# The State of Stress on the Fault Before, During, and After a Major Earthquake

Emily Brodsky, James Mori, Louise Anderson, Frederick Chester, Marianne Conin, Eric Dunham, Nobu Eguchi, Patrick Fulton, Ryota Hino, Takehiro Hirose, et al.

► To cite this version:

Emily Brodsky, James Mori, Louise Anderson, Frederick Chester, Marianne Conin, et al.. The State of Stress on the Fault Before, During, and After a Major Earthquake. Annual Review of Earth and Planetary Sciences, 2020, 48 (1), pp.49-74. 10.1146/annurev-earth-053018-060507. hal-02982122

HAL Id: hal-02982122

https://hal.univ-lorraine.fr/hal-02982122v1

Submitted on 7 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

*Annual Review of Earth and Planetary Sciences*

# The State of Stress on the Fault Before, During, and After a Major Earthquake

Emily E. Brodsky,<fnref n="1" /> James J. Mori,<fnref n="2" /> Louise Anderson,<fnref n="3" />

Frederick M. Chester,<fnref n="4" /> Marianne Conin,<fnref n="5" />

Eric M. Dunham,<fnref n="6" /> Nobu Eguchi,<fnref n="7" /> Patrick M. Fulton,<fnref n="8" />

Ryota Hino,<fnref n="9" /> Takehiro Hirose,<fnref n="10" /> Matt J. Ikari,<fnref n="11" />

Tsuyoshi Ishikawa,<fnref n="10" /> Tamara Jeppson,<fnref n="12" />

Yasuyuki Kano,¹³ James Kirkpatrick,¹⁴

Shuichi Kodaira,¹⁵ Weiren Lin,¹⁶ Yasuyuki Nakamura,¹⁵

Hannah S. Rabinowitz,¹⁷ Christine Regalla,¹⁸

Francesca Remitti,¹⁹ Christie Rowe,¹⁴

Demian M. Saffer,²⁰ Saneatsu Saito,<fnref n="7" /> James Sample,¹⁸

Yoshinori Sanada,<fnref n="7" /> Heather M. Savage,<fnref n="1" />

Tianhaozhe Sun,²⁰ Sean Toczko,<fnref n="7" /> Kohtaro Ujiie,²¹

Monica Wolfson-Schwehr,²² and Tao Yang²³

ANNUAL
REVIEWS

www.annualreviews.org

• Download figures

• Navigate cited references

• Keyword search

• Explore related articles

• Share via email or social media

Annu. Rev. Earth Planet. Sci. 2020. 48:49–74

First published as a Review in Advance on
November 15, 2019

The *Annual Review of Earth and Planetary Sciences* is
online at earth.annualreviews.org

https://doi.org/10.1146/annurev-earth-053018-060507

Copyright © 2020 by Annual Reviews.
All rights reserved

<footnote n="1">¹Department of Earth and Planetary Sciences, University of California, Santa Cruz, California 95064, USA; email: brodsky@ucsc.edu</footnote>

<footnote n="2">²Disaster Prevention Research Institute, Kyoto University, Kyoto 611-0011, Japan</footnote>

<footnote n="3">³Total E&P UK Limited, Westhill AB32 6JZ, United Kingdom</footnote>

<footnote n="4">⁴Department of Geology and Geophysics, Texas A&M University, College Station, Texas 77843, USA</footnote>

<footnote n="5">⁵Université de Lorraine, CNRS, GeoRessources, 54000 Nancy, France</footnote>

<footnote n="6">⁶Department of Geophysics, Stanford University, Stanford, California 94305, USA</footnote>

<footnote n="7">⁷Institute for Marine-Earth Exploration and Engineering, Japan Agency for Marine-Earth Science and Technology, Yokosuka-city, Kanagawa 237-0061, Japan</footnote>

<footnote n="8">⁸Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York 14853, USA</footnote>

<footnote n="9">⁹Graduate School of Science, Tohoku University, Sendai 980-8578, Japan</footnote>

<footnote n="10">¹⁰Kochi Institute for Core Sample Research, Japan Agency for Marine-Earth Science and Technology, Kochi 783-8502, Japan</footnote>

<footnote n="11">¹¹MARUM—Center for Marine Environmental Sciences and Faculty of Geosciences, University of Bremen, D-28359 Bremen, Germany</footnote>

<footnote n="12">¹²Department of Geoscience, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA</footnote>
**Keywords**

earthquake, friction, stress, subduction, fault, tectonics

**Abstract**

Earthquakes occur by overcoming fault friction; therefore, quantifying fault resistance is central to earthquake physics. Values for both static and dynamic friction are required, and the latter is especially difficult to determine on natural faults. However, large earthquakes provide signals that can determine friction in situ. The Japan Trench Fast Drilling Project (JFAST), an Integrated Ocean Discovery Program expedition, determined stresses by collecting data directly from the fault 1–2 years after the 2011 *M*<sub>w</sub> 9.1 Tohoku earthquake. Geological, rheological, and geophysical data record stress before, during, and after the earthquake. Together, the observations imply that the shear strength during the earthquake was substantially below that predicted by the traditional Byerlee’s law. Locally the stress drop appears near total, and stress reversal is plausible. Most solutions to the energy balance require off-fault deformation to account for dissipation during rupture. These observations make extreme coseismic weakening the preferred model for fault behavior.

■ Determining the friction during an earthquake is required to understand when and where earthquakes occur.

■ Drilling into the Tohoku fault showed that friction during the earthquake was low.

■ Dynamic friction during the earthquake was lower than static friction.

■ Complete stress drop is possible, and stress reversal is plausible.

**1. INTRODUCTION**

The earthquake cycle involves a competition between plate motion and frictional forces resisting motion at their edges. Tectonic plates are in continuous motion, while locked plate-boundary faults are usually immobile and therefore accumulate elastic stress. Eventually the increasing stress reaches some threshold associated with the fault strength and an earthquake occurs, which reduces the stress to a lower level. The stress begins to increase again, and the cycle repeats. This simple picture emphasizes the importance of fault strength to the earthquake cycle. Any quantitative understanding of when and how earthquakes rupture must grapple with the problem of the strength of faults.

<footnote n="13"><sup>13</sup>Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan</footnote>

<footnote n="14"><sup>14</sup>Department of Earth and Planetary Sciences, McGill University, Montreal, Quebec H3A 0E8, Canada</footnote>

<footnote n="15"><sup>15</sup>Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan</footnote>

<footnote n="16"><sup>16</sup>Graduate School of Engineering, Kyoto University, Kyoto 606-8507, Japan</footnote>

<footnote n="17"><sup>17</sup>US Department of Energy, Washington, DC 20024, USA</footnote>

<footnote n="18"><sup>18</sup>School of Earth and Sustainability, Northern Arizona University, Flagstaff, Arizona 86011, USA</footnote>

<footnote n="19"><sup>19</sup>Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Modena, Italy 41125</footnote>

<footnote n="20"><sup>20</sup>Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802, USA</footnote>

<footnote n="21"><sup>21</sup>Graduate School of Life and Environmental Sciences, University of Tsukuba, Tsukuba 305-0006, Japan</footnote>

<footnote n="22"><sup>22</sup>Monterey Bay Aquarium Research Institute, Moss Landing, California 95039-0628, USA</footnote>

<footnote n="23"><sup>23</sup>Hubei Subsurface Multi-Scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China</footnote>
Much of what is known about fault strength stems from observations from structural geology that show that faults form and are active when the fault plane is within a restricted range of orientations relative to the principal stress axes (Anderson 1951, Collettini & Sibson 2001, Sibson 1985). This range is governed by friction and has generally been observed to be consistent with Byerlee's law, which is an empirical finding that states that most rocks have a coefficient of friction of 0.85 at shallow depths and 0.6 at pressures higher than 200 MPa (roughly 7 km depth) (Byerlee 1978). However, important counterevidence exists. The lack of high heat flow of the San Andreas Fault is inconsistent with the mechanical dissipation required by Byerlee's law over the slip history of the fault (Fulton et al. 2004, Lachenbruch & Sass 1980). Thus, we have a conundrum: How do we reconcile the observations favoring Byerlee's law with the counterevidence of low friction on faults?

A solution to the problem is to recognize that some of these measurements are sensitive to static friction while others are sensitive to dynamic friction. In most of our everyday experiences, we recognize that friction at high speeds is less than the friction that must be overcome to start slip. Although many minerals can violate this experience and increase their friction with slip at moderate speeds (Dieterich 1992), experiments show that all tested geological materials appear to weaken at the extreme speeds of earthquake slip (Di Toro et al. 2011). It seems possible to reconcile the data if earthquake initiation is governed by high, Byerlee's law-like friction and earthquake slip is governed by a much lower value.

This simple explanation has its problems as well. Seismic waves can effectively measure the average stress change on a fault during an earthquake, and these observed stress drops are generally ~3 MPa (Kanamori & Anderson 1975), which is much less than the stresses of order 100 MPa required to initiate a fault rupture at typical seismogenic depths (>7 km) if the static friction is governed by Byerlee's law. How can radical dynamic weakening occur with such low stress drops?

A possible reconciliation is to imagine that the fault is pervasively weak and that only locally strong asperities must be overcome. Certain clay minerals were acknowledged as exceptions to Byerlee's law even in the original compilation (Byerlee 1978). These weak materials are particularly common in fault zones and can nearly coat the surface (Saffer & Marone 2003). Their presence or absence could determine local strength. Alternatively, fault roughness can result in strength variations even without clay minerals (Zielke et al. 2017). In either case, the average stress drops might be as low as observed and the fault may be weak dynamically everywhere with statically strong spots.

This hybrid model based on heterogeneity is attractive but complex, and scrutiny is warranted. Invoking extreme dynamic weakening has both physical and societal consequences. If dynamic weakening is significant, then an earthquake can create connected ruptures through an otherwise stable part of a fault system such as the creeping section of the San Andreas Fault (Kaneko et al. 2010, Noda & Lapusta 2013). Data from natural faults are necessary to determine if dynamic weakening is an important part of the earthquake process, and without such data our ability to anticipate fault behavior is severely limited.

The 2011 $M_w$ 9.1 Tohoku earthquake demonstrated in vivid terms these limits. The catastrophic tsunami was a direct consequence of the unprecedented and unexpected large slip of the shallow portion of the megathrust, which is analogous to the creeping section of the San Andreas Fault. Previous studies had supposed that the coupling was weak near the trench so that the level of accumulated stress was low, which would inhibit rupture propagation and tsunami generation (Loveless & Meade 2010, figure 10c; Wang & Hu 2006). However, this was not the case, and the huge slip on the shallow fault near the trench contributed to the largest tsunami in Japanese history (Fujiwara et al. 2011, Lay 2017).

Integrated Ocean Discovery Program (IODP) Expedition 343 [Japan Trench Fast Drilling Project (JFAST)] was organized to understand the stress on the fault during the catastrophic
rupture. A major goal was to overcome the fundamental limitation of the time-integrated heat flow
measurements of the San Andreas and measure the dissipated energy associated with this single
earthquake by measuring the temperature over the fault and comparing it to the surrounding rock.
Such temperature measurements could make sense only in the context of core analysis, laboratory
experiments, borehole geophysics, and structural analysis. JFAST was designed to complete this
task.

The extraordinary nature of the Tohoku earthquake demanded the deepwater capabilities of
the drill ship Chikyu to drill boreholes into the fault zone at 800 m below the seafloor (mbsf).
Since the faulting reached the seafloor in one of the world's deepest trenches, the drilling needed
to occur where the ocean depth was nearly 7,000 m. Such extreme deepwater drilling had never
been done before, and the technical achievement by itself was a milestone (Mori et al. 2014).
However, this review focuses on the scientific accomplishments.

The purpose of this review is to synthesize the findings of the JFAST expedition with all other
available information about the best-recorded major earthquake in history to quantify the stress
on the fault before, during, and after a major earthquake. We begin with a brief overview of the
site and constraints on the long-term stress state over geological time. The bulk of the review then
is organized in sections that follow chronologically to assemble the evidence for the stress state of
the Tohoku fault immediately before, during, and after the earthquake. In the final two sections
of this review, we explore the implications for the energy balance of the earthquake rupture and
stress evolution.

## 2. SITE OVERVIEW AND GEOLOGICAL CONSTRAINTS ON THE LONG-TERM STRESS STATE

The JFAST site is located ~7 km landward of the Japan Trench and ~100 km south-southeast of the mainshock epicenter (37°56'34"N 143°54'81"E) (Figure 1). Seismic reflection surveys show that the margin consists of a narrow frontal prism that overlies a horst in the oceanic plate inferred to have formed by outer rise normal faulting in response to plate bending (Chester et al. 2013, Nakamura et al. 2013, Tsuru et al. 2000). The frontal prism contains disrupted, discontinuous reflectors, which are interpreted to represent strata folded, cut, and repeated by shallowly landward-dipping thrust faults. The underthrust units are characterized by shallowly dipping reflectors parallel to the top of the oceanic crust (Chester et al. 2013). A shallowly dipping reflector at ~821 mbsf separates these two domains and is interpreted to be the plate-boundary décollement (Nakamura et al. 2013, 2014). Faults and fractures present in cores recovered from the plate-boundary region, combined with constraints on stratigraphic ages, show a zone of elevated damage in both the hanging wall and the footwall to the 821-mbsf plate boundary (Keren & Kirkpatrick 2016, Kirkpatrick et al. 2015, Rabinowitz et al. 2015). The core recovered from 821 mbsf was a smectite-rich rock containing a pervasive foliation, which can also be described as a scaly fabric. Several discrete faults were identified from crosscutting relations plus a change in foliation characteristics across the fault (labeled Faults A and B by Kirkpatrick et al. 2015) and the presence of an intercalated mudstone interval younger than the smectite-rich rock (Rabinowitz et al. 2015).

Structures observed in the geophysical logs and recovered core record shortening of the frontal
prism in approximately the direction of plate convergence (Chester et al. 2013, Kirkpatrick et al.
2015). Based on ¹⁰Be stratigraphy, the sediment of the frontal prism is likely derived from the
incoming Pacific Plate sediments (Regalla et al. 2019). Bedding attitudes measured in resistivity
images indicate the strata are folded with axes approximately perpendicular to the plate conver-
gence direction. Overturned bedding observed in core recovered from the central part of the prism
also indicates folding, and bedding attitudes measured in core are consistent with folding with axes
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1</figcaption></figure>

Location of the Japan Trench Fast Drilling Project (JFAST) drill site. (Top) Location map with reference slip contours and hypocenter (yellow star). Site C0019 is the JFAST site that is the focus of this paper. This site is referenced as C0019 following the Integrated Ocean Discovery Program (IODP) convention of numbering sites drilled by the *Chikyu* sequentially, all starting with the letter C. Panel adapted from Yue & Lay (2011). (Bottom) Seismic section. Panel adapted from Nakamura et al. (2014)/CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/legalcode). Abbreviations: CDP common depth point; VE, vertical exaggeration.
at a low angle to convergence, although the data are more scattered. In addition, the anisotropy of magnetic susceptibility (AMS) axes of sedimentary rocks in the frontal prism are mostly oblate with maximum axes aligned northeast-southwest and intermediate and minimum axes distributed in the vertical plane, consistent with shortening parallel to the plate convergence direction (Yang et al. 2013). The timing and duration of shortening are unknown but likely occurred over the past few million years (Regalla et al. 2013).

In contrast, bedding in the underthrust sedimentary rocks is subparallel and shallowly dipping, and intermediate AMS axes are subhorizontal with variable trend, suggesting vertical uniaxial shortening. This contrast implies that strain across the plate boundary was decoupled over geologic time (Yang et al. 2013), which is consistent with but does not necessitate a low friction interface. However, the break in wedge slope trenchward of the site indicates that the horst at the JFAST site acted as a relatively highly coupled region, and therefore the coupling was spatially and temporally variable (Bose et al. 2015).

Analyses of the fractures in cores surrounding the plate-boundary fault show a narrow damage zone spanning tens of meters in which fracture orientations are highly variable with both steep reverse and low angle normal kinematics (Keren & Kirkpatrick 2016). The wide range in fracture orientations and kinematics indicates relatively large rotations of the stress field in the near field at some point in its history. These observations are consistent with a weak plate interface at the drilling site over geologic timescales.

### 3. PRE-EARTHQUAKE STRESS STATE

The state of stress in the near-trench region immediately prior to the earthquake was weakly constrained by the data available prior to JFAST. On mechanical grounds, some argued that the near toe area should be creeping (e.g., Byrne et al. 1988). The data from the dense network of on-land geodetic instruments in Japan were ambiguous and can accommodate either creeping or locked conditions at the trench prior to the Tohoku earthquake (Loveless & Meade 2011). The prior occurrence of large tsunamis from the 869 Jogan earthquake and, further north, the 1896 Sanriku earthquake implied that extremely large earthquakes were possible in this area (Sugawara et al. 2012, Tanioka & Sataka 1996).

A more direct indication of the prestress state comes from focal mechanism data. Prior to the mainshock, earthquakes in the region were predominantly thrust and consistent with a convergent stress field aligned with plate motion (Hasegawa et al. 2011). The focal mechanisms of the shallow earthquakes imply that the maximum principal stress orientation plunged 20-30° for shallow earthquakes in the megathrust zone prior to the 2011 earthquake (Hardebeck 2015, Hasegawa et al. 2011). The stress field was distinctly different from that inverted from the aftershocks, which are dominated by normal faulting earthquakes with the maximum principal stress nearly vertical (Ide et al. 2011, Wetzler et al. 2017).

Although no direct sampling of the stress field was done in the rupture area prior to the Tohoku earthquake, localized failure in ocean drilling boreholes observed in 1999, in the shallow portion of the hanging wall immediately north of the rupture, provide an indication of the horizontal stress orientations (Lin et al. 2011). The localized failures are known as breakouts, and their azimuths indicate that the maximum horizontal stress orientations were $N152°E \pm 7°$ in one borehole and $N121°E \pm 15°$ in the other. Both boreholes are in a region where the convergence direction is approximately 110° (Argus et al. 2011), which is consistent with only one of the measurements. The more northward site is the more misaligned and lies above a more seismically active region. We surmise that it is possible that the stress orientation nearest the 2011 rupture was consistent with the plate convergence direction prior to Tohoku. However, the data are not directly on the plate-boundary fault segment of interest and show sufficient heterogeneity that it is difficult to
be certain of the pre-earthquake stress state at the JFAST site based on these data alone. The
sparse and conflicting borehole data highlight the need to put greater effort into establishing pre-
earthquake in situ stress states systematically in regions where large earthquakes are expected in
the future.

An alternative route into constraining the pre-earthquake stress comes from experiments performed on the JFAST core to establish the value of the low-velocity (i.e., interseismic) friction coefficient. This quantity was measured with laboratory shear experiments in a single-direct shear device at room temperature under fluid-saturated conditions and pressures similar to the in situ values. At shear rates comparable to the long-term plate motion, the coefficient of friction of material from the plate-boundary fault was 0.24 (Ikari et al. 2015a). The low value is likely due to the high clay content of the fault zone, which is 60–80% smectite in the core (Kameda et al. 2015).

Although the commonly used form of frictional failure neglects cohesion, in principle, cohesion may be significant. The samples from JFAST allowed direct measurements of cohesion in the single-shear device by measuring the peak shear strength under a condition of zero effective normal stress (Ikari & Kopf 2011, Ikari et al. 2015b). For this fault at least, the common assumption is correct and the fault zone is nearly cohesionless; cohesion was measured as only ~0.4% of the in situ peak shear stress. The lack of fault zone cohesion can be attributed to highly developed foliation, whereas in the structureless wall rocks adjacent to the fault, high cohesion likely results from advanced silica diagenesis. This is supported by overall high levels of aqueous silica concentrations throughout the borehole and the appearance of chert at the bottom of the borehole (Chester et al. 2012).

There is some evidence that the stress or strength of the plate interface fault may have changed immediately prior to the Tohoku earthquake. Over the decade prior to the earthquake, on-land GPS velocities in Japan increased relative to North America, consistent with progressive unlocking of the plate boundary deeper than 22 km (Mavrommatis et al. 2014). The few weeks prior to the mainshock saw a strong foreshock sequence that may have promoted the mainshock by loading the hypocenter directly or through the possible occurrence of aseismic slow slip (Ito et al. 2013, 2017; Kato et al. 2012). In either case, the evidence of stress state change is near the hypocenter (<20 km depth), and there is no indication that this affects the long-term stress state prior to the earthquake near the trench at the JFAST site.

In sum, the pre-earthquake stress indicators at the JFAST site are sparse but on balance suggest a stress state consistent with the long-term convergence direction and a relatively low coefficient of friction of material (μ = 0.24) that is still perceptibly higher than what is discussed next for the coseismic state.

4. COSEISMIC STRESS STATE

The most direct constraint on the stress state during the earthquakes comes from the in situ borehole temperature observatory that was installed across the plate-boundary fault (Fulton et al. 2013). Frictional stress dissipated as heat during rupture should transiently elevate the temperature within the fault zone and diffuse into the surrounding rocks with time. The efficient insulation of the overlying ~800 m of rock ensured that at the time of drilling ~13 months after the earthquake, the heat energy was still measurable in the vicinity of the fault zone. The drilling process itself perturbs the temperature in the borehole; however, since the fault is an extensive, tabular body, it re-equilibrates with the surroundings more slowly than the small-diameter drill hole. Therefore, it was possible to measure the heat energy generated by the earthquake in the fault zone using the borehole observatory.

Heat can either diffuse from the fault zone into the surrounding formation or be advected
by fluid flow. Advection dominates only if the permeability is high enough, and therefore it is
important to constrain the permeability near the fault (Fulton et al. 2010). The time that the borehole takes to re-equilibrate with the formation at each depth provides a useful indicator of borehole fluid penetration into the formation and thus the local permeability relative to other depths. Based on these recovery time measurements, the zone around the fault had notably low permeability (Fulton et al. 2013). The inference of permeability below the threshold for advective perturbation of the fault zone heating low permeability inference was reinforced by core sample measurements (Fulton et al. 2013, Tanikawa et al. 2013). Advective heat by fluid flow is not likely to have significantly perturbed the fault.

The initially published measurements suggested that the dissipated heat energy was 27 MJ/m² with a 90% confidence interval (CI) of 19–51 MJ/m² based on the uncertainty of the thermal diffusivity inferred from the core (Fulton et al. 2013). Assuming a displacement of 50 m and an effective normal stress equal to the overburden minus hydrostatic pore pressure, the resulting median estimate of the shear stress was 0.54 MPa (0.38–1.0 MPa 90% CI), equivalent to a frictional coefficient of μ = 0.08 (0.05–0.15 90% CI). Two new pieces of information warrant revisiting this calculation: The displacement estimate was revised, and a novel method of determining seismically active faults was developed that identifies a larger suite of potential faults.

The slip in the near-trench region was revised using an elastic finite element model to interpret the deformed bathymetry and combine it with all available geodetic information (Sun et al. 2017). The average slip in the entire 40-km near trench is 62 m; based on figure 8 of Sun et al. (2017), the best estimate of slip at the JFAST site is 65 m, which is slightly above the original estimate that used a rigid body model to interpret the bathymetry changes (Fujiwara et al. 2011). See Kodaira et al. (2020) in this volume for a more complete discussion of the constraints on the near-trench slip.

The original fault identification was done based on core and borehole geophysics analyses dur-
ing and immediately after the JFAST expedition. The strongest constraint used was an apparent
temperature reversal of the deepest temperature sensor, leading to a preferred interpretation of a
fault depth of 819.8 mbsf. This depth is consistent with the changes in bedding dip and physical
properties observed in the logging while drilling data. However, recent work on thermal matu-
ration of organic material in the JFAST core samples reveals that several additional faults within
the plate-boundary zone have hosted earthquakes (Rabinowitz et al. 2013, 2015). These faults ap-
pear to have transiently experienced high temperature that permanently altered the structure of
organic compounds. Such high temperature on localized planes during the earthquake can be con-
sistent with the wider, low-temperature anomaly observed by JFAST if slip was highly localized
coseismically and then the heat diffused into the surrounding rock over the subsequent months
(Fulton et al. 2013, figure S8). The new data show that the JFAST cores contain multiple faults that
have hosted earthquakes with displacement ≥10 m, and any of these faults could have hosted the
Tohoku earthquake. It is also possible that these faults slipped in earlier earthquakes and are unre-
lated to the Tohoku event. Due to incomplete core recovery, it is also possible that other faults may
exist at depth, including perhaps the slip zone of the Tohoku event, but are not directly sampled.

These new faults can be incorporated into the interpretation of the temperature observatory
data. Faults with seismic signatures are present at the depths in **Table 1** and **Figure 2**. The upper
four of these faults are within the zone (~15-m region centered on the fault) where heat could
have diffused over the 15 months between the earthquake and drilling. Since the inversion pri-
marily constrained the total energy in this zone, the selection of any of the fault locations in this
region has a relatively minor effect on the inversion, as is quantified below. The lowermost fault
(832.86 mbsf), however, is outside this diffusive zone and would require an unrealistically high
median optimal friction of 0.64 to account for the observed temperature anomaly. This is signifi-
cantly higher than even the low-speed friction of 0.24 observed on the same materials (Ikari et al.
2015b). Therefore, it cannot be a contributor to the dissipated heat energy as measured by the
<table><caption>Table 1 Samples from the Japan Trench Fast Drilling Project (JFAST) core with biomarker anomalies interpreted as signatures of fault heating</caption><thead><tr><td>Sample number</td><td>Sample designation</td><td>Depth (mbsf)</td><td>Maximum fault thickness (m)</td></tr></thead><tbody><tr><td>PP945</td><td>343-C0019E-15R-1W, 110.5–112.5 cm</td><td>817.63</td><td>0.02</td></tr><tr><td>PP727</td><td>343-C0019E-15R-CCW, 14–15 cm</td><td>817.8</td><td>0.09</td></tr><tr><td>PP829</td><td>343-C0019E-17R-1W, 105–110 cm</td><td>822.39</td><td>0.0125</td></tr><tr><td>PP730</td><td>343-C0019E-18R-1W, 33–35 cm</td><td>824.27</td><td>0.06</td></tr><tr><td>PP952</td><td>343-C0019E-20R-2W, 49.5–51 cm</td><td>832.85</td><td>0.04</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure 2</figcaption></figure>

Summary of stratigraphic, structural, and temperature observatory constraints on the plate-boundary structures. (a) Photographs show 10-cm-long portions of representative cores. (b) A summary of core recovery through the plate-boundary zone indicates front prism units (dark gray boxes) and lower plate units (brown boxes). Panel adapted from Kirkpatrick et al. (2015). (c) A time-temperature map shows the subseafloor residual temperature field. Panel adapted from Fulton et al. (2013) with permission from AAAS. (d) A detail on the region of the diffusive zone shows the cores recovered from that zone. Arrows cutting the column indicate faults observed in cores or inferred from stratigraphic age gaps or reversals. Stars left of the column show the samples analyzed for maturity of thermal biomarkers. Red symbols and red arrows indicate seismogenic faults. Panel adapted from Rabinowitz et al. (2020). (e) A detail of the time-temperature map shows the residual temperature field in the region of the observed seismogenic faults. Panel adapted from Fulton et al. (2013) with permission from AAAS.
<table><caption>**Table 2** Best estimates of coseismic heat energy dissipation, shear stress, and coefficient of friction at the Japan Trench Fast Drilling Project (JFAST) site from the temperature measurements</caption><thead><tr><td></td><td>Median estimate</td><td>90% confidence interval<sup>a</sup></td></tr></thead><tbody><tr><td>Energy</td><td>34 MJ/m<sup>2</sup></td><td>20–86 MJ/m<sup>2</sup></td></tr><tr><td>Shear stress</td><td>0.52 MPa</td><td>0.30–1.3 MPa</td></tr><tr><td>Friction</td><td>0.08</td><td>0.05–0.19</td></tr></tbody></table>

observatory. However, it is possible that the deepest fault accounts for some of the displacement. If so, the energy measurements inferred from the observatory temperatures are still robust, but the inferred shear stress and coefficient of friction are overestimates. Similarly, if more than one of the faults inside the diffusive zone moved during the earthquake, the aggregated slip is still constrained by the seafloor observations and thus the total dissipated energy is still robust.

Assuming that each of the upper four fault depths is equally probable as a host of the Tohoku earthquake results in a revised median estimate of the energy dissipated as 34 MJ/m² (Table 2). As emphasized above, the dissipated energy is the most robust measurement from the temperature observatory and is now slightly higher than the original estimates due to the revised suite of fault depths. Since the revised displacement estimate of 65 m is larger than the original value and the overburden estimate remains essentially the same, the inferred equivalent shear stress and coefficient of friction are close to the original estimates of Fulton et al. (2013).

Additional evidence for moderate fault heating comes from measured changes in magnetic properties and mineralogy of the sediments around the faults (Yang et al. 2016, 2018). The magnetic data are consistent with thermal alteration at temperatures up to 500°C, supporting a temperature rise of up to 700–1,100°C on a fault at 821.66 mbsf (termed Fault B by Kirkpatrick et al. 2015), with a symmetrical decay in peak temperature for tens of centimeters on either side of the fault. This temperature rise would be consistent with the observed energy dissipation of displacement (Fulton et al. 2013, figure S8). For a 1-mm- to 1-cm-wide slipping zone, the dissipated energy corresponding to the magnetically inferred temperature rise is 24–70 MJ/m². Using the same assumptions as for the observatory data, this corresponds to a range of coefficient of friction of $\mu = 0.05–0.16$.

A separate constraint is provided by the magnetic mineral pyrrhotite, which appears to have formed by the decomposition of pyrite in only three regions of the core: ~697, ~720, and ~801 mbsf (Yang et al. 2018). The presence of pyrrhotite in combination with pyrite-to-pyrrhotite reaction kinetics constrains the peak temperature to between 640 and 800°C. None of these secondary faults shows any elevated temperature relative to the geotherm in the temperature observatory (Figure 3); therefore, it is likely that the mineralogy is recording heat or hot fluid flow related to a previous earthquake. The implication is that the preferred fault strand may be different for different earthquakes due to evolution of the friction or loading. These peak temperatures are consistent with moderate shear stress (0.8 MPa) assuming 25 m of slip.

Confusingly, some studies indicate that such high temperatures should have resulted in smectite decomposition, even for the very short times experienced during an earthquake (Schleicher et al. 2015). Reconciling the continued presence of smectite in the core samples with the inference of high temperature from both the magnetics and biomarkers is problematic. A plausible solution might be that the decomposition primarily involved a temporary dehydration and later

<footnote><sup>a</sup>The 90% confidence interval is based on bootstrapping the uncertainty on the thermal diffusivity, which is the largest source of uncertainty in the thermal model. The top row is the most direct result, and the results become increasingly assumption dependent from there.</footnote>
<figure><img src="image_6.png" /><figcaption>Figure 3</figcaption></figure>

Microstructures in the Japan Trench Fast Drilling Project (JFAST) cores. (a) A backscattered electron image shows scaly fabric in Core 17. Faint banding in grayscale value shows flow textures in compositionally variable clay. There are unbroken fish bones near the center. (b) Open cracks follow phacoid boundaries (due to drying) in scaly clay. (c) Clasts that are 10s micrometer-scale include volcanic lithics and glass, feldspar grains, nodules of metallic oxide, and biologic fragments. None are fractured. (d) An oxide nodule with delicate structure indicates no granular flow or deformation of clay. (e) Mudstone clast from Core 17 is crisscrossed by numerous deformation bands (distinct from similar mudstones outside the décollement zone, which have much lower abundance of deformation bands). (fg) Plane light and cross-polarized images of Fault B are near the top of Core 17; the clay fabric deflection zone is ~3 mm wide with sharp wavy fault at the base (yellow arrow). White arrows show shear direction.

rehydration of the smectite, but the issue is not yet completely resolved. Note that the same constraint does not necessarily apply to the temperature observatory data, as more distributed deformation could have created the same value of dissipated energy without a particularly high temperature rise.

Further constraints on the coseismic stress come from laboratory tests that were performed in the recovered core. The coseismic shear stress was estimated from high-velocity (1.3–3.5 m/s), large displacement rotary shear friction experiments on smectite-rich pelagic clay recovered from
a plate-boundary fault that slipped during the 2011 Tohoku earthquake (Remitti et al. 2015, Ujiie et al. 2013). The frictional behavior of the plate-boundary fault material in these experiments is characterized by a small stress drop with very low peak and steady-state friction (or shear stress), short slip weakening distance, and small fracture energy. This frictional behavior is consistent with little resistance to earthquake rupture propagation from depth through the shallow fault zone and with large coseismic displacement at shallow depths. Notably, averaging the shear stress reported in Ujiie et al. (2013) over the 50 m of slip in the experiments results in an apparent coefficient of friction of ~0.09. Similar frictional behavior was also reported from high-velocity friction experiments on smectite-rich pelagic clay retrieved from incoming sediments offshore Sanriku (Sawai et al. 2014), and such smectite-rich pelagic clay appears to be widely distributed in the north Pacific Ocean. These results suggest that the same frictional properties may apply in these other regions, where similar pelagic clay is subducted (Kameda et al. 2015, Moore et al. 2015). All high-velocity experiments with water-saturated JFAST gouges yield low friction, indicating that the fundamental result of low friction is robust regardless of the details of the process. The result is further reinforced by the engineering data collected during the drilling itself, which can be considered an in situ frictional experiment at high velocity that is also consistent with these low friction values (Ujiie et al. 2016). The rotary drill slides past the rock at velocities between 0.8 and 1.3 m/s and experiences torques equivalent to an average friction of 0.08–0.19 in the fault zone. Further qualitative evidence for very low friction during slip is provided by Keren & Kirkpatrick (2016), who interpreted minimal damage along the faults preserved in the recovered core as indicative of little frictional resistance.

The information on the specific mechanism of coseismic weakening is more complex. At high velocities, friction tests under poorly drained boundary conditions exhibit lower values of friction (or shear stress), lower axial displacement, and less shear heating in the smectite-rich gouge than tests under well-drained boundary conditions (Ujiie et al. 2013). This result was interpreted as consistent with effective work of thermal pressurization under nearly impermeable (low-drainage) conditions, which is a mechanism that is effective only when slip is sufficiently fast that the heat generated during slip is significant enough to reduce the effective normal stress in the fault zone locally (Mase & Smith 1987, Rice 2006, Sibson 1973). However, similar friction values for water-dampened gouge with the same low-drainage boundary conditions at 10 µm/s–3.5 m/s suggest that fluid trapping even at low velocities may be sufficient to generate the requisite coseismic weakening of the fault (Remitti et al. 2015); these results are consistent with low-velocity shearing tests on other saturated smectite-rich gouges at low sliding velocities (Ikari et al. 2009, Lockner et al. 2011). All high-velocity friction experiments require trapped water as an important component of the weakening process, and no such weakening is observed if shearing is slow enough that water is allowed to escape the gouge during the experiment, as was done in the low-velocity experiments of Ikari et al. (2015b). Since fluids are a significant part of the problem, permeability is likely strongly coupled to the frictional state (Tanikawa et al. 2013).

Microstructural evidence from the core itself could in principle shed light on the weakening mechanism. However, limited core recovery in the fault zone makes these inferences difficult. Rabinowitz et al. (2015) showed through trace element stratigraphic fingerprinting that some faults that were identified in cores as minor structures or as stratigraphic layers might actually have significant stratigraphic throw, even at low dip angles. This suggests that major faults were potentially missed due to core recovery and preservation and also due to cryptic appearance with little or no surrounding damage.

The core studies have not produced a definitive identification of the seismic slip surface for the 2011 earthquake. The faults that had biomarker maturity measurements consistent with significant frictional heating from M8+ earthquakes were discovered both above and below the
previously identified décollement zone (Rabinowitz et al. 2020), that like many faults, the Japan plate boundary does not always rerupture along the same interface (Savage & Brodsky 2011). It is useful to note that all these analyzed faults lie within an ~12-m-thick zone, so the space between them would be indistinguishable to active or passive source seismology.

Nonetheless, a number of thin faults have been identified with the seismically identified décollement zones marked in **Figure 4** that are candidates for the 2011 event or other earthquakes. Four discrete faults were identified in the core in the vicinity of the seismically identified

<figure><img src="image_7.png" /><figcaption>Figure 4</figcaption></figure>

Comparison of faults and fractures identified by multiple methods for two depth intervals at site C0019, from 690 to 730 mbsf in the frontal prism (a) and from 760 to 835 mbsf across the plate boundary décollement (b). Methods used to identify faults and fractures include stratigraphic inversions or omissions inferred from biostratigraphy to infer radiolarian age (Chester et al. 2012), meteoric ¹⁰Be concentrations and ¹⁰Be ages (Regalla et al. 2019), and trace element geochemistry (Rabinowitz et al. 2015); conductive fractures inferred from fluid flow and thermal anomalies (Fulton et al. 2013, Fulton & Brodsky 2016); faults and fractures identified by visual core description (Chester et al. 2012); and borehole resistivity images (Chester et al. 2012). Fault B discussed in the text is within the seismically identified décollement zone as marked (Kirkpatrick et al. 2015). Abbreviation: mbsf; meters below seafloor.
<table><caption>**Table 3** Constraints on coseismic seismic friction</caption><thead><tr><td>Data type</td><td>Inferred coefficient of friction μ</td></tr></thead><tbody><tr><td>Observatory temperature data<sup>a</sup></td><td>0.08 (90% confidence interval 0.05–0.19)</td></tr><tr><td>High-velocity experiments<sup>b</sup></td><td>0.03–0.09</td></tr><tr><td>Drilling torques<sup>c</sup></td><td>0.08–0.19</td></tr><tr><td>Magnetics<sup>d</sup></td><td>0.05–0.16</td></tr></tbody></table>

décollement. The sharpest intact (undamaged by drilling) fault in Core 17 is Fault B. Transmission electron microscopy studies of Fault B revealed a thin layer of amorphous material of identical composition to the surrounding smectites, potentially recording thermal decomposition or melting of the sediment on Fault B. Unfortunately, due to limited sampling, Rabinowitz et al. (2020) were unable to test samples of Fault B, potentially the best candidate for the 2011 rupture surface within the recovered long-term décollement zone.

In summary, all available evidence points to low friction during earthquake slip. The quantitative evidence from the temperature observatory data, high-speed laboratory experiments, drilling data, and magnetic data all result in an overlapping range of coseismic friction between 0.05 and 0.09 (Table 3). The evidence for the specific mechanism of weakening is less conclusive. If the rupture propagated along the fault was recognized as the plate-boundary fault, the high clay content and resulting low permeability mean thermal pressurization likely played a role, but the microstructural studies and laboratory data leave other possibilities such as thermal decomposition, amorphitization, dynamic reduction of normal stress, and local melting open as well.

## 5. POSTEARTHQUAKE STRESS

Several studies have concluded that the Tohoku earthquake completely released the convergence-parallel shear stress on the fault based on both the abundance of normal faulting aftershocks and seafloor surveys showing extensional failure on normal faults (Asano et al. 2011, Ide et al. 2011, Kato et al. 2011, Tsuji et al. 2011). The normal faulting guiding these studies is almost entirely in the overlying wedge. Apart from the drilling data, evidence about the stress state near the fault is only indirectly inferred by observing the absence of thrusting aftershocks on the plate boundary and assessing the force balance required to allow extension in the overriding wedge.

The stress state at the end of the earthquake on the fault locally is more directly constrained by the borehole breakouts observed at the JFAST site (Lin et al. 2013, Brodsky et al. 2017). The azimuth of the breakouts indicates that the orientation of the maximum horizontal stress is 28° from the convergence direction. Although a convergence-parallel orientation cannot be ruled out by the data, it is not the optimal solution. The misorientation suggests stress changes during the earthquake that are comparable to the ambient stress.

Additional information on the stress state comes from combining the width of the breakouts with measurements of rock strength conducted both shipboard and in the laboratory. All possible solutions of the data that utilize available laboratory constraints on rock strength and account for the effects of all three principle stresses on failure through a Modified Wiebols-Cook failure criterion (Zoback 2007) require that the system was in a normal faulting regime 14 months after

<footnote><sup>a</sup>Data from Fulton et al. (2013) with modifications as discussed in the text.</footnote>

<footnote><sup>b</sup>Data from Ujiie et al. (2013) and Remitti et al. (2015).</footnote>

<footnote><sup>c</sup>Data from Ujiie et al. (2016).</footnote>

<footnote><sup>d</sup>Data from Yang et al. (2016) with extensions as discussed in the text.</footnote>
the 2011 Tohoku earthquake, i.e., the subvertical stress is the maximum principal stress (Lin et al. 2013, Brodsky et al. 2017). This inference of a normal faulting regime is consistent with the normal faulting in the hanging wall discussed above (Kato et al. 2011, Tsuji et al. 2011).

Progressing from thrust faulting prior to the earthquake to normal faulting after the earth-
quake implies total stress drop or perhaps even overshoot. The best-fit solution for the breakouts
results in a final shear stress of 0.33 MPa resolved on the fault plane in the direction opposite of the
slip during the earthquake (Brodsky et al. 2017). Note that the plunge of the maximum principal
stress could be 8° from vertical with just as satisfactory a fit to the observed widths; therefore, there
is a fundamental ambiguity in the direction of the resolved shear stress on the fault. Nonetheless,
it is useful to explore the best-fit solution. Although the magnitude of the best-fit final stress is
consistent with the high-velocity laboratory experiments (Remitti et al. 2015, Ujiie et al. 2013), the
orientation requires that the shear stress passed through zero and therefore was transiently below
the laboratory values of shear strength. Even the extreme frictional weakening seen in the labo-
ratory experiments is apparently only part of the process governing the local forces on the fault.
Other contributors could include normal stress reduction due to the inertial dynamics and bima-
terial effects (Kozdon & Dunham 2013, Lotto et al. 2017). Regardless of the cause, the breakout
data strongly suggest that the 2011 Tohoku earthquake reset the local stress field.

Additional evidence for a complete stress drop is provided by a nearly trivial observation. The borehole did not collapse during the 9-month temperature deployment. The entire temperature string was recovered, which indicates that the borehole could not have substantially deformed during the deployment. Therefore, no afterslip occurred on the fault at this site despite geodetic evidence for afterslip elsewhere (Tomita et al. 2017). If the stress drop was incomplete, afterslip might have been expected as the velocity-strengthening material continued to be stressed. The lack of afterslip is further evidence for a complete stress drop.

After the earthquake, the system must continue to evolve as it heal, restrengthen, and ulti-
mately prepares for the next earthquake. JFAST provided a surprising insight into the dynamics
of this process. The temperature observatory was left in the borehole for 9 months to sufficiently
equilibrate with the host rock. In the middle of this deployment, an M7.3 earthquake nearby the
site generated a series of temperature pulses that traveled up and down the borehole (Fulton &
Brodsky 2016). These pulses appear to be generated by the advection of heat by fluids that are
driven through discrete faults and fractures within the damage zone by the 7.3 earthquake and
its aftershocks. The locations are consistent with stratigraphy from ¹⁰Be that identifies faults at
760 and 778 mbsf (Regalla et al. 2019) (Figure 4). After a couple of weeks, the fault zone appears
to heal and becomes less susceptible to fluid pulsing, even from comparable forcing to some of
the initial aftershocks. We conclude both that damage is strongly coupled to the hydrological state
and, by implication, the stress state of the fault and that the damaged state can be quickly overcome
by the healing fault.

Healing also affects friction. **Figure 5** shows slide-hold-slide tests conducted on a disaggre-
gated sample of the fault zone from Site C0019 that exhibit power law–style healing. Such time-
dependent strengthening could be significant in the Tohoku fault zone; however, it is important to
also consider mesoscale healing processes such as fracture closure, sealing, and fabric formation.

6. ENERGY BALANCE CONSTRAINTS

Earthquakes release elastic energy stored in the tectonic plate. That released energy is then either
radiated as seismic waves or absorbed into dissipative processes such as friction, grain breakage,
chemical reactions, fracture of surrounding rocks, or plastic deformation (Kanamori & Brodsky
2004, Shipton et al. 2006). The energy budget can potentially tell us which of these processes
<figure><img src="image_8.png" /><figcaption>Figure 5</figcaption></figure>

Frictional healing (Δμ) as a function of hold time in laboratory slide-hold-slide experiments using a sample of the plate-boundary fault zone (Core 17R-1) recovered during the Japan Trench Fast Drilling Project (JFAST) following the methods described in Ikari et al. (2016).

are important in governing the rupture dynamics. In particular, is friction the most important energy sink, or are the other dissipative processes required to reconcile the energy budget of the earthquake? The JFAST measurements of thermal energy provide an opportunity to explore the energy budget.

Since the JFAST data are focused on a single site, we need to take a control volume approach and consider the flow of energy into the site as balanced by dissipative processes locally. This approach is different than the more common calculation of the global energy budget over the entire rupture plane (Kanamori & Rivera 2006). Fortunately, calculation of the energy flux into the crack tip is foundational to linear elastic fracture mechanics, and powerful methods exist to perform this calculation (Broberg 1999, Freund 1998).

Modeling the site as the edge of a shear crack that has propagated from the hypocenter, we can find the energy release rate G delivered to the site based on the stress drop on the fault, the rupture velocity, and the length of the rupture at the JFAST site. Note that energy release rate in fracture mechanics quantifies the flow of strain and kinetic energy from the surrounding solid into the crack tip per unit fault area ruptured, which is used to propel the crack forward. The term rate refers to the energy released per area rather than per time.

The elastic energy release is balanced by the dissipative processes. Since the fracture tip is massless, it has no momentum (Freund 1998). Inertia enters the problem in the form of a dimensionless dynamic correction factor g(V) to the static energy release rate, which decreases from 1 at V=0 to 0 at the limiting rupture velocity, which is the Rayleigh wave speed for a crack advancing in locally plane strain conditions.
To summarize, for a homogeneous, isotropic whole space,

$$G = G_0 g(V) = E_{dissip}, \qquad 1.$$

where $G_0$ is the energy per unit fault area that flows into the crack tip if the velocity instantly drops to 0, $g(V)$ is the dynamic correction factor that is a function of the rupture velocity, and $E_{dissip}$ is the sum of dissipative processes in excess of the work per unit fault area done against residual strength (Broberg 1999, Palmer & Rice 1973). Since the residual stress is very small at the JFAST site (see Section 8), here we can interpret $E_{dissip}$ as the sum of all the dissipative processes.

We estimate a range of plausible values of $G_0$ based on solutions to the stress intensity factor for geometries approximating the Tohoku fault. We perform a first approximation using a plane strain crack that has the same difference between initial and final stress everywhere,

$$G_0 = (1 - \nu) \pi a (\sigma_0 - \sigma_f)^2 / 2 E_s, \qquad 2.$$

where $a$ is half the crack length, $\sigma_0$ is the initial stress, $\sigma_f$ is the final stress, $E_s$ is shear modulus, and $\nu$ is the Poisson's ratio (Broberg 1999, Kanamori & Brodsky 2004).

We also consider a crack with stress drop varying along the rupture. In this case, the energy release rate is influenced more strongly by the stresses locally than earlier in the rupture. A suitable approximation is the solution for a semi-infinite crack in a whole space with nonzero stress drop over a distance $2a$ behind the tip:

$$G_0 = \frac{(1 - \nu)}{\pi E_s} \left( \int_{0}^{2a} \frac{\sigma_0(x) - \sigma_f(x)}{\sqrt{2a - x}} dx \right)^2 \qquad 3.$$

(Fossum & Freund 1975, Kozdon & Dunham 2013). One of the most important simplifications in Equation 3 is the neglect of the complex geometry of a subduction zone. In particular, the free surface can reflect energy, thus potentially making it more available to assist in propagation than implied by Equation 3. Nonetheless, we proceed to use Equation 3 as a useful approximation for $G_0$.

We now proceed to estimate the parameters of Equations 2 and 3 based on observations of the Tohoku earthquake. The stress drop $\sigma_0 - \sigma_f$ in Equation 2 or $\sigma_0(x) - \sigma_f(x)$ inside the integral in Equation 3 is characterizing the stress drop along the entire slipped part of the fault plane downdip of the site. No knowledge of the final stress is required at any location other than the JFAST site. The average stress drops inferred seismologically for the complete rupture range from 1 to 20 MPa (Lay 2017). The average stress drop for models that include all moments within the 5-m slip contour is 2 MPa (Brown et al. 2015). Since 2 MPa is at the low end of the seismological estimate and will therefore result in a low estimate of $G_0$, we use this value for the rest of these calculations and return to this assumption at the end of this section.

Perhaps coincidentally, the JFAST and seismological data agree. If the stress drop at the JFAST site is complete (see Section 8), the stress drop here can be estimated as $\mu_s\sigma_n$, where $\mu_s$ is the low-velocity laboratory measurement of the static friction (0.24) and $\sigma_n$ is the effective normal (vertical) stress (6.8 MPa). The resulting inferred stress drop is also 2 MPa.

The crack length is approximated as the distance from the hypocenter—that is, approximately 100 km. The rupture is certainly not a simple expanding crack, and a fuller numerical model can account for variations in slip over the complex rupture that continues throughout the process. The crack length approximation used here is based on the fact that the length of the earthquake rupture controls the scale over which elastic energy has been released by the time
the rupture reaches the trench. Equation 3 in particular recognizes that the stress change needs to be integrated over this large distance to obtain the total energy released.

The shear modulus is the most straightforward parameter to estimate directly from the JFAST data. Jeppson et al. (2018) measured the shear modulus in the core to be 1–2 GPa and the Poisson’s ratio to be 0.4.

Using these values, we find a minimum bound estimate for $G_0$ of 92 MJ/m² from the approximation of Equation 2 and the maximum shear modulus (2 GPa). We find an upper bound of 300 MJ/m² from Equation 3 with the minimum shear modulus (1 GPa). We conclude that 92–300 MJ/m² is a range of plausible values of $G_0$.

The last step in estimating the energy release rate $G$ is to account for energy unavailable for rupture propagation due to inertial effects (see Equation 1). The dynamic correction factor $g(V)$ decreases from unity at low velocity to 0 as the local rupture velocity approaches the Rayleigh wave velocity (Freund 1998). In this case, $g(V)$ is poorly constrained. We therefore consider the limiting case of a slow rupture with $g(V) = 1$ and a rapid rupture with $g(V) = 0.5$. This range of $g(V)$ combined with the range of $G_0$ and Equation 1 results in values of $G$ of 46–300 MJ/m².

We now turn to the dissipative constraints on Equation 1. The temperature observatory directly constrained the energy dissipated on the fault plane by frictional heating, and the correspondingly low stress is corroborated by the magnetic and laboratory data. Using the revised interpretation of the temperature data, we find that the preferred value of $E_{dissip}$ is 34 MJ/m² (20–86 MJ/m² 90% CI). This range overlaps with the range of plausible values of $G$ (46–300 MJ/m²) and importantly does not exceed it. This is a reassuring result that the energy balance as considered here is physically consistent and reasonable. There is sufficient energy delivered to the site to account for the frictional energy inferred.

Although the ranges of $G$ and the frictional energy overlap, a significant range of plausible values of $G$ exceeds the observed thermal energy. If $G$ exceeds the observed frictional heat, then some energy must be consumed by off-fault processes such as plastic or other permanent deformation of the surrounding medium. The presence of folds and other geological structures in the wedge indicates that such permanent deformation must have happened over multiple earthquake cycles (Keren & Kirkpatrick 2016). Tsuji et al. (2013) also provide evidence of significant coseismic damage in the wedge. Plastic deformation should also result in dissipated heat energy, but that energetic signal is distributed over a broad region and is distinct from the fault zone thermal energy observed here.

The conservatively small value of the seismologically constrained stress drop (2 MPa) used for this calculation results in low estimates of $G$. Any larger values of stress drop would increase the discrepancy between $G$ and the thermal energy, thus demanding more off-fault dissipation.

Note that energetically significant off-fault plastic deformation over a broad area violates the core assumption of linear elastic fracture mechanics that all nonelastic processes are confined to a small region near the rupture. Although recent work has shown that ruptures in the presence of plasticity can still be surprisingly similar to the predictions of linear elastic fracture mechanics (Andrews 2005, Dunham et al. 2011), we must remain cautious when using analytical expressions with strong simplifying assumptions such as Equations 2 and 3.

## 7. STRESS EVOLUTION

The geophysical, geological and experimental results presented in this review have provided estimates for the pre-, co-, and postseismic stress on the shallow portion of the fault. The combined constraints are illustrated in Figure 6. The initial and final stress states are measured directly from
<figure><img src="image_9.png" /><figcaption>Figure 6</figcaption></figure>

Shear stress resolved on the Tohoku earthquake fault. The dots are the initial and final stress constrained by the low-velocity friction experiments and analyses of wellbore breakouts, respectively. The dotted dark blue line is a linear fit between the initial and final states and is not a physical solution, as discussed in the text. The dashed light blue line is a possible stress path that satisfies integral constraint of the energy data with a 0 shear stress at the infinite slip and a sudden drop in stress to a negative value as suggested by the breakout data. The solid blue line also satisfies the integral constraint and maintains the maximum possible frictional stress at the end of the earthquake. The red line allows for negative slip.

the low-velocity friction experiments that yield an estimate of the static stress and the breakouts, respectively.

The simplest apparent path between the initial and final states is a straight line (dotted line in **Figure 6**). This path, however, is not permissible for two distinct reasons. The integral of stress over displacement for this path results in a total dissipated energy of 48 MJ/m², assuming that both the positive and negative shear stresses dissipate energy. However, such a path would allow for no elastic energy to be radiated. A second problem with the linear path is that it demands positive slip during negative shear stress. Friction is required to operate in the direction opposite slip.

To develop a simple model consistent with all known data, we modify an exponential relationship similar to Rice (2006) to include overshoot. We assume that the slip occurs entirely while the stress is favorable, and then the overshoot occurs at the end of the rupture. For instance, if the fault opens during the rupture, normal stress is reduced dynamically and then the resolved shear stress can be reversed when the sides of fault slam shut at the end of the earthquake. This scenario is schematically captured by modeling the shear stress σ as a function of slip S following the form

$$ \sigma = (\sigma_0 - \sigma_{dyn})\exp(-S/D) + \sigma_{dyn} \quad \begin{array}{l} S < \text{Final Slip} \\ S \ge \text{Final Slip,} \end{array} \quad 4. $$

where σ₀ is the initial shear stress, σₕdyn is the final dynamic stress, and D is a slip weakening distance to be fit. We constrain the initial shear stress on the fault using the observed low-velocity friction (0.24) and using overburden and assuming hydrostatic pore pressure. We can then integrate Equation 4 with respect to slip and set it equal to the observed dissipation (34 MJ/m²) to
solve for *D*. We assume initially that $\sigma_{fdyn}$ is the minimum value (i.e., 0), which is consistent with the above discussion of the plausibility of slip at negative stresses. We revisit this assumption shortly.

The resulting value of the slip weakening distance *D* is 21 m, and the corresponding slip function is shown by the dashed line in **Figure 5**. This large value of *D* is consistent with models of temperature-induced dynamic weakening and is similar to those inferred from seismic energy balances (Abercrombie & Rice 2005, Viesca & Garagash 2015). Like in the seismological work, the slip weakening distance is inferred to be a significant fraction of the final slip. In other words, weakening persists throughout the rupture process. However, seismological studies are bandwidth limited and therefore prone to bias results to larger slip distances (Kanamori & Brodsky 2004). Moreover, the method of inferring the energy balance from the seismological data is prone to creating a spurious increase in slip weakening because the energy balance for a dynamically unstable crack in a homogeneous, infinite space will always require that the elastic energy consumed increases as $L^3$, where *L* is the crack length (Freund 1998). If the only sink of this energy is friction on the fault plane, then the dissipation is proportional to the area of the fault plane (i.e., $L^2$) multiplied by friction. In order to maintain the balance, the frictional stress drop must be proportional to *L* (i.e., friction decreases with fault rupture length) or equivalently slip. An alternative solution is to include off-fault dissipation from damage and plastic deformation. The region affected by these processes also scales as *L* and thus can naturally provide an alternative explanation (Andrews 2005). Thus, the seismological fracture energy constraint is not necessarily a strong constraint on the slip weakening distance, and the consistency with the drilling data is not by itself a reason to accept the model of an exponential decaying stress.

We can also explore larger values of $\sigma_{fdyn}$, which result in correspondingly shorter slip weakening distances to meet the energy balance constraint. The largest possible value of $\sigma_{fdyn}$ that allows the energy constraint to be met with the stress following the functional form of Equation 4 is 0.52 MPa, which corresponds to a dynamic friction of 0.075 and a slip weakening distance *D* of 0.2 m (solid blue line in **Figure 5**). Such extreme, rapid weakening is permitted by the JFAST data. Note that the high-speed laboratory friction experiment data do in fact show such extreme slip weakening with the final frictional stress being reached in <1 m (Ujiie et al. 2013). In this case, the apparent increase in $D_c$ seen in seismological models of large earthquakes is not supported by the frictional data. This interpretation therefore favors off-fault plasticity as a major source of the dissipation inferred by seismological models.

Another possibility is slip reversal. For instance, the red line in **Figure 5** shows slip extended 20% further than the final value and then reversed direction. This curve is also designed to be consistent with the temperature-integral constraint. Backward slip is not normally considered as a plausible scenario but is actually fully consistent with the extreme weakening suggested here. If the final stress is negative, as suggested by the breakout data, backward slip seems likely in the final stages of rupture.

These three models (exponential weakening, rapid weakening, and slip reversal) are all possible based on the thermal and static friction data. The slip reversal is slightly preferred, as it is consistent with the breakout data as well. There is also some supporting evidence for the rapid weakening model from high-speed laboratory experiments. The simplest and most commonly used linear slip weakening law is not supported by the JFAST data.

All three models require that the stress during rupture violates Byerlee's law. Moreover, simply beginning with a weak material such as clay is not sufficient to meet the energy constraint. The stress on the fault must drop during rupture as well.

This requirement of extreme weakening is borne out by more complex dynamic rupture models. Kozdon & Dunham (2013) did not incorporate extreme weakening and predicted energy dissipation of 190 MJ/m² at the JFAST site (Kozdon & Dunham 2013), which is well above
the 34 MJ/m² that best fits the temperature data. A dynamic model incorporating thermal pressurization has dissipated energy of 133 MJ/m² (Hirono et al. 2016, 2019), which still exceeds the dissipation as observed but is less of a discrepancy. Dynamic rupture models can achieve high slip near the toe by incorporating the full inertia of the system even with rate-strengthening materials (Hirono et al. 2016, Lotto et al. 2017); however, the JFAST temperature constraints cannot be met without extreme weakening.

The reduction of stress also means that there was a near-complete release of strain energy. This energy drop, rather than stress drop, is a key feature of the earthquake. If the prestress is in the convergence direction as suggested by the static friction values, then elastic energy was released locally. This energy is no longer available to generate earthquakes, and elastic energy will not be stored again until the toe is locked and reloaded. In principle another plate-rupturing earthquake could occur driven by deeper strain energy release even after the strain energy at the toe is fully released. However, the intraplate aftershocks that usually accompany the M > 7 earthquakes that break through to the seafloor suggest that rupture of the toe is generally accompanied by a stress reversal (Wetzler et al. 2017). If stress reversal is an intrinsic characteristic of breakthrough earthquakes, then plate motion and fault healing must recharge the system before another shallow earthquake can occur. This required passage of time would make earthquakes, at least in a very modest sense, predictable.

## 8. CONCLUSIONS

The Tohoku earthquake is the first earthquake to have been observed in such detail with data sets that directly constrain the fault properties and in situ stress state before, during, and after the earthquake. Using these data in combination with the seafloor and land-based geophysical observations has finally placed us in a position to determine the complete history of stress on the fault in at least one location.

Most importantly, the data robustly show that Byerlee's law is not applicable at the JFAST site. The material of the fault had both a lower static friction than Byerlee's law and a lower stress on the fault during rupture. No dynamic rupture model to date can match the thermal energy constraint without some form of weakening during slip. The acceptance of strong dynamic weakening as an integral part of earthquake physics closes one set of questions on strong versus weak faults and reinvigorates the quest for finding the balance on a single fault. Since both strong and weak areas are now required to explain rupture, what fraction of the fault is strong and what fraction is weak?

Dynamic friction also frames seismic hazard fundamentally differently. Models have already begun to explore the circumstances under which single earthquakes can weaken barriers and hop onto new fault segments (Noda & Lapusta 2013). For instance, a California-wide earthquake is plausible in these models, although geological evidence for such a historic rupture has yet to be found (Harris 2017). Even studies of human-induced earthquakes are obligated to consider dynamic weakening as a mechanism to make an unexpectedly large event (Galis et al. 2017).

A secondary and tantalizing conclusion comes from the comparison of the limited data on the earthquake prestress and poststress. The comparison suggests a complete stress drop at this location with overshoot during rupture. Overshoot is consistent with all known constraints and is therefore the preferred interpretation of the data currently. If pervasive over the fault, overshoot would imply that large earthquakes completely reset the earthquake cycle and thus provide a window of comparative safety on this fault. However, the prestress data are limited, and this frustrating ambiguity highlights the need to systematically measure stress on major faults to capture the situation prior to major earthquakes. JFAST demonstrated that large-scale, technically demanding science can be a successful approach to earthquake physics. The strong support of international
funding agencies, long-term investment in infrastructure, and a focused work plan on a single question made it possible. We can continue with this strategy and hopefully make a little progress before the next devastating earthquake.

## DISCLOSURE STATEMENT

J.S. received funding from IODP and USSSP to support drilling-related research. The other authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.

## AUTHOR CONTRIBUTIONS

E.E.B. and J.J.M. are the primary authors of this review. E.M.D., P.M.F., M.J.I., J.K., Y.N., H.S.R., C. Regalla, F.R., C. Rowe, D.M.S., H.M.S., T.S., and K.U. provided text and figures for this review. L.A., F.M.C., M.C., N.E., R.H., T.H., T.I., T.J., Y.K., S.K., W.L., S.S., J.S., Y.S., S.T., M.W.-S., and T.Y. provided analyses and edits.

## ACKNOWLEDGMENTS

We gratefully acknowledge the crew of the *Chikyu*; support staff at JAMSTEC; staff of IODP; and funders of IODP, including MEXT, NSF, and ECORD, who made this expedition possible. E.E.B.'s work on this manuscript was supported in part by the Gordon and Betty Moore Foundation grant 3289.

## LITERATURE CITED

* Abercrombie RE, Rice JR. 2005. Can observations of earthquake scaling constrain slip weakening? *Geophys. J. Int.* 162(2):406-24

* Anderson EM. 1951. *Dynamics of Faulting and Dyke Formation with Applications to Britain*. London: Oliver & Boyd. 2nd ed.

* Andrews DJ. 2005. Rupture dynamics with energy loss outside the slip zone. *J. Geophys. Res.* 110(B1):B01307

* Argus DF, Gordon RG, DeMets C. 2011. Geologically current motion of 56 plates relative to the no-net-rotation reference frame. *Geochem. Geophys. Geosyst.* 12(11):Q11001

* Asano Y, Saito T, Ito Y, Shiomi K, Hirose H, et al. 2011. Spatial distribution and focal mechanisms of after-shocks of the 2011 off the Pacific coast of Tohoku Earthquake. *Earth Planets Space* 63(7):669-73

* Bose S, Saha P, Mori JJ, Rowe C, Ujiie K, et al. 2015. Deformation structures in the frontal prism near the Japan Trench: insights from sandbox models. *J. Geodyn.* 89:29-38

* Broberg KB. 1999. *Cracks and Fracture*. San Diego: Academic

* Brodsky EE, Saffer D, Fulton P, Chester F, Conin M, et al. 2017. The postearthquake stress state on the Tohoku megathrust as constrained by reanalysis of the JFAST breakout data. *Geophys. Res. Lett.* 44(16):8294-302

* Brown L, Wang K, Sun T. 2015. Static stress drop in the $M_w$ 9 Tohoku-oki earthquake: heterogeneous distribution and low average value. *Geophys. Res. Lett.* 42(24):10595-600

* Byerlee J. 1978. Friction of rocks. In *Rock Friction and Earthquake Prediction*, ed. JD Byerlee, M Wyss, pp. 615-26. Basel, Switz.: Birkhäuser

* Byrne DE, Davis DM, Sykes LR. 1988. Loci and maximum size of thrust earthquakes and the mechanics of the shallow region of subduction zones. *Tectonics* 7(4):833-57

* Chester FM, Mori JJ, Toczko S, Eguchi N, Kido Y, et al. 2012. *Integrated Ocean Drilling Program expedition 343/343T preliminary report, Japan Trench Fast Drilling Project (JFAST)*, 1 April–24 May 2012 and 5–19 July 2012. Prelim. Rep. 343, Integrated Ocean Drilling Program, College Station, TX

* Chester FM, Rowe C, Ujiie K, Kirkpatrick J, Regalla C, et al. 2013. Structure and composition of the plate-boundary slip zone for the 2011 Tohoku-Oki earthquake. *Science* 342(6163):1208-11
Collettini C, Sibson RH. 2001. Normal faults, normal friction? *Geology* 29(10):927–30

Di Toro G, Han R, Hirose T, De Paola N, Nielsen S, et al. 2011. Fault lubrication during earthquakes. *Nature* 471(7339):494–98

Dieterich JH. 1992. Earthquake nucleation on faults with rate-dependent and state-dependent strength. *Tectonophysics* 211(1–4):115–34

Dunham EM, Belanger D, Cong L, Kozdon JE. 2011. Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity, Part 1: planar faults. *Bull. Seismol. Soc. Am.* 101(5):2296–307

Fossum AF, Freund LB. 1975. Nonuniformly moving shear crack model of a shallow focus earthquake mechanism. *J. Geophys. Res.* 80(23):3343–47

Freund LB. 1998. *Dynamic Fracture Mechanics*. Cambridge, UK: Cambridge Univ. Press

Fujiwara T, Kodaira S, No T, Kaiho Y, Takahashi N, Kaneda Y. 2011. The 2011 Tohoku-Oki earthquake: displacement reaching the trench axis. *Science* 334(6060):1240

Fulton PM, Brodsky EE. 2016. *In situ* observations of earthquake-driven fluid pulses within the Japan Trench plate boundary fault zone. *Geology* 44(10):851–54

Fulton PM, Brodsky EE, Kano Y, Mori J, Chester F, et al. 2013. Low coseismic friction on the Tohoku-Oki fault determined from temperature measurements. *Science* 342(6163):1214–17

Fulton PM, Harris RN, Saffer DM, Brodsky EE. 2010. Does hydrologic circulation mask frictional heat on faults after large earthquakes? *J. Geophys. Res.* 115(B9):B09402

Fulton PM, Saffer D, Harris R, Bekins B. 2004. Re-evaluation of heat flow data near Parkfield, CA: evidence for a weak San Andreas Fault. *Geophys. Res. Lett.* 31(15):L15S15

Galis M, Ampuero JP, Mai PM, Cappa F. 2017. Induced seismicity provides insight into why earthquake ruptures stop. *Sci. Adv.* 3(12):eaap7528

Hardebeck JL. 2015. Stress orientations in subduction zones and the strength of subduction megathrust faults. *Science* 349(6253):1213–16

Harris RA. 2017. Large earthquakes and creeping faults. *Rev. Geophys.* 55(1):169–98

Hasegawa A, Yoshida K, Okada T. 2011. Nearly complete stress drop in the 2011 $M_w$ 9.0 off the Pacific coast of Tohoku Earthquake. *Earth Planets Space* 63(7):35

Hirono T, Tsuda K, Kaneki S. 2019. Role of weak materials in earthquake rupture dynamics. *Sci. Rep.* 9(1):6604

Hirono T, Tsuda K, Tanikawa W, Ampuero J-P, Shibazaki B, et al. 2016. Near-trench slip potential of megaquakes evaluated from fault properties and conditions. *Sci. Rep.* 6:28184

Ide S, Baltay A, Beroza GC. 2011. Shallow dynamic overshoot and energetic deep rupture in the 2011 $M_w$ 9.0 Tohoku-Oki earthquake. *Science* 332(6036):1426–29

Ikari MJ, Carpenter BM, Vogt C, Kopf AJ. 2016. Elevated time-dependent strengthening rates observed in San Andreas Fault drilling samples. *Earth Planet. Sci. Lett.* 450:164–72

Ikari MJ, Ito Y, Ujiie K, Kopf AJ. 2015a. Spectrum of slip behaviour in Tohoku fault zone samples at plate tectonic slip rates. *Nat. Geosci.* 8(11):870–74

Ikari MJ, Kameda J, Saffer DM, Kopf AJ. 2015b. Strength characteristics of Japan Trench borehole samples in the high-slip region of the 2011 Tohoku-Oki earthquake. *Earth Planet. Sci. Lett.* 412(C):35–41

Ikari MJ, Kopf AJ. 2011. Cohesive strength of clay-rich sediment. *Geophys. Res. Lett.* 38(16):L16309

Ikari MJ, Saffer DM, Marone C. 2009. Frictional and hydrologic properties of clay-rich fault gouge. *J. Geophys. Res.* 114(B5):B05409

Ito Y, Hino R, Kido M, Fujimoto H, Osada Y, et al. 2013. Episodic slow slip events in the Japan subduction zone before the 2011 Tohoku-Oki earthquake. *Tectonophysics* 600:14–26

Ito Y, Ikari MJ, Ujiie K, Kopf A. 2017. Coseismic slip propagation on the Tohoku plate boundary fault facilitated by slip-dependent weakening during slow fault slip. *Geophys. Res. Lett.* 44(17):8749–56

Jeppson TN, Tobin HJ, Hashimoto Y. 2018. Laboratory measurements quantifying elastic properties of accretionary wedge sediments: implications for slip to the trench during the 2011 $M_w$ 9.0 Tohoku-Oki earthquake. *Geosphere* 14(4):1411–24

Kameda J, Shimizu M, Ujiie K, Hirose T, Ikari M, et al. 2015. Pelagic smectite as an important factor in tsunamigenic slip along the Japan Trench. *Geology* 43(2):155–58

Kanamori H, Anderson D. 1975. Theoretical basis of some empirical relations in seismology. *Bull. Seismol. Soc. Am.* 65(5):1073–95

Kanamori H, Brodsky EE. 2004. The physics of earthquakes. *Rep. Prog. Phys.* 67:1429
Kanamori H, Rivera L. 2006. Energy partitioning during an earthquake. *Geophys. Monogr. Ser.* 170:3–13

Kaneko Y, Avouac J-P, Lapusta N. 2010. Towards inferring earthquake patterns from geodetic observations of interseismic coupling. *Nat. Geosci.* 3(5):363–69

Kato A, Obara K, Igarashi T, Tsuruoka H, Nakagawa S, Hirata N. 2012. Propagation of slow slip leading up to the 2011 M<sub>w</sub> 9.0 Tohoku-Oki earthquake. *Science* 335(6):705–8

Kato A, Sakai S, Obara K. 2011. A normal-faulting seismic sequence triggered by the 2011 off the Pacific coast of Tohoku earthquake: wholesale stress regime changes in the upper plate. *Earth Planets Space* 63(7):745–48

Keren TT, Kirkpatrick JD. 2016. The damage is done: low fault friction recorded in the damage zone of the shallow Japan Trench décollement. *J. Geophys. Res. Solid Earth* 121(5):3804–24

Kirkpatrick JD, Rowe CD, Ujiie K, Moore JC, Regalla C, et al. 2015. Structure and lithology of the Japan Trench subduction plate boundary fault. *Tectonics* 34(1):53–69

Kodaira S, Fujiwara T, Fujie G, Nakamura Y, Kanamatsu T. 2020. Large coseismic slip to the trench during the 2011 Tohoki-Oki earthquake. *Annu. Rev. Earth Planet. Sci.* 48:321–43

Kozdon JE, Dunham EM. 2013. Rupture to the trench: dynamic rupture simulations of the 11 March 2011 Tohoku earthquake. *Bull. Seismol. Soc. Am.* 103(2B):1275–89

Lachenbruch A, Sass J. 1980. Heat-flow and energetics of the San-Andreas Fault Zone. *J. Geophys. Res.* 85(B11):6185–222

Lay T. 2017. A review of the rupture characteristics of the 2011 Tohoku-oki Mw 9.1 earthquake. *Tectonophysics* 733:4–36

Lin W, Conin M, Moore JC, Chester FM, Nakamura Y, et al. 2013. Stress state in the largest displacement area of the 2011 Tohoku-oki earthquake. *Science* 339(6):687–90

Lin W, Saito S, Sanada Y, Yamamoto Y, Hashimoto Y, Kanamatsu T. 2011. Principal horizontal stress orientations prior to the 2011 M<sub>w</sub> 9.0 Tohoku-Oki, Japan, earthquake in its source area. *Geophys. Res. Lett.* 38:L00G10

Lockner DA, Morrow C, Moore D, Hickman S. 2011. Low strength of deep San Andreas fault gouge from SAFOD core. *Nature* 472(7341):82–85

Lotto GC, Dunham EM, Jeppson TN, Tobin HJ. 2017. The effect of compliant prisms on subduction zone earthquakes and tsunamis. *Earth Planet. Sci. Lett.* 458:213–22

Loveless JP, Meade BJ. 2010. Geodetic imaging of plate motions, slip rates, and partitioning of deformation in Japan. *J. Geophys. Res.* 115(B2):B02410

Loveless JP, Meade BJ. 2011. Spatial correlation of interseismic coupling and coseismic rupture extent of the 2011 M<sub>w</sub> 9.0 Tohoku-oki earthquake. *Geophys. Res. Lett.* 38(17):L17306

Mase CW, Smith L. 1987. Effects of frictional heating on the thermal, hydrologic, and mechanical response of a fault. *J. Geophys. Res.* 92:6249–72

Mavrommatis AP, Segall P, Johnson KM. 2014. A decadal-scale deformation transient prior to the 2011 M<sub>w</sub> 9.0 Tohoku-oki earthquake. *Geophys. Res. Lett.* 41(13):4486–94

Moore JC, Plank TA, Chester FM, Polissar PJ, Savage HM. 2015. Sediment provenance and controls on slip propagation: lessons learned from the 2011 Tohoku and other great earthquakes of the subducting northwest Pacific plate. *Geosphere* 11(3):533–41

Mori J, Chester F, Brodsky E, Kodaira S. 2014. Investigation of the huge tsunami from the 2011 Tohoku-Oki, Japan, earthquake using ocean floor boreholes to the fault zone. *Oceanography* 27(2):132–37

Nakamura Y, Kodaira S, Cook BJ, Jeppson T, Kasaya T, et al. 2014. Seismic imaging and velocity structure around the JFAST drill site in the Japan Trench: low *V* p, high *V* p/*V* s in the transparent frontal prism. *Earth Planets Space* 66(1):121

Nakamura Y, Kodaira S, Miura S, Regalla C, Takahashi N. 2013. High-resolution seismic imaging in the Japan Trench axis area off Miyagi, northeastern Japan. *Geophys. Res. Lett.* 40(9):1713–18

Noda H, Lapusta N. 2013. Stable creeping fault segments can become destructive as a result of dynamic weakening. *Nature* 493(7433):518–21

Palmer AC, Rice JR. 1973. The growth of slip surfaces in the progressive failure of over-consolidated clay. *Proc. R. Soc. A Math. Phys. Eng. Sci.* 332(1591):527–48
Rabinowitz HS, Savage HM, Plank T, Polissar PJ, Kirkpatrick JD, Rowe CD. 2015. Multiple major faults at the Japan Trench: chemostratigraphy of the plate boundary at IODP Exp. 343: JFAST. *Earth Planet. Sci. Lett.* 423:57–66

Rabinowitz HS, Savage HM, Polissar PJ, Plank TA, Rowe CD, Kirkpatrick JD. 2013. Detecting the frictional temperature rise during the 2011 Tohoku earthquake using the thermal maturity of biomarkers. *AGU Fall Meet. Abstr.* 2013:T41F–07

Rabinowitz HS, Savage HM, Polissar PJ, Rowe CD, Kirkpatrick JD. 2020. Earthquake slip surfaces identified by biomarker thermal maturity within the 2011 Tohoku-Oki Earthquake fault zone. *Nat. Commun.* 11:533

Regalla C, Bierman P, Rood D. 2019. Meteoric $^{10}$Be reveals a young, active accretionary prism and structurally complex décollement in the vicinity of the 2011 Tohoku earthquake rupture. *Geochem. Geophys. Geosyst.* 20:4956–71

Regalla C, Fisher DM, Kirby E, Furlong KP. 2013. Relationship between outer forearc subsidence and plate boundary kinematics along the Northeast Japan convergent margin. *Geochem. Geophys. Geosyst.* 14(12):5227–43

Remitti F, Smith SAF, Mittempergher S, Gualtieri AF, Di Toro G. 2015. Frictional properties of fault zone gouges from the J-FAST drilling project ($M_w$ 9.0 2011 Tohoku-Oki earthquake). *Geophys. Res. Lett.* 42:2691–99

Rice JR. 2006. Heating and weakening of faults during earthquake slip. *J. Geophys. Res.* 111(B5):B05311

Saffer DM, Marone C. 2003. Comparison of smectite- and illite-rich gouge frictional properties: application to the updip limit of the seismogenic zone along subduction megathrusts. *Earth Planet. Sci. Lett.* 215(1–2):219–35

Savage HM, Brodsky EE. 2011. Collateral damage: evolution with displacement of fracture distribution and secondary fault strands in fault damage zones. *J. Geophys. Res.* 116(B3):B03405

Sawai M, Hirose T, Kameda J. 2014. Frictional properties of incoming pelagic sediments at the Japan Trench: implications for large slip at a shallow plate boundary during the 2011 Tohoku earthquake. *Earth Planetы Space* 66(1):65

Schleicher AM, Boles A, van der Pluijm BA. 2015. Response of natural smectite to seismogenic heating and potential implications for the 2011 Tohoku earthquake in the Japan Trench. *Geology* 43(9):755–58

Shipton Z, Evans J, Abercrombie R, Brodsky EE. 2006. The missing sinks: slip localization in faults, damage zones, and the seismic energy budget. In *Earthquakes: Radiated Energy and the Physics of Faulting*, ed. R. Abercrombie, pp. 217–22. Washington, DC: Am. Geophys. Union

Sibson RH. 1973. Interactions between temperature and pore-fluid pressure during earthquake faulting and a mechanism for partial or total stress relief. *Nat. Phys. Sci.* 243(126):66–68

Sibson RH. 1985. A note on fault reactivation. *J. Struct. Geol.* 7:751–54

Sugawara D, Goto K, Imamura F, Matsumoto H, Minoura K. 2012. Assessing the magnitude of the 869 Jogan tsunami using sedimentary deposits: prediction and consequence of the 2011 Tohoku-oki tsunami. *Sediment. Geol.* 282:14–26

Sun T, Fujiwara T, Kodaira S, He J, Wang K. 2017. Large fault slip peaking at trench in the 2011 Tohoku-oki earthquake. *Nat. Commun.* 8:14044

Tanikawa W, Hirose T, Mukoyoshi H, Tadai O, Lin W. 2013. Fluid transport properties in sediments and their role in large slip near the surface of the plate boundary fault in the Japan Trench. *Earth Planet. Sci. Lett.* 382:150–60

Tanioka Y, Sataka K. 1996. Fault parameters of the 1896 Sanriku tsunami earthquake estimated from tsunami numerical modeling. *Geophys. Res. Lett.* 23(13):1549–52

Tomita F, Kido M, Ohta Y, Inuma T, Hino R. 2017. Along-trench variation in seafloor displacements after the 2011 Tohoku earthquake. *Sci. Adv.* 3(7):e1700113

Tsuji T, Ito Y, Kido M, Osada Y, Fujimoto H, et al. 2011. Potential tsunamigenic faults of the 2011 off the Pacific coast of Tohoku earthquake. *Earth Planetы Space* 63(7):58

Tsuji T, Kawamura K, Kanamatsu T, Kasaya T, Fujikura K, et al. 2013. Extension of continental crust by anelastic deformation during the 2011 Tohoku-oki earthquake: the role of extensional faulting in the generation of a great tsunami. *Earth Planet. Sci. Lett.* 364:44–58
Tsuru T, Park J-O, Takahashi N, Kodaira S, Kido Y, et al. 2000. Tectonic features of the Japan Trench convergent margin off Sanriku, northeastern Japan, revealed by multichannel seismic reflection data. *J. Geophys. Res.* 105(B7):16403–13

Ujiie K, Inoue T, Ishiwata J. 2016. High-velocity frictional strength across the Tohoku-oki megathrust determined from surface drilling torque. *Geophys. Res. Lett.* 43(6):2488–93

Ujiie K, Tanaka H, Saito T, Tsutsumi A, Mori JJ, et al. 2013. Low coseismic shear stress on the Tohoku-oki megathrust determined from laboratory experiments. *Science* 342(6163):1211–14

Viesca RC, Garagash DI. 2015. Ubiquitous weakening of faults due to thermal pressurization. *Nat. Geosci.* 8(11):875–79

Wang K, Hu Y. 2006. Accretionary prisms in subduction earthquake cycles: the theory of dynamic Coulomb wedge. *J. Geophys. Res.* 111(B6):B06410

Wetzler N, Lay T, Brodsky EE, Kanamori H. 2017. Rupture-depth-varying seismicity patterns for major and great ($M_w \ge 7.0$) megathrust earthquakes. *Geophys. Res. Lett.* 44(19):9663–71

Yang T, Dekkers MJ, Chen J. 2018. Thermal alteration of pyrite to pyrrhotite during earthquakes: new evidence of seismic slip in the rock record. *J. Geophys. Res. Solid Earth* 123(2):1116–31

Yang T, Dekkers MJ, Zhang B. 2016. Seismic heating signatures in the Japan Trench subduction plate-boundary fault zone: evidence from a preliminary rock magnetic ‘geothermometer.’ *Geophys. J. Int.* 205(1):332–44

Yang T, Mishima T, Ujiie K, Chester FM, Mori JJ, et al. 2013. Strain decoupling across the décollement in the region of large slip during the 2011 Tohoku-oki earthquake from anisotropy of magnetic susceptibility. *Earth Planet. Sci. Lett.* 381(C):31–38

Yue H, Lay T. 2011. Inversion of high-rate (1 sps) GPS data for rupture process of the 11 March 2011 Tohoku earthquake ($M_w 9.1$). *Geophys. Res. Lett.* 38(7):L00G09

Zielke O, Galis M, Mai PM. 2017. Fault roughness and strength heterogeneity control earthquake size and stress drop. *Geophys. Res. Lett.* 44(2):777–83

Zoback MD. 2007. *Reservoir Geomechanics*. Cambridge, UK: Cambridge Univ. Press