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 La
boratories, California Institute of Technology, Pasadena, California,
USA
4
Division of Engineering and Applied Science, California Institute of Technology, Pasadena,
California, USA
Keywords:
Thrust fault
s
,
Dynamic ruptures, Laboratory earthquakes, G
round motion,
Digital
image correlation
, Supershear
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
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. Please cite this article as
doi: 10.1029/2021JB023733
.
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Abstract
We study
how
t
he 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
o
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
displacement
s
and velocit
ies
.
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 han
ging 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
v
elocit
y components
are
found to be
larger at the footwall than at the hanging wall.
T
he
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 thrus
t earthquakes.
Nondimensional analysis
shows that the experimental
measurements
are
consistent
with larger
-
scale numerical simulations
as well as field observations from thrust earthquakes
.
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Plain language summary
The asymmetric interaction of thrust
earthquake
s
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 associate
d 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 up
-
dip 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.
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Introduction
The asymmetric geometry of thrust faults with respect to the Earth’s surface leads to complex
dynamic behavior of up
-
dip ruptures
an
d amplification of ground motions
,
with asymmetry
between the
hanging
wall
and
foot
wall.
S
eismological observations
have
generally
show
ed
larger
ground motions at the hanging wall for
both blind
and surface
-
rupturing
thrust earthquakes
.
Th
e
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
wal
l
(Brune, 1996; Nason,
1973)
.
L
arger peak ground accelerations
at
the hanging wall
were
observed for t
he 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 acceleration
s
at
periods below 1.0 s, but
was absent at
larger period
s
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 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 n
ear
-
fault observations
from thrust earthquakes are limited to few earthquakes
,
the
y
cannot fully
constrain the geometri
cal
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 et al., 1998, 2000; Oglesby & Day, 2001; Scala et al., 2019;
Shi et al., 1998; Yin &
Denolle, 2021)
also show
ed
larger ground motion at the hanging wall
than at the footwall
,
with
t
he amplification at
hanging wall
increas
ing
as
the
dip angle
of the fault
decreases
(Oglesby et al.,
1998)
.
Si
mulations of multiple earthquake cycles on thrust fault
with dip angle of 45
o
(Duan &
Oglesby, 2005)
reveal
ed
the occurrence of
a
dominant
vertical component of ground motion at the
hanging wall, but
a
dominant
hor
izontal component
at
the footwall.
Several n
umerical and
theoretical studies
show
ed
that
the interaction of the
thrust
ruptures with the free surface
r
esults 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
decrease
s
behind it
.
Because cha
nges in
the normal
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traction affect the frictional shear resistance,
its decrease
can
lead to
l
arger slip and slip rate
on the
fault
and
amplif
ication
the ground motion
(Oglesby et al., 1998)
.
Brune
(1996)
performed laboratory experiments
on a foam
-
rubber model with thrust wedge
geometry
of
d
i
p angle of 25
o
and
show
ed
that
,
in the presence of large deformations,
the interaction
of the rupture with t
he free surface
leads to
significant
fault opening near the free surface
that trap
s
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 opening 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
o
under
u
n
iaxial
compressive loading of 2.5 MPa,
Gabuchian et al.
(
2017)
confirmed
that
even within the linear, small deformation
,
regime
ty
pical of natural faults,
classical sub
-
Raleigh
thrust ruptures may open the fault
s
near the free surface.
For super
-
shear
ruptures, their results indicated that the opening, although present
,
was not as pronounced.
Based
on complementary numerical simulat
ions
,
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 app
roaches 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., 200
1)
, 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
p
hotoelasticity and la
s
er velocimetry,
Gabuchian et al.
(2014)
quantitatively
explored
the
dynamics of
vertical
ground motions with a s
imilar
experimental configuration, but with the laser velocimeters located
at discreet points along
the
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free surface
.
They also highlighted the substantial differences in ground motion behavior
resulting when
either sub
-
Rayleigh or super
-
shear ruptures, travelling up
-
dip, reach the free
surface.
Similar to the seismological observations and numerical simulations, the
se 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
quantitative
full
-
field measurements in order to
explore this complex phenomenon in detail
and at differ
ent rupture
-
speed regimes
.
Tal et al.
(2020)
analyzed the
evolution of fault
-
normal traction and frictional resistance
response
during the
interaction of
laboratory
thrust
ruptures with the free surface
in an
experimental configuration similar
to that of
Gabuchian et al.
(
2014, 2017)
, but with a new
full
-
field
imaging technique
,
which
combines ultra
-
high speed photography and digital image
correlation (DIC)
(Rosakis et al., 2020; Rubino et al., 2017, 2019, 2020; Tal et al., 2019)
.
Similarly
to the numerical simulations
of
Ma & Beroza
(2008)
,
Nielsen
(1998)
and
Oglesby et al.
(1998,
2000)
,
significant
reduction
s
in
normal stress
w
ere
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
, t
he experiments also showed
a significant delay in the response of frictional s
hear
resistance to the variation in normal traction,
consistent with some earlier studies
(Linker &
Dieterich, 1992; Prakash & Clifton, 1993)
,
which might
decrease the eff
ect of
normal traction
reduction
s
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 t
he free surface
on
the near
-
fault ground motion
.
The original version of this set
-
up
(Gabuchian
et al., 2014)
u
sed 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
stud
y
allows
us
to produce
full
-
field maps of displacement and particle
-
velocit
y histories
of the ruptures as they interact with
the free surface at
time intervals of 1
s
. Th
is
versatile
technique provides
m
easurements of
both
the
horizontal and vertical
components of surface
velocities
and displacements
, which
enables us
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to study the differences
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 betw
een 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 reac
h 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 demonstrated experimentally through optical
experiments of the dynamic shear rupture process
(Rosakis et al., 1999; Rosakis, 2002; Xia et al.,
2004)
of the type present
ed
here. “Super
-
shear”
(more precisely,
“
i
ntersonic”
)
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 g
row with a sub
-
Rayleigh rupture speed and then
transition to supershear speeds. The mechanics of sub
-
Rayleigh to supershear rupture transition
ha
s
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, considering
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
differenc
es 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 dynamic
s
of
thrust
-
fault
laboratory earthquakes
2.1.
Laboratory
earthquake
setup
and
ultrahigh
-
speed
diagnostic
s
Thrust earthquakes
are
modeled by dynamic ruptures propagating along a preexisting
interface
(experimental fault)
with a dip angle of
= 61
o
between two Homalite
-
100 quadrilateral plates
(
sample
dimensions
of 25
x
18 cm)
(Fig. 1).
The plates
are
loaded
under uniaxial compression
P
,
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resulting in
the
initial shear and normal stresses on the
fault
of
0
=
P
sin(
61
o
)cos(
61
o
) and
0
=
P
sin
2
(
61
o
), respectively.
The experimental apparatus is described more in detail in our prior work
(Rubino et al., 2017; Rubino et al., 2019; Tal et al. 2020).
In this paper
,
we report the results of
four experiments with
P
= 4.9, 7.4, 10, an
d 15.1 MPa.
In all experiments, t
he interface
s
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
rupture
s
are
nucleated
at a distance of
x
f
=
11
.5
centimeters 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
0
and
0
.
With
= 61
o
, the ratio
of shear to normal stress on the fault enables to load the plates to the desired initial stress with
out
sliding and to obtain intensive ruptures.
T
he low shear modulus of Homalite
(
= 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 x 12 mm
2
)
coated with a random
black
-
dot
s
pattern
is
monitored
near the free
surface
using an ultrahigh
-
speed camera
system (Shimadzu HPV
-
X)
and a high
-
speed light system
(Cordin 605).
T
he camera record
s
a sequence of 128 images of the patterns distorted by the
propagating rupture with a resolution of 400 x 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
w
i
th
the
digital image correlation
method
Similarly to
Rubi
no et al
.
(201
7, 2019, 2020)
, we use the local digital image correlation (DIC)
software Vic
-
2D (Correlation Solutions Inc.)
to produce evolving
maps of
displacement
s
parallel
(
푢
푝
)
and normal (
푢
푛
)
to the fault from the sequence of images acquired with the ultrahig
h
-
speed
camera.
In local DIC
methods
,
displacements
are calculated
by using
pattern
matching algorithms
over
image
subset
s,
separated by a distance, referred to as step
.
In this study,
the correlation is
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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
boundar
ies
,
Vic
-
2D
extrapolate
s
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
,
th
en
a self
-
developed post
-
processing algorithm
(Tal et al., 2019)
that locally adjust
s
the 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 ruptur
es 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)
allow
ed
capturing rapid normal stress variations across the interface
(Tal et al., 2020)
due to the interaction of
dynam
ic
shear
rupture
s
with the free surface.
The
fault
-
parallel
velocity
(
푢
̇
푝
)
and
fault
-
normal
velocity
(
푢
̇
푛
)
are computed from the
sequence of the displacement components
푢
푝
and
푢
푛
,
respectively,
using a central
-
difference
scheme.
The slip
훿
is computed as the difference betwe
en the fault
-
parallel velocity just above and
below the
fault
, and the slip
rate
,
훿
̇
, is its time derivative.
To discuss the ground motions, the
velocity and displacement field
s
are also rotated
from
the
coordinate system
(
푥
푝
,
푥
푛
)
with axes
parallel and normal to
the
fault into a coordinate system
(
푥
1
,
푥
2
)
that is parallel and normal to the
free surface (Figure 1)
.
We estimate the
rupture speed
V
r
in
the
experiment
s
by tracking the rupture
tip
a
s it pro
pagate
s
across the field of view (FOV)
.
We compute the rupture arrival time at each
location along the
fault
as the
time
in which
훿
̇
initially exceeds a threshold value of
훿
̇
푡
ℎ
푟
= 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
훿
̇
푡
ℎ
푟
.
We
smooth the
curve of
the
rupture tip
position
versus
time
with a Butterworth filter
and
estimate
V
r
from t
he
av
erage
slope of
the curve
.
3. Experimental results
of laboratory thrust earthquakes
3.
1.
D
ynamic
r
upture
behavior during interaction with the free surface
Before
analyzing
the ground motions
, we
start by
explor
ing
the
full
-
field behavior of the
dynamic
ruptures
as they
approach and
interact with the free surface
.
A
series of
f
ull
-
field images of the
fault
-
parallel and fault
-
normal velociti
e
s 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
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= 1.
63
c
s
.
As t
he rupture propagate
s
through the
FOV
(
t
= 54
s after nucleation)
,
푢
̇
푝
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
t
he fau
lt
show
a
positive normal movement (
toward the footwall
),
with
maximum values of
푢
̇
푛
~ 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
s
)
,
there is
a
significant increase in
푢
̇
푝
and
푢
̇
푛
, as well as
a
change in
direction
of
푢
̇
푛
into
mostly
negative normal
movement
.
The supershear rupture is followed by another
rupture
, traveling at
the
speed of
the
Rayleigh
wave
. Th
is
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
(Gabuchian et al., 2014; Mello et al., 2010, 2016; Rosakis et al., 2007;
Rubino et a
l., 2020)
.
The
propagation
of the
trailing
-
Rayleigh
rupture
through the FOV
(
t
= 91
s)
is
mostly observed in
the
푢
̇
푛
component
(as is characteristic of all sub
-
Rayleigh ruptures)
,
which
shows
an elongated feature
of
푢
̇
푛
<
-
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
arrive
s
at the free surface
(
t
= 102
s)
,
b
oth
푢
̇
푝
and
푢
̇
푛
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
,
퐿
푡푟푎푛푠
, with the following expression
(Rubino et al., 2020)
:
퐿
푡푟푎푛푠
=
푐
푅
(
푥
푑
−
푡
푑
푉
푟
)
(
푐
푅
−
푉
푟
)
,
(1)
where
t
d
is arrival time of the rupture at a given distance
x
d
from the nucleation site.
T
he
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
퐿
푡푟푎푛푠
=
5.6 mm
from the
nucleation site.
Plot
s
of the
time histories of
slip rate,
훿
̇
,
at different locations along the fault
(Fig
ure
3
a
)
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
훿
̇
that correspond
to the arrival
(
훿
̇
=
6
.
5
m
/
s
at
t
=
54
s
)
and
reflection (
훿
̇
=
9
m
/
s
at
t
=
69
s
)
of the supershear
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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
훿
̇
=
12.5 m/s
n
ear the free surface
(
x
f
= 1.5 mm)
.
The t
railing
-
Rayleigh
rupture
show
s
a
c
lear peak of
훿
̇
=
9.5 m/s at
x
f
= 1.5 mm
, but
a
s
x
f
increases,
the peak becomes smaller and wider, with a weak signal at
x
f
= 13.5
mm
.
Experiments under lower
compressive load
s
are characterized by weaker ruptures with
smaller slip rates
.
T
he
rupture
s
show
similar
characteristics to those described above,
featuring
a
supershear rupture
in the
front
followed by a trailing Rayleigh
rupture
.
However, a
s
P
decreases
,
th
e
re is a transition from a dominant
supershear
rupture
to a
dominant trailing
Rayleigh
rupture
.
In
Exp. #
4
, which was
co
n
ducted under the lowest
c
ompressive load
of
P
= 4.9 MPa
(Figure 3b)
,
the peak slip rate of the s
upershear
rupture
near the free surface (
x
f
= 1.5 mm)
is
훿
̇
=
2.8
m/s
,
while
that of the trailing Rayleigh is
훿
̇
=
5
m/s
.
Moreover, there is a delay of ~5
s in
the arrival of the
supershear rupture to FOV compare
d 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
퐿
푡푟푎푛푠
=
12.8 mm.
3.2
.
Experimental measurements of the g
round motion
3
.
2
.
1.
Su
pershear
rupture
front
Snapshots of the of full
-
field
particle
velocity magnitude
,
|
퐮
̇
|
,
with overlaid velocity vectors on
the fault and on the free surface,
during
d
ifferent 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
effect
s
on the ground motion
.
The
supershear
rupture
(
Figure 4, top panels
)
approaches the free surface
(
t
= 57
s)
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
,
t
he right
part of the hanging wall, which
is
already behind
the ruptur
e front,
moves parallel to the fault
with
a velocity
magnitude
of
|
퐮
̇
|
,
=
2
m/s
.
T
he surface velocities
,
퐮
̇
푠
,
decrease
and rotate
in
locations
on the surface
that
are
ahead
the rupture front
(decreasing
x
1
)
.
During t
he
interaction of the
r
upture
with
the
free surface (
t
= 6
3
s)
,
|
퐮
̇
|
increase
s
and
become
s
asymmetric
with respect to the fault
,
with
peak
val
u
es
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
s)
,
sliding continues
at
smaller particle velocit
ies
,
with a
sub
-
vertical motion of
the hanging wall
and motion at a dip of
훽
≈
40°
of
the footwall
.
At this