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1. Introduction
The asymmetric geometry of thrust faults with respect to the Earth's surface leads to complex dynamic behavior
of updip ruptures and amplification of ground motions, with asymmetry between the hanging wall and footwall.
Seismological observations have generally showed larger ground motions at the hanging wall for both blind
and surface-rupturing thrust earthquakes. The larger motions were attributed to the closer proximity of hanging
wall seismic stations to the fault (Abrahamson & Somerville,
1996
) and to waves trapped in the hanging wall
(Brune,
1996
; Nason,
1973
). Larger peak ground accelerations at the hanging wall were observed for the 1971
Mw 6.6 San Fernando (Allen et al.,
1998
; Nason,
1973
; Steinbrugge et al.,
1975
), the 1994 Mw 6.7 Northridge
(Abrahamson & Somerville,
1996
), and the 1999 Mw 7.7 Chi-Chi (Chang et al.,
2004
; Shin & Teng,
2001
)
earthquakes. For the 2008 Mw 7.9 Wenchuan earthquake, the hanging-wall effect was observed for the peak
ground accelerations at periods below 1.0 s, but was absent at larger periods or for the peak ground velocities
(Li et al.,
2010
; Liu & Li,
2009
). Zhang et al. (
2019
) observed the hanging-wall effects for both the vertical
Abstract
We study how the asymmetric geometry of thrust faults affects the dynamics of supershear
ruptures and their associated trailing Rayleigh ruptures as they interact with the free surface, and investigate
the resulting near-field ground motions. Earthquakes are mimicked by propagating laboratory ruptures along
a frictional interface with a 61° dip angle. Using an experimental technique that combines ultrahigh-speed
photography with digital image correlation, we produce sequences of full-field evolving measurements of
particle displacements and velocities. Our full-field measurement capability allows us to confirm and quantify
the asymmetry between the experimental motions of the hanging and footwalls, with larger velocity magnitudes
occurring at the hanging wall. Interestingly, because the motion of the hanging wall is generally near-vertical,
while that of the footwall is at dip direction shallower than the dip angle of the fault, the horizontal surface
velocity components are found to be larger at the footwall than at the hanging wall. The attenuation in surface
velocity with distance from the fault trace is generally larger at the hanging wall than at the footwall and it is
more pronounced in the vertical component than in the horizontal one. Measurements of the rotations in surface
motions confirm experimentally that the interaction of the rupture with the free surface can be interpreted
through a torqueing mechanism that leads to reduction in normal stress near the free surface for thrust
earthquakes. Nondimensional analysis shows that the experimental measurements are consistent with larger-
scale numerical simulations as well as field observations from thrust earthquakes.
Plain Language Summary
The asymmetric interaction of thrust earthquakes with the Earth's
surface leads to complex dynamic behavior and strongly asymmetric ground motions. Near-fault measurements
from such earthquakes are rare and do not allow for detailed characterization of the earthquake rupture and
the associated near-field ground motions. In this study, we create controlled ruptures in a laboratory set-up
mimicking the thrust fault earthquake process. We utilize a unique, optical, ultrahigh-speed imaging technique
to observe such updip laboratory earthquakes at high spatial resolution and in real time, and to analyze their
complex dynamic interactions with the free surface. Such a study would be difficult to achieve in the field
because of the typical spatial sparsity of the recorded data. The experiments allow us to quantify the differences
in ground motion between the two sides of the fault, the decrease of ground motion with distance from the fault,
and the dynamic surface rotations. Moreover, the experimental observations enable us to directly relate the
measured near-field ground motion to the state of the earthquake rupture on the fault.
TAL ET AL.
© 2022. American Geophysical Union.
All Rights Reserved.
Dynamics and Near-Field Surface Motions of Transitioned
Supershear Laboratory Earthquakes in Thrust Faults
Yuval Tal
1,2
, Vito Rubino
3
, Ares J. Rosakis
3
, and Nadia Lapusta
2,4
1
Department of Earth and Environmental Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel,
2
Seismological
Laboratory, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA,
3
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA, USA,
4
Division of Engineering and
Applied Science, California Institute of Technology, Pasadena, CA, USA
Key Points:
We characterize laboratory thrust
ruptures as they interact with the
free surface after transitioning to
supershear at various distances
Our full-field analysis enables
studying the relationship between
near-field ground motion and the
dynamics of the ruptures on the fault
Velocity magnitudes are larger at
the hanging wall, but the horizontal
velocities are larger at the footwall
because of rotations
Correspondence to:
Y. Tal,
yuvtal@bgu.ac.il
Citation:
Tal, Y., Rubino, V., Rosakis, A. J.,
& Lapusta, N. (2022). Dynamics
and near-field surface motions of
transitioned supershear laboratory
earthquakes in thrust faults.
Journal
of Geophysical Research: Solid Earth
,
127
, e2021JB023733.
https://doi.
org/10.1029/2021JB023733
Received 29 NOV 2021
Accepted 12 MAR 2022
Author Contributions:
Conceptualization:
Yuval Tal, Vito
Rubino, Ares J. Rosakis, Nadia Lapusta
Data curation:
Yuval Tal
Formal analysis:
Yuval Tal, Vito Rubino
Funding acquisition:
Ares J. Rosakis,
Nadia Lapusta
Investigation:
Yuval Tal, Vito Rubino,
Ares J. Rosakis, Nadia Lapusta
Methodology:
Yuval Tal, Vito Rubino
Project Administration:
Ares J. Rosakis,
Nadia Lapusta
Supervision:
Ares J. Rosakis, Nadia
Lapusta
Writing – original draft:
Yuval Tal, Vito
Rubino, Ares J. Rosakis, Nadia Lapusta
Writing – review & editing:
Yuval Tal,
Vito Rubino, Ares J. Rosakis, Nadia
Lapusta
10.1029/2021JB023733
RESEARCH ARTICLE
1 of 20
Journal of Geophysical Research: Solid Earth
TAL ET AL.
10.1029/2021JB023733
2 of 20
and horizontal components, but with the former significantly more prominent than the latter. The 2013 Mw 6.6
Lushan earthquake also showed the hanging-wall effect only for short periods (Bai,
2017
). Because near-fault
observations from thrust earthquakes are limited to few earthquakes, they cannot fully constrain the geometrical
effect of thrust fault on the ground motions (Donahue & Abrahamson,
2014
). Moreover, seismic observations
may be affected by the other factors, such as the lithology and topography.
Numerical studies of thrust earthquakes (Duan & Oglesby,
2005
; Ma & Beroza,
2008
; Oglesby & Day,
2001
;
Oglesby et al.,
1998
,
2000
; Scala et al.,
2019
; Shi et al.,
1998
; Yin & Denolle,
2021
) also showed larger ground
motion at the hanging wall than at the footwall, with the amplification at hanging wall increasing as the dip
angle of the fault decreases (Oglesby et al.,
1998
). Simulations of multiple earthquake cycles on thrust fault with
dip angle of 45° (Duan & Oglesby,
2005
) revealed the occurrence of a dominant vertical component of ground
motion at the hanging wall, but a dominant horizontal component at the footwall. Several numerical and theo-
retical studies showed that the interaction of the thrust ruptures with the free surface results in a time-dependent
fault-normal traction (Aldam et al.,
2016
; Kozdon & Dunham,
2013
; Ma & Beroza,
2008
; Madariaga,
2003
;
Nielsen,
1998
; Oglesby et al.,
1998
,
2000
), in which the normal traction increases ahead of the rupture front and
decreases behind it. Because changes in the normal traction affect the frictional shear resistance, its decrease can
lead to larger slip and slip rate on the fault and amplification the ground motion (Oglesby et al.,
1998
).
Brune (
1996
) performed laboratory experiments on a foam-rubber model with thrust wedge geometry of dip
angle of 25° and showed that, in the presence of large deformations, the interaction of the rupture with the free
surface leads to significant fault opening near the free surface that traps the energy at the hanging wall. Foam
rubber, however, is not a linear elastic and brittle material and it is not an optimal analogue material for the rocks
in the upper crust. Furthermore, the ruptures in those experiments already developed initial opening near the
growing shear rupture tip, well before arriving at the free surface, a phenomenon which is clearly an indication of
large deformations. Hence, the foam-rubber results did not conclusively resolve the issue of whether fault open-
ing is feasible and whether this phenomenon is not merely an artifact of the large-deformation, non-linear elastic
behavior of foam rubber, which is not exhibited by brittle rocks.
Using photoelastic images and highly resolved discrete laser-velocimetry measurements from dynamic ruptures
experiments on brittle Homalite specimens with a pre-existing fault at a dip angle of 61° under uniaxial compres-
sive loading of 2.5 MPa, Gabuchian et al. (
2017
) confirmed that even within the linear, small deformation,
regime typical of natural faults, classical sub-Raleigh thrust ruptures may open the faults near the free surface.
For super-shear ruptures, their results indicated that the opening, although present, was not as pronounced. Based
on complementary numerical simulations, they suggested that the opening and decrease of normal traction are
the results of a geometrically induced torque mechanism (Madariaga,
2003
), in which the hanging-wall wedge
undergoes pronounced rotation in one direction as the earthquake rupture approaches the free surface, then, as
rupture breaks the free surface, the torque is released with unclamping of the hanging-wall near the free surface.
Moreover, they suggested that this mechanism can explain the large shallow slip observed for the 2011 Mw 9.0
Tohoku earthquake in Japan and the 1999 Mw 7.7 Chi-Chi earthquake in Taiwan (Fujiwara et al.,
2011
; Lay
et al.,
2011
; Ma et al.,
2001
), despite the existence of frictionally stable sediments at shallow depth (e.g., Saffer
& Marone,
2003
), as demonstrated in numerical models (Kozdon & Dunham,
2013
).
In an earlier study using dynamic photoelasticity and laser velocimetry, Gabuchian et al. (
2014
) quantitatively
explored the dynamics of vertical ground motions with a similar experimental configuration, but with the laser
velocimeters located at discreet points along the free surface. They also highlighted the substantial differences
in ground motion behavior resulting when either sub-Rayleigh or super-shear ruptures, travelling updip, reach
the free surface. Similar to the seismological observations and numerical simulations, these early experimental
surface-normal motions verified in detail the substantial asymmetry between the hanging wall and the footwall,
with larger velocity amplitudes for the hanging wall. The experimental results also highlighted the need for quan-
titative full-field measurements in order to explore this complex phenomenon in detail and at different rupture-
speed regimes.
Tal et al. (
2020
) analyzed the evolution of fault-normal traction and frictional resistance response during the inter
-
action of laboratory thrust ruptures with the free surface in an experimental configuration similar to that of Gabu-
chian et al. (
2014
,
2017
), but with a new full-field imaging technique, which combines ultra-high speed photogra-
phy and digital image correlation (DIC; Rosakis et al.,
2020
; Rubino et al.,
2017
,
2019
,
2020
; Tal et al.,
2019
).
21699356, 2022, 3, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JB023733 by California Inst of Technology, Wiley Online Library on [06/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Journal of Geophysical Research: Solid Earth
TAL ET AL.
10.1029/2021JB023733
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Similarly to the numerical simulations of Ma and Beroza (
2008
), Nielsen (
1998
), and Oglesby et al. (
1998
,
2000
),
significant reductions in normal stress were observed during the interaction of the experimental ruptures with
the free surface. Moreover, a temporary complete release of normal traction was observed for experiments under
the initial compressive stresses of less than 7.4 MPa, which is consistent with the opening measured by the nodal
velocimeters in the experiments of Gabuchian et al. (
2017
). In contrast to standard friction formulation often
used in numerical simulations, the experiments also showed a significant delay in the response of frictional shear
resistance to the variation in normal traction, consistent with some earlier studies (Linker & Dieterich,
1992
;
Prakash & Clifton,
1993
), which might decrease the effect of normal traction reductions on the rupture process.
In this study, we use the same experimental set up and imaging technique as in Tal et al. (
2020
), but focus on
dynamics of thrust ruptures as they interact with the free surface and the effect of the free surface on the near-
fault ground motion. The original version of this set-up (Gabuchian et al.,
2014
) used dynamic photoelasticity
to qualitatively visualize the rupture process and particle velocimeters to record the resulting ground motion at a
few discrete locations at the free surface. The coupled ultrahigh-speed photography and DIC method used in this
study allows us to produce full-field maps of displacement and particle-velocity histories of the ruptures as they
interact with the free surface at time intervals of 1 μs. This versatile technique provides measurements of both the
horizontal and vertical components of surface velocities and displacements, which enables us to study the differ
-
ences in ground motion between the hanging and footwall, the attenuation of surface velocities with distance from
the fault in the near field, and the relationship between the near-field ground motions and the rupture on the fault.
In addition, measurements of the rotations of velocities and displacements during the interactions of the rupture
with the free surface allow us to examine experimentally the geometrically induced torque mechanism suggested
earlier (e.g., Gabuchian et al.,
2017
; Madariaga,
2003
).
The experimental ruptures in this study are supershear when they reach the free surface. The physical existence
of supershear, mode-II, cracks and frictional ruptures propagating along weekly bonded or frictional interfaces
(faults), previously considered to be a theoretical possibility (Burridge,
1973
; Freund,
1979
), was first demon-
strated experimentally through optical experiments of the dynamic shear rupture process (Rosakis,
2002
; Rosakis
et al.,
1999
; Xia et al.,
2004
) of the type presented here. “Super-shear” (more precisely, “intersonic”) cracks or
ruptures are defined as dynamic ruptures whose speeds have exceeded the shear wave speed but is still below the
pressure wave speed of the surrounding solid. Such ruptures may sometimes be born intersonic or in other cases,
they may initially grow with a sub-Rayleigh rupture speed and then transition to supershear speeds. The mechan-
ics of sub-Rayleigh to supershear rupture transition has been studied both theoretically (Andrews,
1976
; Dunham
& Archuleta,
2004
; Liu & Lapusta,
2008
) and experimentally (Mello et al.,
2016
; Rosakis et al.,
2007
; Xia
et al.,
2004
) but it is still an active subject of research in geophysics. In the context of the present study, consid-
ering transitioned supershear ruptures enables us to carefully investigate the interaction of both the supershear
front and the associated trailing Rayleigh rupture (a rupture trailing the supershear rupture tip which is generated
following the speed transition) with the free surface, and the differences between them. Such a comparison is
especially valuable since it is uncertain whether thrust earthquakes are mostly sub-Rayleigh or supershear as they
approach the free surface due to limitations in density of field measurements and inversion techniques.
2.
Monitoring the Dynamics of Thrust-Fault Laboratory Earthquakes
2.1.
Laboratory Earthquake Setup and Ultrahigh-Speed Diagnostics
Thrust earthquakes are modeled by dynamic ruptures propagating along a preexisting interface (experimental fault)
with a dip angle of
β
= 61° between two Homalite-100 quadrilateral plates (sample dimensions of 25 × 18 cm;
Figure
1
). The plates are loaded under uniaxial compression
P
, resulting in the initial shear and normal stresses on
the fault of
τ
0
=
P
sin (61°) cos (61°) and
σ
0
=
P
sin
2
(61°), respectively. The experimental apparatus is described
more in detail in our prior work (Rubino et al.,
2017
,
2019
; Tal et al.,
2020
). In this paper, we report the results
of four experiments with
P
= 4.9, 7.4, 10, and 15.1 MPa. In all experiments, the interfaces are first polished to
remove machining defects, and then bead-blasted with microbeads of 104–211 μm to introduce a reproducible
roughness (Lu et al.,
2010
; Mello et al.,
2010
; Rubino et al.,
2019
). The ruptures are nucleated at a distance of
x
f
= 11.5 cm from the free surface by a local pressure release provided by the expansion of a NiCr wire due to an
electrical discharge (2 kV) of a high-voltage capacitor (Cordin 640), where
x
f
is the distance along the fault. Once
nucleated, the ruptures propagate spontaneously, driven by the far-field stresses
τ
0
and
σ
0
. With
β
= 61°, the ratio
of shear to normal stress on the fault enables to load the plates to the desired initial stress without sliding and to
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Journal of Geophysical Research: Solid Earth
TAL ET AL.
10.1029/2021JB023733
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obtain intensive ruptures. The low shear modulus of Homalite (μ = 1.96 GPa) enables to produce well-developed
dynamic ruptures in samples of tens of centimeters. Homalite-100 is a highly strain-rate-sensitive material (Singh
& Parameswaran,
2003
), and the local high-strain-rate wave speeds control the rupture speed (Gori et al.,
2018
;
Rubino et al.,
2019
). The shear and pressure wave speeds for Homalite-100 are
c
s
= 1.28 km/s and
c
p
= 2.6 km/s
(Mello et al.,
2010
), respectively, and the Rayleigh wave speed is
c
R
= 0.92
c
s
= 1.18 km/s.
In order to obtain full-field measurements of the deformation associated with the ruptures, a target area
(19 × 12 mm
2
) coated with a random black-dots pattern is monitored near the free surface using an ultrahigh-speed
camera system (Shimadzu HPV-X) and a high-speed light system (Cordin 605). The camera records a sequence
of 128 images of the patterns distorted by the propagating rupture with a resolution of 400 × 250 pixels
2
, at
temporal sampling of 1 million frames/second and exposure time of 200 ns. To minimize optical aberrations, we
employ a fixed focal distance telephoto lens (Nikon Micro-Nikkor 200 mm f/4D IF-ED).
2.2.
Full-Field Analysis of Thrust-Fault Ruptures With the Digital Image Correlation Method
Similarly to Rubino et al. (
2017
,
2019
,
2020
), we use the local DIC software Vic-2D (Correlation Solutions Inc.)
to produce evolving maps of displacements parallel (
퐴퐴퐴퐴
푝푝
) and normal (
퐴퐴퐴퐴
푛푛
) to the fault from the sequence of images
acquired with the ultrahigh-speed camera. In local DIC methods, displacements are calculated by using pattern
matching algorithms over image subsets, separated by a distance, referred to as step. In this study, the correlation
is performed separately for the domains above and below the fault employing image subsets of 41 × 41 pixels
2
that are overlapped with a step of 1 pixel. While standard local DIC techniques provide the displacement map
up to half a subset away from the boundaries, Vic-2D extrapolates the displacements up to the fault. We use a
non-local filter (Buades et al.,
2006
,
2008
; Rubino et al.,
2015
) to remove the high-frequency noise from the
displacement fields, then a self-developed post-processing algorithm (Tal et al.,
2019
) that locally adjusts the
Figure 1.
Experimental setup. Dynamic shear ruptures are initiated by a small burst of a NiCr wire at distance
x
f
= 11.5 cm
from the free surface and propagate spontaneously along a frictional interface inclined at a dip angle
β
= 61° between two
Homalite plates, which are loaded under a compressional load
P
. An ultrahigh-speed camera system (Shimadzu HPV-X) and
a high-speed white light source system (Cordin 605) are used to record 128 images of a target area of 19 × 12 mm
2
near the
free surface at a rate of 1 million frames/second. The images are analyzed with the digital image correlation method to obtain
full-field displacement and velocity fields.
21699356, 2022, 3, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JB023733 by California Inst of Technology, Wiley Online Library on [06/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Journal of Geophysical Research: Solid Earth
TAL ET AL.
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displacements near the fault to ensure continuity of tractions across the fault. Ensuring traction continuity across
the fault is a key feature in the analysis of dynamic ruptures approaching the free surface, as small deviations in
the displacement measurements due to noise would result in unphysical tractions. Our post-processing procedure
(Tal et al.,
2019
) allowed capturing rapid normal stress variations across the interface (Tal et al.,
2020
) due to the
interaction of dynamic shear ruptures with the free surface.
The fault-parallel velocity (
퐴퐴퐴퐴퐴
푝푝
) and fault-normal velocity (
퐴퐴퐴퐴퐴
푛푛
) are computed from the sequence of the displacement
components
퐴퐴퐴퐴
푝푝
and
퐴퐴퐴퐴
푛푛
, respectively, using a central-difference scheme. The slip
퐴퐴퐴퐴
is computed as the difference
between the fault-parallel velocity just above and below the fault, and the slip rate,
퐴퐴
̇
훿훿
, is its time derivative. To
discuss the ground motions, the velocity and displacement fields are also rotated from the coordinate system
퐴퐴
(
푥푥
푝푝
,푥푥
푛푛
)
with axes parallel and normal to the fault into a coordinate system
퐴퐴
(
푥푥
1
,푥푥
2
)
that is parallel and normal to
the free surface (Figure
1
). We estimate the rupture speed
V
r
in the experiments by tracking the rupture tip as it
propagates across the field of view (FOV). We compute the rupture arrival time at each location along the fault
as the time in which
퐴퐴
̇
훿훿
initially exceeds a threshold value of
퐴퐴
̇
훿훿
푡푡푡푡푡
= 0.5 m/s. Because this time may not coincide
with an actual data point, a linear interpolation is performed between frames right before and after exceeding
퐴퐴
̇
훿훿
푡푡푡푡푡
.
We smooth the curve of the rupture tip position versus time with a Butterworth filter and estimate
V
r
from the
average slope of the curve.
3.
Experimental Results of Laboratory Thrust Earthquakes
3.1.
Dynamic Rupture Behavior During Interaction With the Free Surface
Before analyzing the ground motions, we start by exploring the full-field behavior of the dynamic ruptures as
they approach and interact with the free surface. A series of full-field images of the fault-parallel and fault-normal
velocities near the free surface is shown in Figure
2
during Exp. #1 performed under the largest compressive load
of
P
= 15.1 MPa. The experimental conditions generate a supershear rupture, propagating through the FOV at a
rupture speed of
V
r
= 2.09 km/s = 1.63
c
s
. As the rupture propagates through the FOV (
t
= 54 μs after nucleation),
Figure 2.
Snapshots of full-field fault-parallel (top panels) and fault-normal velocities (bottom panels) at the following stages of Exp #1 (
P
= 15 MPa): Propagation
of the supershear rupture through the field of view (FOV) (
t
= 54 μs), interaction of the supershear rupture with the free surface (
t
= 63 μs), propagation of the trailing
Rayleigh rupture through the FOV (
t
= 91 ms), and interaction of the trailing Rayleigh with the free surface (
t
= 102 ms). The location of the rupture tip in the images
where the ruptures propagate through the field of view is marked by a gray arrowhead. The velocity field of the supershear rupture shows dominant fault-parallel
motion, while that of the trailing Rayleigh shows dominant fault-normal motion.
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퐴퐴퐴퐴퐴
푝푝
shows an antisymmetric pattern, in which the hanging wall slides upward and the footwall slides downward,
both with maximum values of ∼3 m/s on the fault, at a location 5 mm behind the rupture tip. At this stage, both
sides of the fault show a positive normal movement (toward the footwall), with maximum values of
퐴퐴퐴퐴퐴
푛푛
∼ 0.8 m/s
at the same location. A more detailed description of the features associated with propagating supershear and sub
Rayleigh ruptures, away from the free surface, is given by Rubino et al. (
2020
). As the rupture reaches the free
surface (
t
= 63 μs), there is a significant increase in
퐴퐴퐴퐴퐴
푝푝
and
퐴퐴퐴퐴퐴
푛푛
, as well as a change in direction of
퐴퐴퐴퐴퐴
푛푛
into mostly
negative normal movement. The supershear rupture is followed by another rupture, traveling at the speed of the
Rayleigh wave. This disturbance is what remains from the initial rupture that gave rise to the supershear one (Xia
et al.,
2004
), and subsequently trails behind it as documented by previous experimental measurements (Gabu-
chian et al.,
2014
; Mello et al.,
2010
,
2016
; Rosakis et al.,
2007
; Rubino et al.,
2020
). The propagation of the
trailing-Rayleigh rupture through the FOV (
t
= 91 μs) is mostly observed in the
퐴퐴퐴퐴퐴
푛푛
component (as is characteristic
of all sub-Rayleigh ruptures), which shows an elongated feature of
퐴퐴퐴퐴퐴
푛푛
<
−2.5 m/s (large rightward movement)
perpendicular to the fault. The observation of such a trailing Rayleigh rupture indicates that a transition from
a sub-Rayleigh to supershear rupture had occurred (Andrews,
1976
; Burridge,
1973
; Lu et al.,
2010
; Rosakis
et al.,
2007
; Xia et al.,
2004
). When the trailing-Rayleigh rupture arrives at the free surface (
t
= 102 μs), both
퐴퐴퐴퐴퐴
푝푝
and
퐴퐴퐴퐴퐴
푛푛
increase (in absolute value). Assuming a constant propagation speed of the rupture at each regime and
that the rupture propagated at the Rayleigh wave speed before the transition to supershear, we can estimate the
sub-Rayleigh to supershear transition distance,
퐴퐴퐴퐴
trans
, with the following expression (Rubino et al.,
2020
):
퐿퐿
μ∼−

푐푐
푅푅
(
푥푥
푑푑
푡푡
푑푑
푉푉
푟푟
)
(
푐푐
푅푅
푉푉
푟푟
)
,
(1)
where
t
d
is arrival time of the rupture at a given distance
x
d
from the nucleation site. The estimated rupture speed
of
V
r
= 2.09 km/s in Exp. #1 indicates that the rupture transitioned to supershear at a small transition distance of
퐴퐴퐴퐴
trans
=
5.6 mm from the nucleation site.
Plots of the time histories of slip rate,
퐴퐴
̇
훿훿
, at different locations along the fault (Figure
3a
) provide further insight
into the effect of the free surface on the rupture process itself. At the largest distance from the free surface
(
x
f
= 13.5 mm), there are two separated peaks in
퐴퐴
̇
훿훿
that correspond to the arrival (
퐴퐴
̇
훿훿
=6
.
5m∕s
at
t
= 54 μs) and
reflection (
퐴퐴
̇
훿훿
=9m∕s
at
t
= 69 μs) of the supershear rupture. As the distance to the free surface decreases, the
peaks of arrival and reflection merge together, with a transition into a single peak of
퐴퐴
̇
훿훿
=
12.5 m/s near the free
surface (
x
f
= 1.5 mm). The trailing-Rayleigh rupture shows a clear peak of
퐴퐴
̇
훿훿
=
9.5 m/s at
x
f
= 1.5 mm, but as
x
f
increases, the peak becomes smaller and wider, with a weak signal at
x
f
= 13.5 mm.
Experiments under lower compressive loads are characterized by weaker ruptures with smaller slip rates. The
ruptures show similar characteristics to those described above, featuring a supershear rupture in the front followed
by a trailing Rayleigh rupture. However, as
P
decreases, there is a transition from a dominant supershear rupture
to a dominant trailing Rayleigh rupture. In Exp. #4, which was conducted under the lowest compressive load
of
P
= 4.9 MPa (Figure
3b
), the peak slip rate of the supershear rupture near the free surface (
x
f
= 1.5 mm) is
퐴퐴
̇
훿훿
=
2.8 m/s, while that of the trailing Rayleigh is
퐴퐴
̇
훿훿
=
5 m/s. Moreover, there is a delay of ∼5 μs in the arrival of the
supershear rupture to FOV compared to Exp. #1 because of a slightly slower rupture speed of
V
r
= 2 km/s = 1.57
c
s
and a larger transition distance of
퐴퐴퐴퐴
trans
=
12.8 mm.
3.2.
Experimental Measurements of the Ground Motion
3.2.1.
Supershear Rupture Front
Snapshots of the of full-field particle velocity magnitude,
퐴퐴
|
̇
퐮퐮
|
, with overlaid velocity vectors on the fault and on the
free surface, during different stages of Exp. #1 (Figure
4
), shed light on the dynamics of the supershear rupture
and the subsequent trailing Rayleigh rupture during the interaction with the free surface, as well as their effects
on the ground motion. The supershear rupture (Figure
4
, top panels) approaches the free surface (
t
= 57 μs) with
a peak particle velocity magnitude of 4 m/s and transition from a dominant fault-normal particle motion ahead of
the rupture front to a fault-parallel particle motion behind it. Correspondingly, at the surface, the right part of the
hanging wall, which is already behind the rupture front, moves parallel to the fault with a velocity magnitude of
퐴퐴
|
̇
퐮퐮
|
,
=2
m/s. The surface velocities,
퐴퐴
̇
퐮퐮
푠푠
, decrease and rotate in locations on the surface that are ahead the rupture
front (decreasing
x
1
). During the interaction of the rupture with the free surface (
t
= 63 μs),
퐴퐴
|
̇
퐮퐮
|
increases and
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becomes asymmetric with respect to the fault, with peak values of 8 and 4.5 m/s at the hanging and foot walls,
respectively. The walls slide in opposite directions, with small deviations from the orientation of the fault. After
the rupture is reflected from the free surface (
t
= 78 μs), sliding continues at smaller particle velocities, with a
sub-vertical motion of the hanging wall and motion at a dip of
퐴퐴퐴퐴
≈40
of the footwall. At this stage, the magni-
tude of accumulated surface displacements,
퐴퐴
|
퐮퐮
푠푠
|
, on the hanging wall ranges between
퐴퐴
|
퐮퐮
푠푠
|
=
100 μm near the fault
and
퐴퐴
|
퐮퐮
푠푠
|
=
90 μm at
퐴퐴퐴퐴
1
=
5 mm, while that on the footwall ranges between
퐴퐴
|
퐮퐮
푠푠
|
=
74 μm near the fault and
퐴퐴
|
퐮퐮
푠푠
|
=
65 μm at
퐴퐴퐴퐴
1
=
−5 mm (Figure
5
).
Plots of particle velocity vectors along the surface at time intervals of 2 μs (Figure
6
) show the rapid variations
and significant rotations of
퐴퐴
̇
퐮퐮
푠푠
during the interaction of the supershear rupture with the free surface in greater
detail. As the supershear rupture arrives at the free surface (
t
= 55–59 μs), the surface velocity magnitude,
퐴퐴
|
̇
퐮퐮
푠푠
|
,
initially increases at the right side of the hanging wall, then at smaller
x
1
. The rupture initially generates a veloc-
ity field that is rotated in a counter-clockwise fashion (
t
= 55–57 μs) relatively to the propagation direction. As
it breaks the free surface (
t
= 59 μs), the hanging wall surface experiences clockwise rotation relatively to its
previous state, while the footwall undergoes additional counter-clockwise rotation. At
t
= 61–63 μs, the hanging
Figure 3.
Slip rate versus time at five locations on the fault with different distances (
x
f
) from the free surface for (a) Exp
#1 (
P
= 15 MPa) and (b) Exp #4 (
P
= 4.9 MPa). The locations are shown in Figure
2
. Dashed lines marked with
T
p
,
T
s
, and
T
R
indicate the arrival times of P, S, and Rayleigh waves. Note that the peaks in
퐴퐴
̇
훿훿
increase near the free surface for both the
supershear rupture and the trailing Rayleigh. The lower level of applied loading
P
in Exp #4 results in a weaker rupture with
smaller slip rates.
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Journal of Geophysical Research: Solid Earth
TAL ET AL.
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8 of 20
wall shows an additional increase in
퐴퐴
|
̇
퐮퐮
푠푠
|
, which starts near the fault and continues at locations with larger
x
1
. The
rotations of
퐴퐴
̇
퐮퐮
푠푠
continue in both walls, with a flapping of the hanging wall near the fault, in which the rotation
near the fault is larger at
t
= 61 μs than at
t
= 63 μs. As the rupture is reflected from the free surface and prop-
agates downward along the fault (
t
= 65–69 μs),
퐴퐴
|
̇
퐮퐮
푠푠
|
generally decreases, with additional rotations into a nearly
vertical motion of the hanging wall and right-downward of the footwall. A temporary additional rotation of
퐴퐴
̇
퐮퐮
푠푠
with a decrease in
퐴퐴
|
̇
퐮퐮
푠푠
|
is observed at
t
= 71–75 μs, especially at the footwall. As shown by plots of the average
direction and magnitude of
퐴퐴
̇
퐮퐮
푠푠
at different stages of the interaction of the supershear rupture with the free surface
(Figure
7a
), the foot wall shows a total counter-clockwise rotation of ∼115° in the average direction of
퐴퐴
̇
퐮퐮
푠푠
between
t
= 57 and 77 μs, while the hanging wall shows a clockwise rotation of ∼80°.
3.2.2.
Trailing-Rayleigh Rupture
The trailing-Rayleigh rupture also generates increase in particle velocities with asymmetry between the hanging
and footwalls, but the pattern and direction of the velocity field are different than those associated with the super
-
shear rupture. The trailing-Rayleigh rupture approaches the free surface (
t
= 95 μs) with an elongated feature of
increased fault-normal velocity at the bulk, which initially interacts with the free surface at the right part of the
hanging wall, resulting in larger
퐴퐴
|
̇
퐮퐮
|
values at the upper-right corner rather than on the fault (Figure
4
). At this
stage, the velocity field near the fault is rotated such that the footwall moves horizontally and the hanging wall
has both vertical and horizontal positive velocities. The interaction of the trailing-Rayleigh rupture with the free
Figure 4.
Snapshots of the particle velocity magnitude at different stages of Exp. #1 (
P
= 15 MPa), with overlaid vectors showing the direction and magnitude of
particle velocities near the interface and at the free surface. The deformation is exaggerated by a factor of 10. The free surface generates asymmetry in the velocity field,
with larger velocities at the hanging wall compared to the footwall. The first panel (top left) also shows the surface locations (color triangles) used in Figure
9
to study
the attenuation of the ground motion with distance from the fault.
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Journal of Geophysical Research: Solid Earth
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surface (
t
= 102 μs) leads to an increase in
퐴퐴
|
̇
퐮퐮
|
, with larger values at the hanging wall (Figure
4
). After reflection
(
t
= 114 μs), sliding continues with smaller slip velocities. Because the camera records 128 images, we cannot
measure the permanent surface deformation after a complete stop of the rupture, but observe the displacements
up to
t
= 130 μs. At this stage, the values of
퐴퐴
|
퐮퐮
푠푠
|
on the hanging wall ranges between
퐴퐴
|
퐮퐮
푠푠
|
=
257 μm near the fault
and
퐴퐴
|
퐮퐮
푠푠
|
=
248 μm at
퐴퐴퐴퐴
1
=
5 mm, while that on the footwall ranges between
퐴퐴
|
퐮퐮
푠푠
|
=
200 μm near the fault and
퐴퐴
|
퐮퐮
푠푠
|
=
190 μm at
퐴퐴퐴퐴
1
=
−5 mm (Figure
5
). Moreover, the directions of
퐴퐴
u
푠푠
are nearly vertical and at dip of
퐴퐴퐴퐴
≈32
for the
hanging wall and footwalls, respectively.
The spatiotemporal evolution of
퐴퐴
̇
퐮퐮
푠푠
during the interaction of the trailing-Rayleigh rupture with the free surface
is explored in greater detail in Figures
7b
and
8
. As it approaches the free surface (
t
= 89–93 μs),
퐴퐴
̇
퐮퐮
푠푠
decreases
in magnitude and rotates counter-clockwise near the fault at both walls. At the arrival of the trailing-Rayleigh
Figure 5.
Snapshots of accumulated displacements along the surface,
퐴퐴
u
푠푠
, at different stages of Exp. #1 (
P
= 15 MPa). The
vector sizes are amplified by a factor of 10. The left (
t
= 59–78 μs) and right (
t
= 95–130 μs) panels capture the interactions
of the supershear and trailing Rayleigh ruptures with the free surface, respectively. The figure highlights the differences in
퐴퐴
|
u
푠푠
|
between the hanging and footwalls, as well as the rotations of
퐴퐴
u
푠푠
throughout the experiment into motions that are nearly
vertical at the hanging wall and at a dip of
퐴퐴퐴퐴
≈32
at the footwall.
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