development of stress singularities at where there is a rapid change in the amount or direction of fault slip, for instance, at the periphery of a large slip patch or at geometrical irregularities. Thus, the overall spatial scale at which the stress perturbation occurs is mostly governed by the length scale of the area of highest slip. For example, in the edge dislocation model in Figure 10, stress concentration occurs at the edge of the fault where there is an abrupt termination of fault slip, and the stress perturbation extends in the entire region surrounding the fault. Slip distribution on the Chi-Chi earthquake has been inverted by many authors based on GPS, InSAR, and teleseismic data (Ji et al., 2001; Johnson et al., 2001; Ma et al., 2001; L. Zhang et al., 2008). Despite the differences between these results at finer scales, a common feature that arises in these models is a large slip patch under the TCDP borehole with a length scale of at least 10 km. The slip distribution in this northern slip patch is also suggested to be homogeneous based on the depletion of high frequency content in the strong motion record from the northern section of the Chi-Chi slip plane. Therefore, we expect that the stress perturbation caused by the Chi-Chi earthquake fault slip around TCDP boreholes would manifest itself over the entire extent of the borehole rather than locally at the fault zone depths.

7.3 Pre-Earthquake Stress Compared With Frictional Limits

The crossplot of pre-earthquake horizontal principal stress magnitudes (Figure 12c), normalized by the vertical stress, show that our stress calculation results are valid within the physical limits set by a frictional coefficient of 0.85. Majority of the data points plot within the stress polygon and very few plot within the reverse faulting regime. This signifies that the pre-earthquake stress was not in a state of criticality by reverse faulting in the northern part of the fault where TCDP encountered the fault. This may indicate that the state of stress was critical by reverse faulting only in the southern part of the fault where the rupture nucleated (Ma et al., 2003) and subcritical in the northern part of the fault. However, the largest fault slip was observed in the slip patch identified around the TCDP borehole area reaching fault slips of about 10 m. This high slip amount despite subcritical stress state in the region may be consistent with the notion that a dynamic fault-weakening mechanisms operated at the northern segment of the fault suggested by various authors, such as hydrodynamic lubrication (Kanamori & Brodsky, 2004) and thermal pressurization (Noda & Lapusta, 2013; Sone, Noda, & Shimamoto, 2007; Tanikawa & Shimamoto, 2009). Our preseismic and postseismic stress results provide an important constraint in studying the coseismic mechanical processes along seismogenic faults.

7.4 Uncertainty in the Coseismic Stress Model

Various simplifications were made when calculating the coseismic stress change. One can prefer to use three-dimensional heterogeneous coseismic slip distributions determined from inversion of seismic and geodetic data, which may be better than the uniform slip assumption we made. However, between the various slip models of the Chi-Chi earthquake (Ji et al., 2001; Johnson et al., 2001; Ma et al., 2001; Yu et al., 20012003; L. Zhang et al., 2008), there is agreement only in the first-order pattern where there is more slip in the northern half of the fault and less in the southern half. The finer details are different depending on the data and methodology used, which would lead to nonunique results if one were to employ the slip models to calculate coseismic stress change.

Although the along-strike length of the ruptured Chelungpu fault (∼85 km) was much greater than the depth extent (∼15 km), the plane strain boundary condition assumed in the displacement solution may not fully hold because of along-strike variability in fault slip. The assumption of uniform fault slip in the model also does not capture the along-dip heterogeneity found in Chi-Chi earthquake slip models. The coseismic stress change was also calculated neglecting the strike-parallel slip components, but the Chelungpu fault did not rupture in a pure reverse faulting sense close to the TCDP drill site. Rake angles are close to 45° according to some studies (Ji et al., 20012003). Such oblique slip component will cause out-of-plane components of the coseismic stress change which is not accounted for in our calculations. However, TCDP is situated within the largest slip patch of the Chi-Chi earthquake, suggesting that the slip distribution was relatively homogeneous around TCDP. The magnitude of the coseismic stress change is also found to be relatively small compared to the absolute stress magnitude, thus the influence of heterogeneous slip and oblique fault slip will not largely change our estimate of the pre-earthquake stress state. Although the result presented here should be taken as a first-order estimate, conclusions of our study are not expected to change upon acknowledgment of the finer details of the fault slip pattern.

8 Conclusions

Our study shows that the appearance and disappearance of wellbore failures in image logs of the TCDP boreholes are dependent on lithology. Along TCDP, there is ∼70 MPa difference in compressive strength of rocks between the compliant sandstone and stiffer siltstone layers measured in the laboratory. Integrating these observations with extended leak-off test results, we deduce that the post-earthquake in-situ horizontal stress magnitudes are lower in sandstone and higher in siltstone. Inferred stress magnitudes fall within limits set by the frictional coefficient and captures the variability in stress states reported by previous studies in TCDP. Detailed borehole analysis also captures the relatively isotropic stress state within the Chelungpu fault system. Our study highlights the importance of understanding spatial variations of stress at various scales.

We provide another snapshot of the stress state in the seismic cycle by calculating the state of stress before the Chi-Chi earthquake. Majority of the pre-earthquake stress magnitude data fall within the stress polygon, indicating subcritical stress state in the region where TCDP encountered the fault.

Acknowledgments

This research was funded by the National Science Foundation (EAR1727661). We thank Wei-Ting Lin for help in collecting samples and Kevin R. Cashman for support in preparing core plugs for laboratory testing. The authors would also like to thank the anonymous reviewers and editors for their constructive comments that helped to improve the manuscript.

    Data Availability Statement

    Data obtained from laboratory experiments are uploaded to MINDS@UW repository at https://doi.org/10.21231/9558-5F63.