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The sharp turn: backward rupture branching during the 2023 Mw 7.8 Turkey earthquake
Xiaotian Ding1, Shiqing Xu1*, Yuqing Xie2, Martijn van den Ende2, Jan Premus2, and Jean-Paul Ampuero2
1Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, China
2Université Côte d’Azur, IRD, CNRS, Observatoire de la Côte d’Azur, Geoazur, Nice, France
*Corresponding author: Shiqing Xu (xusq3@sustech.edu.cn)
Key points
1. Rupture started on a splay fault, then branched bilaterally on the East Anatolian Fault (EAF),
including onto a fault segment at acute angle to the splay fault.
2. Dynamic rupture models explain the mainshock rupture path, including its apparent backward
branching, and provide insight on its controlling factors.
3. Rupture on the SW EAF segment can be triggered by rupture on the NE EAF segment or, if the EAF
is highly pre-stressed, by the initial splay-fault rupture.
Abstract
Multiple lines of evidence indicate that the 2023 Mw 7.8 Turkey earthquake started on a splay fault, then
branched bilaterally onto the nearby East Anatolian Fault (EAF). This rupture pattern includes one feature
deemed implausible, called backward rupture branching: rupture propagating from the splay fault onto
the SW EAF segment through a sharp corner (with an acute angle between the two faults). To understand
this feature, we perform 2.5-D dynamic rupture simulations considering a large set of possible scenarios.
We find that both subshear and supershear ruptures on the splay fault can trigger bilateral ruptures on
the EAF, which themselves can be either subshear, supershear, or a mixture of the two. In most cases,
rupture on the SW segment of the EAF starts after rupture onset on its NE segment: the SW rupture is
triggered by the NE rupture. Only when the EAF has initial stresses very close to failure, its SW segment
can be directly triggered by the initial splay-fault rupture, earlier than the activation of the NE segment.
These results advance our understanding of the mechanisms of multi-segment rupture and the complexity
of rupture processes, paving the way for a more accurate assessment of earthquake hazards.
Plain language summary
The 2023 Mw 7.8 Turkey earthquake ruptured multiple fault segments, featuring an unexpected backward
rupture branching through a sharp corner: rupture initially propagated toward northeast on a splay fault
and then made a nearly U-turn onto the southwest segment of the nearby East Anatolian Fault (EAF). To
understand such intriguing feature, we conduct a series of computer simulations of earthquake ruptures.
Our results show that the sharp-turn rupture can be realized in two different ways: (i) rupture first jumps
ahead from the splay fault to the northeast segment of the EAF, which later triggers rupture on the
southwest segment the EAF, and (ii) the initial splay-fault rupture directly triggers rupture on the
southwest segment of the EAF. The realization of (i) or (ii) depends on the initial stress and friction
conditions, and hence provides useful clues for understanding the preconditions and detailed rupture
process of the 2023 Mw 7.8 earthquake. The results also shed light on anticipating possible rupture paths
and maximum earthquake magnitude in other regions containing multiple fault segments.
1. Introduction
Multiple fault segments can rupture during a single earthquake or earthquake sequence. Examples include
the 1992 Mw 7.3 Landers earthquake in the Eastern California Shear Zone (ECSZ) (Sieh et al., 1993), the
2010 Mw 7.2 El Mayor-Cucapah earthquake in Baja California (Wei et al., 2011), the 2012 Mw 8.6
earthquake off the coast of Sumatra (Meng et al., 2012a; Yue et al., 2012), the 2016 Mw 7.8 Kaikōura
earthquake in New Zealand (Hamling et al., 2017; Wang et al., 2018), and the 2019 Ridgecrest earthquake
sequence to the north of the ECSZ (Ross et al., 2019). Theoretical, numerical and laboratory studies have
been conducted to understand how and why multi-segment ruptures can occur (DeDontney et al., 2012;
Duan and Oglesby, 2007; Harris and Day, 1993; Kame et al., 2003; Poliakov et al., 2002; Rousseau and
Rosakis, 2009) and to reproduce the patterns of observed multi-segment earthquakes in dynamic rupture
simulations (Wollherr et al, 2019; Ulrich et al., 2019).
In addition to stimulating scientific investigations on earthquake physics, the occurrence of multi-segment
ruptures is a challenge for earthquake hazard assessment: how to estimate the maximum magnitude of
earthquakes in a region that contains multiple fault segments? Rules of thumb have been proposed based
on past earthquake observations, geometrical parameters of faults, and dynamic rupture theory and
simulations (Biasi and Wesnousky, 2021; Bohnhoff et al., 2016; Mignan et al., 2015; Walsh et al., 2023).
One scenario that has been deemed implausible is rupture branching through a sharp corner
characterized by an acute angle (<90 degrees) between the two faults—called backward rupture
branching. The main reasons for discarding this scenario are that earlier dynamic rupture studies only
considered rupture branching through a gentle corner associated with an obtuse angle between the two
faults—called forward rupture branching (Poliakov et al., 2002; Kame et al., 2003), and that backward
rupture branching was generally thought to be inhibited by the shear stress release (stress shadow effect)
on the backward quadrants induced by the first fault rupture. Nonetheless, backward rupture branching
has been observed during some strike-slip earthquakes, with the same or opposite sense(s) of slip along
different fault segments (Fliss et al., 2005; Li et al., 2020; Oglesby et al., 2003). Backward rupture branching
can occur in subduction zones as well, with thrust or mixed thrust/normal faulting mechanism(s) along
different fault segments (Cubas et al., 2013; Melnick et al., 2012; Wendt et al., 2009; Xu et al., 2015). All
these new results challenge the simple consideration of the stress shadow effect, and raise questions
about the possible rupture paths during large earthquakes, in particular how and why backward rupture
branching may occur.
The February 6, 2023 Mw 7.8 Turkey earthquake, while devastating (Dal Zilio and Ampuero, 2023; Hussain
et al., 2023), was densely recorded and provides a unique opportunity to address the aforementioned
questions related to rupture branching. This earthquake struck in the southwestern stretch of the East
Anatolian Fault (EAF) zone, an active plate boundary that accommodates the deformation between the
Anatolian plate (AT) and the Arabian plate (AR), dominated by left-lateral shear (Figure 1). The rupture
started on a previously unmapped splay fault, about 15 km away from the main EAF strand (Melgar et al.,
2023). After arriving at the fault junction, the rupture continued on the Pazarcık segment of the EAF and
then propagated bilaterally along the EAF, thus comprising a forward rupture branching to the northeast
(NE) and a backward rupture branching to the southwest (SW). The NE-ward rupture finally stopped at
around 38oN/38.5oE along the Erkenek segment, while the SW-ward rupture terminated at around
36oN/36oE along the Amanos segment (Figure 1). The total rupture length reached about 350 km and the
peak slip 8-12 m (Barbot et al., 2023; Goldberg et al., 2023; Mai et al., 2023; Melgar et al., 2023; Okuwaki
et al., 2023). The overall co-seismic slip was dominated by left-lateral strike-slip, along both the splay fault
where the earthquake hypocenter was located and the EAF where most of the strain energy was released.
This multi-segment rupture came as a surprise, since the most recent large events (with magnitude around
and above 7) in the region were confined within individual segments, such as the 1795 M 7.0 earthquake
on the Pazarcık segment, the 1872 M 7.2 earthquake on the Amanos segment, and the 1893 M 7.1
earthquake on the Erkenek segment (Güvercin et al., 2022). The multi-segment rupture with an apparent
backward rupture branching feature motivates us to investigate the rupture process of the Mw 7.8
earthquake, especially in its early stage.
In Section 2, we characterize the rupture path of the 2023 Mw 7.8 Turkey earthquake using multiple types
of observations, and further confirm that it includes an apparent pattern of backward branching. In
Section 3, we develop 2.5-D dynamic rupture models (two-dimensional models that account for the finite
rupture depth) to understand this rupture pattern, and find that it may be realized in two different modes.
In the first mode, the SW segment of the EAF is triggered (possibly with a delay) not by the initial splay-
fault rupture but by the rupture on the NE segment of the EAF. The second mode involves early dynamic
triggering of the SW segment of the EAF by the initial splay-fault rupture. Our simplified modeling
approach focuses on exploring a range of possible scenarios, not on a meticulous comparison between
simulated results and observations. Finally, we discuss the implications of the obtained results in Section
4 and draw conclusions in Section 5.
2. Mainshock rupture path inferred from observations
Here, we summarize multiple types of observations that help constrain the rupture path during the 2023
Mw 7.8 Turkey earthquake. Although similar results have now been published by various teams, we
document here observations that were available immediately after the earthquake (on the same day and
up to a few days later) to highlight how rapid seismological products shaped our view of the earthquake
rupture and motivated our theoretical work.
2.1. Mainshock epicenter, aftershocks and surface rupture trace
The fault geometry is constrained to a first order by the aftershock catalog from the AFAD (Turkey Disaster
and Emergency Management Authority, https://deprem.afad.gov.tr) and the surface rupture trace from
the USGS (U.S. Geological Survey) (Reitman et al., 2023), as shown in Figure 1. Both an aftershock cluster
and a short segment of surface rupture trace delineate a splay fault, where the Mw 7.8 mainshock
epicenter was located. Also considering the large offset (15 km) between the relocated earthquake
hypocenter and the trace of EAF (Melgar et al., 2023), we can reasonably conclude that the rupture started
on the splay fault and then continued on the EAF. The next step is to constrain the rupture branching
process, as will be discussed in the following two subsections.
Figure 1. Distributions of mainshock and aftershock epicenters and surface rupture traces of the 2023
Turkey earthquake sequence. Red and yellow stars show the epicenter location of the Mw 7.8 and Mw 7.6
events, respectively. The beachballs indicate their focal mechanisms determined by the AFAD (Turkey
Disaster and Emergency Management Authority) (https://deprem.afad.gov.tr/event-focal-mechanism).
The aftershock catalog is also from the AFAD (https://deprem.afad.gov.tr/event-catalog, last accessed on
May 29, 2023). Surface rupture traces (black curves with red trimming) are from the USGS (U.S. Geological
Survey) (Reitman et al., 2023). EAFZ: East Anatolian Fault Zone. SFZ: Sürgü Fault Zone. From north to south,
Erkenek, Pazarcık, and Amanos denote different segments of the EAFZ in the study region (Güvercin et al.,
2022). Blue dashed lines depict the simplified fault geometry adopted in our numerical simulations. The
inset shows the regional map and tectonic plates. AS: Aegean Sea plate. EU: Eurasian plate. AT: Anatolian
plate. AF: African plate. AR: Arabian plate. EAF: East Anatolian Fault. NAF: North Anatolian Fault.
2.2. Teleseismic back-projection
Figure 2. Teleseismic back-projection imaging of the high-frequency radiation from the Mw 7.8 Turkey
earthquake using the Alaska array. (a) Map view of the locations of radiators, color-coded by time and
size-coded by power. The yellow star indicates the epicenter reported by the USGS. The brown lines are
active faults in Turkey reported by Emre et al. (2013). The inset shows the location of the Alaska array. The
pink triangles represent the broadband stations, the red star indicates the epicenter as reported by the
USGS. The dashed lines indicate the strike direction of three main fault segments; for clarity, they are offset
from the segment traces. (b) Spatiotemporal distribution of radiators. Distance refers to the position along
the strike directions shown in (a) as dashed lines; the strike values are shown in (b). The positions of
radiators before 19 s are relative to the epicenter, the later ones are relative to the junction between the
splay fault and the EAF (37.208ºE, 37.531ºN, according to the surface rupture map from Reitman et al.
(2023)), which is indicated by a yellow triangle in (a) and (b). The dashed lines show reference rupture
speeds for each segment.
We image the rupture process by teleseismic back-projection, a method that can image multi-fault
ruptures without making strong assumptions on the fault system geometry (e.g., Meng et al., 2012a) and
that can be applied rapidly after large earthquakes as soon as teleseismic P-wave data are available (the
results reported here were ready for our analysis on February 7th, see Ampuero (2023). The method can
be automated to deliver results within 1 hour of any large earthquake). We used data from the Alaska
array (Figure 2), which consists of 293 broadband seismic stations within 30 to 90° from the epicenter. Its
high station density and large aperture allows an excellent spatial resolution in the source region. We
employed the Multitaper-MUSIC back-projection method (Meng et al., 2011; Schmidt, 1986), which tracks
the coherent sources of high frequency radiation with finer spatial resolution than conventional back-
projection techniques. Our ray tracing for back-projection adopts the spherically symmetric IASP91
velocity model (Kennett and Engdahl, 1991). We first aligned the vertical components of the initial P waves
using a standard iterative, cross-correlation technique (Reif et al., 2002) to correct for the travel time error
caused by horizontal variations of velocity structure. We selected only the waveforms with a correlation
coefficient greater than 0.6 to increase the waveform coherence and improve result quality. We then
filtered the seismograms from 0.5 to 2 Hz and applied back-projection on a sliding window of 10 s. The
back-projection is relative to the earthquake epicenter reported by the USGS, which is located off the EAF,
in agreement with that determined by the AFAD (Figure 1).
The back-projection results provide a first-order view of the multi-fault rupture pattern. Figure 2a shows
the resulting locations of high-frequency radiators. They coincide well with the active faults. The back-
projection results reveal that the rupture initially propagated to the NE for the first 20 s, along a strike
direction consistent with the splay fault. After reaching the junction with the EAF, the rupture became
bilateral, propagating NE-ward and SW-ward simultaneously along the EAF, until the earthquake
terminated at approximately 70 s. Due to the limited resolution and possibly interference between waves
from multiple rupture fronts, it is challenging to determine whether the SW-ward rupture initiated
simultaneously with the NE-ward rupture or after a delay. Although this issue may be resolved by later
observational studies, the current ambiguity motivates us to examine a range of possible scenarios in
Section 3. In any case, the back-projection results clearly confirm a pattern of rupture branching from the
splay fault to the EAF, with a forward component to the NE and a backward component to the SW.
The back-projection results also provide constraints on rupture speed. Figure 2b illustrates that the
rupture speed is approximately 3.2 to 3.5 km/s, indicating an overall subshear rupture (the shear wave
speed
!!
at the depth of 8 to 10 km is ~ 3.15 to 3.6 km/s, Delph et al. (2015)). However, Rosakis et al.
(2023) proposed an early supershear transition on the splay fault ~ 20 km away from the epicenter, based
on the relative amplitudes of the fault-parallel and fault-normal components of near-field seismic
recordings. Their estimated instantaneous rupture speed is approximately
"#$$%!!
(or ~ 4.88 to 5.58
km/s). Unfortunately, the spatial and temporal scales of the proposed supershear rupture are smaller
than the resolutions of teleseismic back-projection. Nonetheless, the average rupture speed of 3.2 to 3.5
km/s resolved by back-projection suggests that the proposed supershear rupture on the splay fault
probably did not persist for long, if it indeed occurred, likely due to the impeding effect of the intersection
with the EAF. A later finite source inversion study achieved detailed modeling of the recordings near the
splay fault with a subshear rupture (Delouis et al., 2023). To cover different possible situations, we explore
both subshear and supershear rupture speeds in our numerical simulations in Section 3.
2.3. Strong ground motion observations
The strong ground motion data also provide a first-order constraint on the rupture process, especially
during the early stage. We retrieved the acceleration waveforms for a selected set of stations (Figure 3a)
from the AFAD, with additional corrections for instrument response and baseline. We then filtered the
corrected waveforms in the 1-20 Hz frequency band, and subsequently obtained the ground motion
amplitude as
& '
(
)"*+"* ,"
, where
)
,
+
, and
,
are the north, east, and vertical components of the
recordings. As shown in Figure 3a, the nearest stations to the southwest (4615), west (4624, 4625, and
4616), north (4611 and 4631) and northeast (0208 and 0213) of the junction between the splay fault and
the EAF permit a rough estimation of the early rupture process around the fault junction. By aligning these
stations in the east-west direction relative to the fault junction, two groups of signals can be observed for
those stations located in the west (Figure 3b). First, the onsets of large ground motion amplitudes
recorded prior to 20 s since the origin time coincide with the P- and S-wave arrivals emanating from the
hypocenter. Second, an additional phase of strong motions is observed >20 s after the origin time, which
we interpret to originate from the passage of the rupture front. Assuming that the initial rupture arrived
at the junction at around 16 s, we argue that a new rupture initiated along the EAF and then propagated
bilaterally to the NE and SW, according to the moveouts of coherent high-frequency signals later than 20
s (indicated by the dashed green lines in Figure 3b). A simple estimation, based on the onsets of these late
signals, yields a propagation speed of ~ 3.5 km/s along the EAF west of the junction. Although
uncertainties still remain about the exact initiation location and earlier propagation speed of the rupture
along the EAF, the strong ground motion data confirm a pattern of bilateral rupture branching from the
splay fault to the EAF, consistent with the back-projection results.
Figure 3. Distribution map of strong ground motion stations and estimation of rupture process. (a)
Discretization of the fault segments for the strong ground motion analysis and location of the stations
included in the analysis. (b) Strong ground motion amplitudes (with a 1-20 Hz bandpass filtering) recorded
by the stations around the fault junction. The distances are measured as the projection onto the nearest
fault shown in (a) and are relative to the junction. The predicted direct P and S-arrivals emanating from
the hypocenter and the average rupture trajectory are indicated by the solid and dashed lines, respectively.
3. Dynamic rupture models explaining the observed rupture path
To better understand the observed rupture branching pattern, we conduct numerical simulations of
dynamic ruptures exploring a range of possible scenarios, taking into account the uncertainty and diversity
of rupture properties (e.g., fault slip, first triggered location(s) on the EAF, rupture speed) reported by
different studies (Delouis et al., 2023; Melgar et al., 2023; Okuwaki et al., 2023; Rosakis et al., 2023).
3.1. Model settings
We build the fault model based on the surface rupture trace and aftershock distribution of the Mw 7.8
mainshock, focusing on the area of the junction of the splay fault and the EAF (Figure 1). This region
roughly falls into the Pazarcık segment of the EAF. Hereafter, we refer to the EAF in the numerical model
as the main fault. Specifically, we consider a simplified model, where both the splay fault and the main
fault are assumed to be planar and dipping vertically. For convenience, we rotate the view to define a
Cartesian coordinate system aligned with the main fault (Figure 4). We set the angle
-
between the two
faults at
./0
, based on the aftershock distribution (Figure 1). According to the results of stress inversion
from historic seismicity (Güvercin et al., 2022), the regional stress orientation changes systematically
along the strike of the EAF. For the Pazarcık segment, we set the angle
1
between the maximum
compressive stress
2#$%
&
and the main fault at
3/0
. Assuming fluid overpressure (Rice, 1993) and after
some trial tests, we consider a regionally uniform initial stress field:
2''
&' 4$5#/$6789:2'(
&'
4;/6789:2((
&' 4$/6789
(negative sign for compression or left-lateral shear). Since our focus is on how
rupture can propagate from the splay fault to the main fault, we truncate the main fault at a total length
of
;;/6<=
, roughly centered at the junction, ignoring subsequent rupture propagation further to the NE
and SW. We initiate the rupture along the splay fault, setting the hypocenter (red star in Figure 4) at
.$6<=
from the fault junction. In the southward portion of the splay fault (dashed grey line in Figure 4),
we assume a fault cohesion of
"/6789
to artificially terminate the rupture at around
;/6<=
from the
hypocenter.
Figure 4. Model setup for numerical simulations. The main fault (horizontal black line) mimics the EAF,
while the splay fault (inclined grey line) mimics the short fault segment that hosted the hypocenter (red
star). The angle
-
between the two faults is set at
./0
. A time-weakening friction is used to nucleate the
rupture inside a finite-length zone along the splay fault. Elsewhere, a linear slip-weakening friction is
adopted. A fault cohesion of
"/6>?@
is set to terminate the southward rupture along the splay fault
(dashed grey line). The angle
A
between the maximum compressive stress
2)*'
&
and the main fault is set
at
3/0
. Off-fault materials are assumed linearly elastic. Absorbing boundary conditions are applied to the
four edges of the domain. The inset shows the spectral element mesh near the fault junction. Other
specifications of the numerical model can be found in the main text.
We discretize the simulation domain with a quadrilateral element mesh generated in a previous study (Xu
et al., 2015) with the software CUBIT (https://cubit.sandia.gov/). The elements have a size of
;//6=
on
average, which translates into a spatial resolution of about
$/6=
(there are multiple internal nodes within
each element). The treatment of the fault junction follows the convention commonly adopted for fault
branching problems (DeDontney et al., 2012; Xu et al., 2015), where split nodes run continuously across
the junction along the main fault but converge to a single non-split node at the junction along the splay
fault. Such treatment allows for through-going rupture along the main fault but terminated rupture along
the splay fault (zero splay-fault slip at the junction), which is supported by the relative maturity of the
main fault (the EAF) and source inversion results (Melgar et al., 2023; Okuwaki et al., 2023).
We use a time-weakening friction with prescribed rupture speed of
;6<=BC
to artificially nucleate the
rupture along the splay fault (Andrews, 1985; Bizzarri, 2010). Once the rupture exceeds a critical length,
it spontaneously transitions to a linear slip-weakening friction law (Palmer and Rice, 1973; Andrews, 1976)
in which the friction coefficient
D
depends on slip
EF
as
D '
G
D+4
H
D+4D,
I
JF K-
L
:666666666MN6/ O JF O K-
D,:666666666666666666666666666666666666MN6JF P K-
(1)
where
D+
,
D,
, and
K-
are the static friction coefficient, dynamic friction coefficient and critical slip-
weakening distance, respectively. Due to the lack of near-field dynamic stress measurements, we cannot
directly constrain
D+
and
D,
; we thus set their values based on trial and error. In contrast, there are many
strong ground motion stations near the ruptured faults (Figures S1-S3), with which we estimate
K-
following the approach of Fukuyama and Mikumo (2007). In that approach,
K-
is estimated by a proxy
K-Q
defined as two times the fault-parallel displacement at the time of peak ground velocity measured directly
at the fault surface. In practice, stations are at some distance from the fault and we measure
K-QQ
, an off-
fault estimate of
K-Q
(Figure S2). Numerical experiments indicate that
K-QQ
increases (Cruz-Atienza et al.,
2009) with distance from the fault and thus provides an upper bound on
K-Q
. The resulting values of
K-QQ
,
shown along strike in Figure S3, range from 1.0 to 2.0 m. We note a heterogeneous distribution of
K-QQ
in
the southern portion of the EAF, with lower values at 90-110 km from the junction. In numerical
simulations, we explore
K-
values in the range of 0.5-2.0 m, as a compromise between observational
constraint and computational cost. Smaller
K-
values are possible but require finer numerical resolution
and hence increased computational cost. Larger
K-
values in general do not favor successful rupture
branching and hence can be readily ruled out.
Based on the assumed initial stresses and friction coefficients, we calculate the seismic
R
ratio to judge
the relative closeness to failure and hence the rupture mode along each fault (Andrews, 1976; Das and
Aki, 1977; Liu et al., 2014):
R '
|
/!
|
0
"1
|
2!
|
|
2!
|
1
|
/!
|
0#
(2)
where
S&
and
2&
are the initial shear and normal stress resolved on the faults. The parameter
R
generally
has a strong control on the properties of single-fault ruptures, such as their rupture speed (Andrews,
1976). However, in our multi-fault rupture case,
R
as defined in Eq. (2) can only roughly characterize the
rupture mode along the main fault after branching, because the effective initial stress field for the main
fault can be modified by the rupture along the splay fault (Xu et al., 2015).
Viscous damping (Day et al., 2005) and normal stress regularization (Rubin and Ampuero, 2007; Xu et al.,
2015) are applied to both faults to stabilize the simulation. For simplicity, we assume the surrounding
medium is elastic and hence ignore any permanent deformation off the faults. To take into account the
finite width of the seismogenic zone while keeping the computational efficiency of 2-D modeling, we
adopt the 2.5-D approximation as in Weng and Ampuero (2019, 2020). A parameter
T
is introduced to
mimic the fault width, which causes a saturation of slip once the along-strike propagation distance
exceeds a value proportional to
T
(Day, 1982). In this study, we choose
T ' 3/6<=
, equivalent to a fault
width of
;/6<=
in a half space (Luo et al., 2017), to match the observations of co-seismic slip and
aftershocks for the Mw 7.8 mainshock (Barbot et al., 2023; Melgar et al., 2023; Okuwaki et al., 2023). We
carefully choose the values for other model parameters so that the simulated slip is comparable to the
one found in source inversions. Unless mentioned otherwise, we assume model parameters are uniformly
distributed along each fault. Their specific values may vary from one simulation case to another. Table 1
summarizes the key model parameters and their values. Superscripts
UV
and
W
indicate parameters along
the splay fault and the main fault, respectively. We conduct the dynamic rupture simulations with the
spectral-element-method software SEM2DPACK (Ampuero, 2012).
Table 1. Model parameters and their values
Parameters
Values
Shear modulus X
.;#36Y89
P-wave speed !3
Z///6=BC
S-wave speed !!
.3Z36=BC
Rayleigh-wave speed !4
."[$6=BC
Critical rupture speed
!56
to define the end of nucleation
"///6=BC
Width of the seismogenic zone (full space) T
3/6<=
Angle between maximum compressive stress and the main fault 1
3/0
Angle between the main fault and splay fault -
./0
Initial normal stress along x direction 2''
&
4$5#/$6789
Initial normal stress along y direction 2((
&
4$/6789
Initial shear stress 2'(
&
4;/6789
Initial normal stress along the splay fault 277
&
4.3#36789
Initial shear stress along the splay fault 278
&
4Z#\$6789
Static friction coefficient along the splay fault D+
+9
/#;"]/#.$
Dynamic friction coefficient along the splay fault
D,
+9
/#"/
Critical slip-weakening distance along the splay fault K-
+9
/#$/]"#//6=
Static friction coefficient along the main fault D+
)
/#3;]/#3[
Dynamic friction coefficient along the main fault D,
)
/#"/]/#.$
Critical slip-weakening distance along the main fault K-
)
/#$/];#//6=
3.2. Delayed rupture triggering on the SW segment of the main fault
We first show the spatiotemporal evolution of Coulomb failure stress changes
J^_`
for a case of
successful rupture branching from the splay fault to the main fault (Figure 5). Here,
J^_`
is defined as:
J^_` ' JS *D:00 % J2;
(3)
where
JS
and
J2;
are respectively the shear and normal stress changes induced by the splay-fault
rupture, and
D:00
is an effective friction coefficient that includes the contribution from pore fluid pressure
(Freed, 2005). In the plots,
J^_`
is either projected along the main fault (Figure 5a), or resolved onto
planes parallel to the main fault (Figure 5b-e). Positive
J^_`
indicates increased chance for triggering left-
lateral slip along faults parallel to the main fault.
Figure 5. Spatiotemporal distribution of Coulomb failure stress change (
JabR
, positive promoting left-
lateral shear) induced by a subshear rupture along the splay fault. (a) Evolution of
JabR
along the main
fault. Four times
c<
to
c=
are selected to highlight: (1) when a transient positive
JabR
lobe can operate on
the SW segment of the main fault, (2) when rupture just hits the junction (X = 0 km) along the splay fault,
(3) when the NE segment of the main fault starts to slip, and (4) when the SW segment of the main fault
starts to slip. (b)-(e) Spatial distribution of
JabR
, resolved onto faults parallel to the main fault, at the four
selected times defined in (a).
D:00 ' /#3[
is assumed for computing
JabR
(Eq. 3). Other model
parameters are:
D+
+9 ' /#;[
,
D,
+9 ' /#"/
,
K-
+9 ' "#//6W
;
D+
)' /#3[
,
D,
)' /#;\
,
K-
)' "#//6W
.
In Figure 5, rupture initially propagates at subshear speed along the splay fault. As the rupture front
approaches the fault junction, a positive
J^_`
lobe sweeps over the SW segment of the main fault,
moving towards the fault junction (before and around
c<
in Figures 5a and 5b). However, the amplitude
of this positive
J^_`
lobe is not strong enough to trigger slip on the main fault. Once the splay-fault
rupture arrives at the junction, positive and negative
J^_`
lobes persistently operate on the NE and SW
segments of the main fault, respectively (
c"
to
c>
in Figures 5a, c and d). These two stress lobes with
opposite signs are caused by the terminated rupture along the splay fault. They are long-lived and hence
modify the effective initial stress of the main fault, promoting left-lateral slip on the NE segment and
suppressing left-lateral slip on the SW segment. Indeed, a new rupture along the main fault is triggered
around
c>
on the NE side of the junction, and starts to propagate to the NE (Figure 5d). Only after this
rupture propagates beyond some distance, it transfers enough stress to the opposite side of the junction
(Tada et al., 2000), allowing the SW segment to overcome the initial stress shadow (
c"
to
c>
in Figure 5a)
and to finally start propagating in the SW direction (
c=
in Figures 5a and 5e).
Therefore, for the case in Figure 5, backward rupture branching is not achieved by a direct rupture
branching from the splay fault to the SW segment of the main fault (Fliss et al., 2005), but through a
cascade process from the splay fault to the NE segment of the main fault and then to the SW segment of
the main fault. If the NE segment is forced to remain locked, then the SW segment is not successfully
triggered (not shown here but confirmed by simulations), at least when the seismic S ratio on the main
fault is not extremely low. We also test another case (Figure S4) with supershear rupture along the splay
fault, as proposed by Rosakis et al. (2023), and find the above conclusion still holds.
After understanding the basic process of rupture branching, we proceed to investigate other aspects of
the simulated results. Figure 6 shows the evolutions of slip rate and slip for the case in Figure 5. Rupture
is not instantaneously triggered along the main fault, but displays a slow nucleation phase (Ohnaka, 1992)
before accelerating to a speed close to the Rayleigh wave speed
!4
(Figure 6a). The NE segment of the
main fault is activated earlier and hosts a faster rupture than the SW segment (Figure 6a). This is consistent
with our previous judgement that the NE-ward rupture serves as a prerequisite for the SW-ward rupture
along the main fault.
The asymmetry in rupture behaviors along the main fault is also manifested in the slip distribution along
the main fault (Figure 6b). First, slip starts to accumulate around 15 s, first on the NE side of the junction.
Second, the average slip is always larger along the NE segment than on the SW segment, despite the same
initial stress and frictional properties along both segments. The asymmetry in slip distribution supports
our earlier statement that the effective initial stress field for the main fault is modified by the rupture
along the splay fault, featuring long-lived positive
J^_`
for the NE segment but negative
J^_`
for the SW
segment (
c"
to
c>
in Figure 5a). Such asymmetric slip distribution is also observed in the case with
supershear rupture along the splay fault (Figure S5), in the source inversion results for the Mw 7.8
mainshock (Barbot et al., 2023; Melgar et al., 2023; Okuwaki et al., 2023), and in other studies of the
rupture branching problem (Bhat et al., 2007a; Fliss et al., 2005; Templeton et al., 2009; Xu et al., 2015),
suggesting that it should be a common feature around fault junctions (Andrews, 1989).
Figure 6. Spatiotemporal distribution of (a) slip rate and (b) slip for the case shown in Figure 5. In (a), the
evolution of slip rate along the splay fault is projected onto the plane parallel to the main fault.
!?Q
,
!@Q
and
!AQ
represent the apparent P-, S- and Rayleigh-wave speed projected onto the same plane. For the NE
and SW segments of the main fault, the delay time is defined as the interval between when splay-fault
rupture just arrives at the junction and when triggered main-fault rupture attains a critical propagation
speed
!8-
of
"6dWBU
.
!8
(
;\$/6WBU
) denotes the instantaneous speed of the splay-fault rupture prior to
the arrival at the junction. In (a) and (b), grey star represents the projection of the rupture hypocenter (red
star) onto the main fault.
3.3. Controls on rupture triggering on the main fault
To provide quantitative understanding of what controls the rupture branching from the splay fault to the
main fault, we have conducted two sets of numerical simulations. In the first set, we fix the parameters
along the splay fault (same as in Figures 5 and 6), but vary those along the main fault, in particular the
critical slip-weakening distance
K-
)
and the seismic S ratio
R)
(by varying the dynamic friction coefficient
D,
)
). We investigate how main fault properties affect the triggering process, especially the delay time
defined as the interval between when rupture arrives at the junction along the splay fault and when the
rupture triggered along the main fault reaches a propagation speed
!56
of
"6<=BC
(see the definition in
Figure 6a). The value of
!56
is arbitrary; nonetheless, the chosen value of
"6<=BC
does provide a reference
for judging the end of the nucleation process along the main fault. According to the scenario in Figures 5
and 6, the main-fault rupture starts only after the splay-fault rupture arrives at the junction; therefore,
the delay time is positive for both segments of the main fault.
Figure 7 summarizes the results of delay time for varying parameters along the main fault. The delay time
is shorter for the NE segment than for the SW segment (compare Figures 7a and 7b), again supporting our
previous judgement of NE-ward rupture as a prerequisite for the SW-ward rupture along the main fault
(Figure 5). On each segment, the delay time, a proxy of rupture nucleation time, increases with the critical
slip-weakening distance
K-
)
and the seismic S ratio
R)
. Given that rupture length scales with time during
the nucleation process, the observed trend is consistent with the theory on rupture nucleation under
quasi-static loading (Uenishi and Rice, 2003), despite that in this study rupture can be dynamically
triggered along the main fault. With a decrease of
R)
, there is a transition of rupture mode from subshear
to supershear along the main fault, which is in general agreement with the results of previous studies
(Andrews, 1976; Liu et al., 2014). Moreover, the transition boundary usually occurs at larger
R)
for the
NE segment (Figure 7b) than for the SW segment (Figure 7a). This again can be explained by the
modification of the effective initial stress on the main fault: under an overall positive (or negative)
J^_`
for the NE (or SW) segment (Figure 5), the actual seismic S ratio can be smaller (or larger) than the nominal
one used in Figure 7b (or Figure 7a).
Figure 7. Summary of delay time as a function of seismic S ratio (
R)
) and critical slip-weakening distance
(
K-
)
) along the main fault. (a) and (b) are for the delay time along the SW and NE segment of the main
fault, respectively. We fix the parameters along the splay fault (
D+
+9 ' /#;[
,
D,
+9 ' /#"/
,
K-
+9 ' "#//6W
),
resulting in a subshear rupture (
!8';\$/6WBU
, same as in Figure 6) prior to the arrival at the junction.
For the main fault, we vary
D,
)
(under fixed
D+
)' /#3[
) to obtain different values for
R)
. Under this
consideration, rupture can always be triggered along the main fault (at least for the NE segment), as
predicted by the
JabR
computation in Figure 5.
In the second set of numerical simulations, we fix the parameters along the main fault (same as in Figures
5 and 6), but vary those along the splay fault. We first show three examples in Figure 8, from which three
prominent features are observed. First, the triggered rupture along the main fault can be asymmetric,
featuring supershear towards NE but subshear towards SW (Figure 8b and c), which can still be attributed
to the asymmetric
J^_`
across the junction along the main fault. Second, with a decrease of rupture
speed
!5
along the splay fault (from Figure 8a to 8c), the speed of the triggered rupture along the main
fault increases, especially on the NE segment, which is unexpected. Third, the delay time is the shortest
for the case in Figure 8c, despite having the slowest rupture speed along the splay fault. Our parametric
study further confirms that the delay time tends to be shorter when rupture speed is slower (under larger
R+9
) along the splay fault (Figure 9). To deepen the understanding of rupture triggering along the main
fault, we further evaluate the loading applied by the splay fault rupture on the main fault. Specifically, we
examine how shear stressing rate e
S
fe, evaluated at the splay-fault rupture front right before it hits the
junction (Figure 10a-c), influences the rupture nucleation and propagation along the main fault.
Figure 8. Evolution of slip rate for three examples featuring diverse rupture behaviors. (a) Splay-fault
rupture transitions to supershear at an earlier time; main-fault rupture remains subshear in both
directions. (b) Splay-fault rupture transitions to supershear at a later time; along the main fault, the NE-
ward rupture transitions to supershear while the SW-ward rupture remains subshear. (c) Splay-fault
rupture remains subshear; along the main fault, the NE-ward rupture transitions to supershear while the
SW-ward rupture remains subshear. For simulating the three examples, we fix the parameters along the
main fault (
D+
)' /#3[
,
D,
)' /#;\
,
K-
)' "#//6W
) and some parameters along the splay fault (
D,
+9 '
/#"/
,
K-
+9 ' /#$/6W
). We vary the static friction coefficient along the splay fault to obtain different rupture
behaviors: (a)
D+
+9 ' /#;"
, (b)
D+
+9 ' /#;$
, and (c)
D+
+9 ' /#..
. In (a)-(c).
!8
denotes the instantaneous
propagation speed of splay-fault rupture prior to the arrival at the junction. We also pick the same
moment, when splay-fault rupture is about to hit the junction, to evaluate the shear stressing rate e
S
fe (to
be shown in Figure 10).
We find e
S
fe partly explains the unexpected results of the rupture process along the main fault (Figures 8
and 9). First, e
S
fe for a splay-fault subshear rupture is higher than that for a splay-fault supershear rupture
(Figure 10d and e), at least for the cases investigated in this study, which can be attributed to the higher
degree of stress singularity in the subshear regime (Freund, 1990). Higher e
S
fe along the splay fault
corresponds to higher loading rate along the main fault, based on the compatibility condition for elasticity.
Second, previous studies indicate that higher loading rate can reduce the time or length required for
rupture nucleation and can promote faster rupture propagation beyond nucleation (Guérin-Marthe et al.,
2019; Gvirtzman and Fineberg, 2021; Kato et al., 1992; McLaskey and Yamashita, 2017; Xu et al., 2018; Yu
et al., 2002). Taken together, it becomes clear that subshear rupture along the splay fault can exert a
higher loading rate to the junction region, which favors earlier triggering and faster rupture propagation
along the main fault, at least for the NE segment where
J^_`
remains positive (Figure 9b). Using a similar
argument for the main fault, one can also explain the triggering of SW-ward rupture (Figure 9a) aided by
the stress transfer from the NE segment. Loading rate is not the only factor that can affect the rupture
process under dynamic loading. Loading duration (Xu et al., 2015), successive loading (e.g., due to
supershear front, S-wave Mach front, and Rayleigh front) (Aben et al., 2016; Smith and Griffith, 2022; Xu
and Ben-Zion, 2017) and arrest waves (Rubin and Ampuero, 2007; Ryan and Oglesby, 2014) can also play
a role, but are beyond the scope of this study.
Figure 9. Delay time as a function of seismic S ratio (
R+9
) and critical slip-weakening distance (
K-
+9
) along
the splay fault. (a) and (b) are for the delay time along the SW and NE segment of the main fault,
respectively. We fix the parameters along the main fault (
D+
)' /#3[
,
D,
)' /#;\
,
K-
)' "#//6W
), which
are the same as in Figures 5 and 6. For the splay fault, we vary
D+
+9
(under fixed
D,
+9 ' /#"/
) to obtain
different values for
R+9
. Under this consideration, the simulated maximum slip (
].6W
) along the splay
fault remains comparable to the one inferred by source inversion of the Mw 7.8 mainshock.
Figure 10. Simulated shear stress waveforms for (a) a subshear rupture, (b) a supershear daughter rupture
that is just born ahead of a subshear mother rupture, and (c) a supershear rupture that is already well
established. In each panel of (a)-(c), two versions of shear stressing rate e
S
fe are estimated, based on the
loading (red) and unloading (blue) stage around the primary rupture front. More details about the three
rupture modes in (a)-(c) can be found in Liu et al. (2014) and Xu et al. (2023). Summary of e
S
fe during (d)
loading and (e) unloading for a range of seismic S ratio (
R+9
) and critical slip-weakening distance (
K-
+9
)
along the splay fault (same as in Figure 9).
3.4. Early rupture triggering on the SW segment of the main fault
We also find cases in which rupture is triggered first on the SW segment of the main fault. Although we
do not know whether this scenario indeed occurred during the mainshock, it is interesting to explore its
features for the following three reasons. First, the splay-fault rupture exerts a transient positive
J^_`
on
the SW segment of the main fault before the splay-fault rupture arrives at the junction (Figures 5 and S4).
We aim at determining whether the amplitude and duration of this transient stress are enough for a
successful triggering of the SW segment (Figures S6 and S7). Second, the last two large earthquakes (with
a magnitude around or above 7) along the Pazarcık segment of the EAF occurred in 1795 (M 7.0) and 1513
(Ms 7.4) (Ambraseys, 1989; Güvercin et al., 2022). Therefore, it is possible that the Pazarcık segment
(corresponding to our modeled main fault) was already close to failure before the 2023 Mw 7.8 mainshock,
which could permit an earlier triggering along its SW segment. Third, two prominent seismic clusters,
associated with relatively low Gutenberg-Richter b-values, have been observed around the fault junction
before the 2023 Mw 7.8 mainshock (Kwiatek et al., 2023), suggesting that this region could have been
already stressed close to failure before the mainshock.
Figure 11 shows one case in which the SW segment of the main fault is successfully triggered, before a
subshear rupture arrives at the junction along the splay fault. Additional simulations (not shown here)
confirm that the SW-ward rupture along the main fault can continue propagating even without activation
of the NE segment. We find similar results for a supershear rupture along the splay fault (Figure S8). Our
detailed investigation reveals that, as long as the main fault is initially close to failure (extremely low
R)
),
successful earlier triggering occurs along the SW segment of the main fault, leading to ruptures that can
easily reach supershear speeds (Figure S9), are often characterized by a negative delay time (Figures 11a
and S9), and appear to propagate “faster” (if mis-counted from the junction) than the NE-ward rupture
(Figure 11b). Nonetheless, the final slip along the main fault is still smaller on the SW side of the junction
(Figure 11b), similar to the previous case without earlier triggering on this side (Figure 6b). This may be
explained by the fact that the final slip distribution along the main fault is more sensitive to the static
J^_`
, which is established only after the splay-fault rupture is terminated at the junction.
Figure 11. Spatiotemporal distribution of (a) slip rate and (b) slip for a case with earlier triggering on the
SW segment of the main fault. The splay-fault rupture remains subshear, while the main-fault rupture
eventually reaches supershear in both directions. In (a), the delay time is still defined as the interval
between the times when the splay-fault rupture just arrives at the junction and when the triggered main-
fault rupture attains a propagation speed of
"6dWBU
. This delay time is now negative for the SW-ward
rupture along the main fault. Due to the complex rupture behavior towards NE along the main fault,
involving a second rupture triggering at the junction, we do not estimate the delay time for that rupture
direction. The relevant model parameters are:
D+
+9 ' /#;\
,
D,
+9 ' /#"/
,
K-
+9 ' /#$/6W
;
D+
)' /#3;
,
D,
)'
/#;3
,
K-
)' /#$/6W
.
4. Discussion
4.1. The need to consider backward rupture branching in earthquake hazard assessment
Previous earthquake hazard analyses only considered scenarios of forward rupture branching to estimate
the maximum magnitude of earthquakes in the Anatolian region (Mignan et al., 2015). By contrast,
backward rupture branching occurred during the 2023 Mw 7.8 Turkey earthquake, involving rupture
propagation from a splay fault onto the SW segment of the EAF (Figures 1-3). According to our 2.5-D
numerical simulations, such backward rupture branching can be realized in two different modes. In the
first mode (Figures 5, 6, 8, S4 and S5), rupture does not make a direct transition from the splay fault to
the backward segment of the main fault; rather, it triggers rupture along the forward segment, which in
turn triggers rupture along the backward segment at a later time. In other words, a complex cascade
process occurs sequentially over three fault segments, in which the intermediate segment plays a vital
role in transferring positive
J^_`
first in the forward direction and then in the backward direction. In the
second mode (Figures 11, S6-S8), rupture on the splay fault directly triggers rupture along the backward
segment of the main fault, if the latter is initially close to failure. Whether the forward segment of the
main fault is present is not important, although its presence may facilitate the triggering of an additional
rupture at a later time (Figures S7 and S8). In both modes, successful backward rupture branching can be
realized for a range of rupture speeds along the splay fault (Figures 9 and S9).
Together with other known examples of backward rupture branching observed on strike-slip faults (Fliss
et al., 2005; Li et al., 2020; Oglesby et al., 2003; see more examples in Xu, 2020), dip-slip faults (Xu et al.,
2015, and references therein), as well as during laboratory earthquakes (Rousseau and Rosakis, 2003,
2009), our results suggest that backward rupture branching should be considered more systematically in
earthquake hazard analyses. Future studies can be conducted to explore other conditions (e.g., 3-D
effects, gap or overlap between different fault segments) that can promote or impede backward rupture
branching. Efforts can also be made to classify the detailed situations for backward rupture branching,
e.g., whether backward rupture branching is realized on pre-existing or newly-formed faults, with the
same or opposite sense of slip, on the extensional or compressional side, and through a direct or indirect
triggering process.
4.2. Anticipating rupture directivity
Rupture directivity exerts a first-order control on ground motion pattern, activation of secondary faults,
and final earthquake size (Andrews and Ben-Zion, 1997; Lozos, 2016; Oglesby and Mai, 2012; Xu et al.,
2015). Although modern observational networks, especially those installed near active faults, allow
rupture directivity to be unambiguously determined, the number of instrumentally recorded earthquakes
is still sparse. To gain confidence on the possible rupture paths in a given fault system, inferences are
often drawn from a wealth of historic earthquakes, e.g., based on the fault geometry configuration (Fliss
et al., 2005; Platt and Passchier, 2016; Scholz et al., 2010) and the permanent damage markers preserved
in the field (Di Toro et al., 2005; Dor et al., 2006; Rowe et al., 2018). Taking the 2023 Mw 7.8 Turkey
earthquake as an example, based on the information of fault geometry (Figure 1) and the scenarios
considered by Mignan et al. (2015), one would have expected the earthquake to nucleate in the middle
of the Pazarcık segment of the EAF and then propagate bilaterally along different segments of the EAF,
occasionally producing forward rupture branching in the extensional or compressional quadrants.
However, the earthquake actually nucleated on a splay fault and then continued on the EAF, featuring a
forward rupture branching to the NE and a backward rupture branching to the SW. Therefore, more works
are needed to improve the methods to assess the possible rupture directivity of future events, especially
when direct seismological constraints are not available.
4.3. The impacts of splay-fault rupture on the main fault
The initiation of the Mw 7.8 Turkey earthquake on a splay fault raises several interesting questions about
its possible impacts on the rupture of the main fault (the EAF). First, our numerical simulations show that,
even with uniform initial stress and frictional properties, the rupture behavior on the main fault can be
highly asymmetric across the junction, e.g., featuring a quicker rupture nucleation, a faster rupture speed
and a larger slip on the NE side than on the SW side (Figures 6 and 8). According to our stress analysis
(Figures 5 and S4), such asymmetric rupture behavior can be explained by the asymmetric stress change
imposed by the splay-fault rupture. Without the latter, if the earthquake had started on the EAF, the
evolution of rupture would have been smooth and continuous along the main fault, unless other
complexities (e.g., nonlinear dynamics, spatial heterogeneity, inherent discreteness) are invoked (Cochard
and Madariaga, 1996; Madariaga, 1979; Rice and Ben-Zion, 1996). Second, our numerical simulations also
show that sometimes multiple ruptures can be almost simultaneously nucleated along the main fault
(Figures S7 and S8), which is otherwise difficult to achieve under a slowly increased background loading
unless strong heterogeneities are involved (Albertini et al., 2021; Cattania and Segall, 2021; Lebihain et
al., 2021; McLaskey, 2019; Schär et al., 2021; Selvadurai et al., 2023; Yamashita et al., 2022). Again, such
seemingly surprising result (no strong heterogeneities in our simulations) can be explained by the high-
rate dynamic loading imposed by the splay-fault rupture, which is known to be capable of nucleating
multiple ruptures (Doan and d’Hour, 2012), sometimes even with supershear speed (Xu et al., 2018, 2023).
Finally, a third point can be raised by considering the failure time of the main fault and the associated
earthquake size. Without the transient and static stress perturbations imposed by the splay-fault rupture,
the main fault would have failed later (Gomberg et al., 1998), after accumulating additional strain energy,
potentially leading to larger slip and a faster rupture speed. Alternatively, the high-rate dynamic loading
imposed by the splay-fault rupture might have promoted the main-fault rupture to attain a very fast speed
from the beginning (Guérin-Marthe et al., 2019; Gvirtzman and Fineberg, 2021; Kato et al., 1992;
McLaskey and Yamashita, 2017; Xu et al., 2023; Yu et al., 2002), allowing it to expand further than ever
before (Güvercin et al., 2022) under a rate-dependent feedback mechanism (Xu et al., 2018), despite that
the failure time has been advanced: rate-enhanced rock brittleness and co-seismic weakening could
overtake the shortened healing time, leading to larger slip and a faster rupture speed (Hatakeyama et al.,
2017; McLaskey, 2019).
In short, although the actual rupture behavior along the EAF during the Mw 7.8 Turkey earthquake remains
to be refined by ongoing observational studies, all three points above suggest that the rupture pattern on
the EAF could have been different if the earthquake had started on the EAF as a result of slow tectonic
loading. The same points may also apply to other regions (e.g., Baja and southern California) where a large
earthquake is inferred to have started on a subsidiary fault (Fletcher et al., 2016; Lozos, 2016).
4.4. Back-propagating rupture mediated by fault geometry
If the observations of the 2023 Mw 7.8 Turkey earthquake had been too coarse to resolve that it initiated
on a splay fault, its backward rupture branching would have been interpreted as a case of back-
propagating rupture, in which the rupture first propagated to the NE on the EAF and then turned around
to the SW on the same fault. Back-propagating rupture has been reported in slow earthquakes (Houston
et al., 2011; Obara et al., 2012), regular earthquakes (Hicks et al., 2020; Ide et al., 2011; Meng et al., 2012b)
and laboratory earthquakes (Gvirtzman and Fineberg, 2021; Xu et al., 2023). Multiple mechanisms have
been proposed to explain its occurrence: stress transfer along a heterogeneous fault (Luo and Ampuero,
2017), pore-pressure wave (Cruz-Atienza et al., 2018), low-velocity fault damage zone (Idini and Ampuero,
2020), free-surface reflection (Oglesby et al., 1998). Xu et al. (2021) argued that back-propagating rupture
is an intrinsic feature of dynamic ruptures, whose observability is usually masked by the superposition
effect but can be enhanced by various types of perturbation. For the previously reported cases, it was
either observed or assumed that the rupture propagated back and forth along the same fault, and quite
often the back-propagating rupture propagated faster than the forward rupture (Houston et al., 2011;
Obara et al., 2012). However, this is clearly not the case for the Turkey earthquake, where at least two
distinct faults were involved in the back-and-forth rupture propagation (Figures 1-3). Moreover, the back-
propagating rupture could have been slower than the initial forward rupture, according to our (Figures 6
and 8) and other simulation results (Abdelmeguid et al., 2023). The multi-segment fault geometry plays
the most important role in exciting the back-propagating rupture during the Turkey earthquake. Since
multiple fault strands and triple junctions are common (Faulkner et al., 2003; Platt and Passchier, 2016;
Rowe et al., 2013; Şengör et al., 2019; Vannucchi et al., 2012; Wolfson-Schwehr and Boettcher, 2019),
some of the previously-reported back-propagating ruptures might have also been mediated by a multi-
fault geometry that was not resolved in the available observations. Future efforts could aim at improving
the methods for imaging fault zone structure and earthquake rupture processes, to assess the importance
of fault geometry in back-propagating ruptures or to compare back-propagating ruptures on single faults
and on multiple faults.
5. Conclusions
Motivated by the multi-segment rupture observed during the 2023 Mw 7.8 Turkey earthquake, we have
conducted 2.5-D numerical simulations of dynamic ruptures in a splay-and-main fault system, with
rupture initiation on the splay fault. In particular, we focused on processes enabling the unexpected
feature of backward branching involving rupture propagation from the splay fault to the southwest
segment of the EAF, which makes an acute angle to the splay fault and lies in its static stress shadow. The
simulated results show that bilateral rupture branching onto the main fault (representing the East
Anatolian Fault, EAF) can be realized by both subshear and supershear ruptures along the splay fault. Two
distinct modes of the branching process are identified. In the first mode, rupture branches from the splay
onto the forward (NE) segment of the main fault which, after some delay, triggers the backward (SW)
segment, revealing a complex cascade process across three fault segments. In the second mode, the
backward segment of the main fault is directly activated by the splay-fault rupture, provided that the main
fault is initially close to failure. While our numerical model is simplified in many aspects, including fault
geometry, initial stresses and friction properties, the simulation results provide useful insights for
understanding possible scenarios of rupture branching in configurations similar to the 2023 Mw 7.8 Turkey
earthquake. Especially, our study suggests that backward rupture branching, a feature deemed
implausible by previous studies, should be considered in earthquake hazard analyses.
Acknowledgments
SX was supported by the National Key R&D Program of China 2021YFC3000700 and the NSFC grant
42074048. YX and JPA were supported by the EU project “DT-GEO, A Digital Twin for Geophysical Extremes”
(No 101058129). JPA was also supported by the French government through the UCA-JEDI Investments in
the Future project (ANR-15-IDEX-01) managed by the National Research Agency (ANR). MvdE was
supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation program (grant agreement No. 101041092 – ABYSS). JP was supported by fellowships from
the Interdisciplinary Institute for Artificial Intelligence 3IA Côte d’Azur.
Author contributions
Project design and supervision: J. P. Ampuero and S. Xu. Back-projection analysis: Y. Xie. Strong ground
motion data analysis: M. van den Ende and J. Premus. Numerical simulations: X. Ding. Original draft
writing: All authors.
Competing interests
There are no competing interests.
Data and code availability
The software SEM2DPACK is freely available at: https://github.com/jpampuero/sem2dpack. The key input
parameters for running numerical simulations are within the paper. The information for the Mw 7.8
mainshock can be found from the AFAD (Turkey Disaster and Emergency Management Authority) at:
https://deprem.afad.gov.tr/event-focal-mechanism, or from the USGS (U.S. Geological Survey) at:
https://earthquake.usgs.gov/earthquakes/eventpage/us6000jllz/origin/detail. The aftershock catalog
was downloaded from the AFAD at: https://deprem.afad.gov.tr/event-catalog (last accessed on May 29,
2023). The surface rupture trace was from the USGS (Reitman et al., 2023) at:
https://doi.org/10.5066/P985I7U2. The teleseismic data of the Alaska array were downloaded through
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Supplementary material
S1. Estimation of
h𝒄
based on
h𝒄QQ
Figures S1-S3 show the information for estimating the critical slip-weakening distance
K-
and the
obtained results. We use unfiltered seismograms with baseline correction: we remove the mean value of
acceleration recordings before the earthquake and a fitted quadratic function from velocity. As mentioned
in the main text,
K-
is not directly measured but estimated by a proxy
K-QQ
, defined as two times the fault-
parallel displacement at the time of peak ground velocity measured at short distance from the fault (Figure
S2). The proxy
K-QQ
is an upper bound of the value
K-Q
that would be measured exactly on the fault, and
K-Q
itself is a representative approximation of the actual
K-
. We use the data retrieved from the entire
portion of the EAF southwest of the junction with the initial splay fault (Figures S1 and S3), whereas in our
numerical simulations we only focus on the region near the junction. Figure S3 shows our
K-QQ
estimates,
their uncertainties and their spatial variability.
Figure S1: Location of selected stations close to the fault surface rupture. We focus on the southern portion
of the EAF, SW from its junction with the initial splay fault. The grey lines show surface ruptures (Reitman
et al., 2023), the black line shows the simplified geometry considered to compute along-strike positions in
Figure S3, and triangles show the position of stations at a distance from the fault shorter (red) and larger
(blue) than 1 km.
Figure S2. Fault-parallel velocity (blue) and displacement (black) obtained by integrating acceleration data
with baseline correction. The horizontal red-dashed line denotes the displacement level right before the
passage of the SW-ward rupture front near the station; this value is taken as the reference to estimate
K-QQ
. The vertical black dashed line indicates the time of maximum velocity. The red cross shows an
estimate of the uncertainty of maximum velocity (horizontally) and corresponding displacement
(vertically). The red dot in their intersection indicates a mean value of peak-velocity time and displacement.
Figure S3. Along-strike distribution of estimated
K-QQ
. The distance in the horizontal axis is relative to the
junction between the splay and main faults (see Figure S1). Large black dots show the value of
K-QQ
estimated from the displacement at the time of maximum velocity. Vertical bars show the
K-QQ
uncertainty
inferred from the maximum velocity uncertainty, while small dots (in blue or red) show
K-QQ
at the center
of the uncertainty interval. Colors indicate stations at a distance from the fault shorter (red) and larger
(blue) than 1 km, as in Figure S1.
S2. Additional results for delayed rupture triggering on the SW segment of the main fault
In addition to the subshear case shown in the main text (Figures 5 and 6), we report here a case of
supershear rupture along the splay fault, which successfully triggers first the NE segment of the main fault
(Figures S4 and S5). The overall behavior of the triggered rupture along the main fault (Figure S5) is similar
to that of the previous case (Figure 6). The main differences lie in the transient stress field before the
splay-fault rupture is fully terminated at the junction. In the supershear case (Figure S4), the stress field
comprises three parts that sequentially sweep along the SW segment of the main fault (Mello et al., 2010,
2016). The first one is carried by the dilatational field (zero curl) of the supershear front (Bhat et al., 2007b)
and exerts a transient positive
J^_`
(
c<
to
c"
in Figure S4a, Figure S4b and c). The second one is carried
by the S-wave Mach front and exerts a transient negative
J^_`
(around
c>
in Figure S4a, Figure S4d). The
third one is carried by the trailing Rayleigh wave but is too weak to observe (Figure S4d). None of these
three parts triggers a rupture along the SW segment of the main fault in the case shown in Figure S4;
successful triggering along the SW segment occurs only after the NE segment is activated (Figure S4f and
g), similar to the previous case shown in Figure 5.
Figure S4. Spatiotemporal distribution of Coulomb failure stress change (
JabR
) induced by a supershear
rupture along the splay fault. (a) Evolution of
JabR
projected along the main fault. Six times
c<
to
cC
are
selected to highlight (1) when a dilatational stress lobe (
JabR P /
) operates on the SW segment of the
main fault, (2) when the S-wave Mach front (
JabR i /
) is about to sweep over the SW segment next to
the junction, (3) when the supershear rupture front just hits the junction along the splay fault, (4) when
arrest waves start to radiate outward from the junction, (5) when rupture is just triggered along the NE
segment of the main fault, (6) when the SW segment is activated by the stress transfer from the NE-ward
propagating rupture. (b)-(g) Spatial distribution of
JabR
, resolved onto faults parallel to the main fault,
at the six different times defined in (a).
D:00 ' /#3[
is assumed to compute
JabR
(Eq. 3). Other model
parameters are:
D+
+9 ' /#;"
,
D,
+9 ' /#"/
,
K-
+9 ' /#$/6W
;
D+
)' /#3[
,
D,
)' /#;\
,
K-
)' "#//6W
.
Figure S5. Spatiotemporal distribution of (a) slip rate and (b) slip for the case shown in Figure S4. In (a),
!8
(
$[\[6WBU
) denotes the instantaneous propagation speed of the splay-fault rupture prior to its arrival at
the junction with the main fault. The delay time is defined in the same way as in Figure 6.
S3. Additional results for early rupture triggering on the SW segment of the main fault
Here, we document the possibility of rupture triggering first on the SW segment of the main fault (Section
3.4) by reporting additional numerical simulation results. Figure S6 shows the evolution of
J^_`
for the
case in Figure 11, in which a splay-fault subshear rupture triggers first the SW segment. The rupture along
the SW segment is initiated around
c"
(Figure S6c) and shows bilateral propagation from
c>
to
c=
(Figure
S6d and e). Earlier triggering can also be achieved by a supershear rupture along the splay fault (Figures
S7 and S8). The dilatational stress carried by the splay-fault supershear front produces the earliest
triggering along the SW segment (around
c"
in Figure S7). The following S-wave Mach front, though
associated with a negative
J^_`
, does not stop the rupture triggered along the SW segment (
c>
to
c=
in
Figure S7). Upon the arrival of the splay-fault rupture at the junction, a second rupture is triggered (after
c=
in Figure S7a), slightly skewed to the NE side of the junction along the main fault. Second rupture
triggering can also be observed in the subshear case, initiated at the junction along the main fault (Figure
S6), but is somewhat overshadowed by the first rupture. We expect this second rupture to follow the
same mechanism as analyzed in Section 3.2.
Finally, we report an additional set of results on the delay time along the main fault (Figure S9). Here, we
focus on the SW-ward rupture triggered along the main fault, including cases triggered first on the NE
segment (marker with black edge color, as in Figure 6) and first on the SW segment (marker with red edge
color, as in Figure 11). We do not consider second rupture triggering, even if it contains a SW-ward
component (e.g., initiated at the fault junction in Figures S7 and S8). We overall find that, to trigger first
the SW segment, the main fault must be initially close to failure (extremely low values of
R)
).
Figure S6. Similar to Figure S4 but for a subshear rupture along the splay fault that triggers rupture of the
main fault first along its SW segment, before the splay-fault rupture arrives at the junction.
D:00 ' /#3;
is assumed to compute
JabR
(Eq. 3). Other model parameters can be found in Figure 11, which shows the
corresponding evolutions of slip rate and slip.
Figure S7. Similar to Figure S6 but for a supershear rupture along the splay fault. Here also, rupture of the
main fault is triggered first along its SW segment, before the splay-fault rupture arrives at the junction,
and
D:00 ' /#3;
. Other model parameters are:
D+
+9 ' /#;"
,
D,
+9 ' /#"/
,
K-
+9 ' /#$/6W
;
D+
)' /#3;
,
D,
)' /#;/
,
K-
)' /#$/6W
.
Figure S8. Spatiotemporal distribution of (a) slip rate and (b) slip for the case shown in Figure S7.
Figure S9. Delay time along the SW segment of the main fault as a function of the seismic S ratio along the
main fault (
R)
) and along the splay fault (
R+9
, indicated by curve and symbol-fill-in colors). Symbols with
black and red edges correspond, respectively, to the cases with triggering first along the NE segment and
SW segment of the main fault. Earlier triggering on the SW segment (negative or small positive delay time)
occurs only at extremely low values of
R)
, i.e. when the main fault is initially very close to failure. For the
main fault, we vary
D,
)
(under fixed
D+
)' /#3;
) to obtain different values of
R)
. For the splay fault, we
vary
D+
+9
(under fixed
D,
+9 ' /#"/
) to obtain different values of
R+9
. For both the main and splay faults,
K-
is fixed at
/#$/6W
.
References for Supplementary Material
Bhat, H. S., Dmowska, R., King, G. C., Klinger, Y., and Rice, J. R. (2007b). Off-fault damage patterns due to
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Geophysical Research: Solid Earth, 112(B6). doi: 10.1029/2006JB004425.
Mello, M., Bhat, H. S., Rosakis, A. J., and Kanamori, H. (2010). Identifying the unique ground motion
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10.1016/j.tecto.2010.07.003.
Mello, M., Bhat, H. S., and Rosakis, A. J. (2016). Spatiotemporal properties of Sub-Rayleigh and supershear
rupture velocity fields: Theory and experiments. Journal of the Mechanics and Physics of Solids, 93, 153–
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