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Coupled, Physics-based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

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The September 2018, Mw 7.5 Sulawesi earthquake occurring on the Palu-Koro strike-slip fault system was followed by an unexpected localized tsunami. We show that direct earthquake-induced uplift and subsidence could have sourced the observed tsunami within Palu Bay. To this end, we use a physics-based, coupled earthquake-tsunami modeling framework tightly constrained by observations. Our model combines rupture dynamics, seismic wave propagation, tsunami propagation and inundation. The earthquake scenario, featuring sustained supershear rupture propagation, matches key observed earthquake characteristics, including the moment magnitude, rupture duration, fault plane solution, teleseismic waveforms and inferred horizontal ground displacements. In our model, a straight fault segment dipping 65 degree East beneath Palu Bay hosts a combination of up to 6 m left-lateral slip and up to 2 m normal slip determined by a regional transtensional stress regime. The time-dependent, 3D seafloor displacements are translated into bathymetry perturbations with a mean vertical offset of 1.5 m across the submarine fault segment. This sources a tsunami with wave amplitudes and periods that match those measured at the Pantoloan wave gauge and inundation that reproduces observations from field surveys. We conclude that a source related to earthquake displacements is probable and that landsliding may not have been the primary source of the tsunami. Our results have important implications for submarine strike-slip fault systems worldwide. Physics-based modeling offers rapid response specifically in tectonic settings which are currently underrepresented in operational tsunami hazard assessment.
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Coupled, Physics-based Modeling Reveals Earthquake
Displacements are Critical to the 2018 Palu, Sulawesi Tsunami
T. Ulrich1, S. Vater2, E. H. Madden1,3, J. Behrens4, Y. van Dinther5, I.
van Zelst6, E. J. Fielding7, C. Liang8, and A.-A. Gabriel1
corresponding author: Thomas Ulrich, ulrich@geophysik.uni-muenchen.de
Abstract
The September 2018,
Mw
7.5 Sulawesi earth-
quake occurring on the Palu-Koro strike-slip fault system
was followed by an unexpected localized tsunami. We
show that direct earthquake-induced uplift and subsi-
dence could have sourced the observed tsunami within
Palu Bay. To this end, we use a physics-based, coupled
earthquake-tsunami modeling framework tightly con-
strained by observations. Our model combines rupture
dynamics, seismic wave propagation, tsunami propaga-
tion and inundation. The earthquake scenario, featuring
sustained supershear rupture propagation, matches key
observed earthquake characteristics, including the mo-
ment magnitude, rupture duration, fault plane solution,
teleseismic waveforms and inferred horizontal ground
displacements. In our model, a straight fault segment
dipping 65
East beneath Palu Bay hosts a combina-
tion of up to 6 m left-lateral slip and up to 2 m nor-
mal slip determined by a regional transtensional stress
regime. The time-dependent, 3D seafloor displacements
are translated into bathymetry perturbations with a
mean vertical offset of 1.5 m across the submarine fault
segment. This sources a tsunami with wave amplitudes
1
Department of Earth and Environmental Sciences, Ludwig-
Maximilians-Universität München, Munich, Germany
2
Institute of Mathematics, Freie Universität Berlin, Berlin,
Germany
3
Observatório Sismológico, Instituto de Geociências, Univer-
sidade de Brasília, Brasília, Brazil
4
Numerical Methods in Geosciences, Department of Mathe-
matics, Universität Hamburg, Hamburg, Germany
5
Department of Earth Sciences, Utrecht University, Utrecht,
The Netherlands
6
Seismology and Wave Physics, Institute of Geophysics, De-
partment of Earth Sciences, ETH Zürich, Zürich, Switzerland
7
Jet Propulsion Laboratory, California Institute of Technol-
ogy, Pasadena, California, USA
8
Seismological Laboratory, California Institute of Technology,
Pasadena, California, USA
and periods that match those measured at the Pantoloan
wave gauge and inundation that reproduces observations
from field surveys. We conclude that a source related
to earthquake displacements is probable and that land-
sliding may not have been the primary source of the
tsunami. Our results have important implications for
submarine strike-slip fault systems worldwide. Physics-
based modeling offers rapid response specifically in tec-
tonic settings which are currently underrepresented in
operational tsunami hazard assessment.
Keywords
Sulawesi, tsunami, earthquake dynamics,
coupled model, physics-based modeling, strike slip
1 Introduction
Tsunamis occur due to abrupt perturbations to the wa-
ter column, usually caused by the seafloor deforming
during earthquakes or submarine landslides. Devastating
tsunamis associated with submarine strike-slip earth-
quakes are rare. While such events may trigger landslides
that in turn trigger tsunamis, the associated ground dis-
placements are predominantly horizontal, not vertical,
which does not favor tsunami genesis.
However, strike-slip fault systems in complex tectonic
regions, such as the Palu-Koro fault zone cutting across
the island of Sulawesi, may produce vertical deformation.
Strike-slip systems may also include complicated fault
geometries, such as non-vertical faults, bends or en
echelon step-over structures. These can host complex
rupture dynamics and produce a variety of displacement
patterns when ruptured, which may promote tsunami
generation (Legg and Borrero, 2001; Borrero et al, 2004).
To mitigate the commonly under-represented hazard
of strike-slip induced tsunamis, it is crucial to funda-
mentally understand the direct effect of coseismic dis-
2
placements on tsunami genesis. Globally, geological set-
tings similar to that governing the Sulawesi earthquake-
tsunami sequence are not unique. Large strike-slip faults
crossing off-shore and running through narrow gulfs in-
clude the elongated Bodega and Tomales bays in north-
ern California, USA, hosting major segments of the
right-lateral strike-slip San Andreas fault system, and
the left-lateral Anatolian fault system in Turkey, extend-
ing beneath the Marmara Sea just south of Istanbul.
Indeed, historical data do record local tsunamis gener-
ated from earthquakes along these and other strike-slip
fault systems, such as in the 1906 San Francisco (Cal-
ifornia), 1994 Mindoro (Philippines), and 1999 Izmit
(Turkey) earthquakes (Legg et al, 2003) and, more re-
cently, the 2016 Kaik¯oura, New Zealand earthquake
(Ulrich et al, 2019; Power et al, 2017).
In most tsunami modelling approaches, the tsunami
source is computed according to the approach of Mansin-
ha and Smylie (1971) and subsequently parameterized
by the Okada model (Okada, 1985), which translates
finite fault models into seafloor displacements. Okada’s
model allows computing analytically static ground dis-
placements generated by a uniform dislocation over a
finite rectangular fault assuming a homogeneous elastic
half space. Heterogeneous slip can be captured by link-
ing several dislocations in space, and time-dependence is
approximated by allowing these dislocations to move in
sequence (e.g., Tanioka et al, 2006). While seafloor and
coastal topography are ignored, the contribution of hori-
zontal displacements may be additionally accounted for
by a filtering approach suggested by Tanioka and Satake
(1996), which includes the gradient of local bathymetry.
Applying a traditional Okada source to study tsunami
genesis is specifically limited for near-field tsunami ob-
servations and localized events due to its underlying,
simplifying assumptions.
Realistic modeling of earthquakes and tsunamis ben-
efits from physics-based approaches. Finite fault models
are affected by inherent non-uniqueness, which may
spread via the ground displacement fields to the mod-
eled tsunami genesis. Constraining the kinematics of
multi-fault rupture is especially challenging, since initial
assumptions on fault geometry strongly affect the slip
inversion results. Mechanically viable earthquake source
descriptions are provided by dynamic rupture model-
ing combining spontaneous frictional failure and seismic
wave propagation. Dynamic rupture simulations fully
coupled to the time-dependent response of an overlying
water layer have been performed by Lotto et al (2017a,b,
2018). These have been instrumental in determining the
influence of different earthquake parameters and mate-
rial properties on coupled systems, but are restricted
to 2D. Ryan et al (2015) couple a 3D dynamic earth-
quake rupture model to a tsunami model, but these are
restricted to using the final, static seafloor displacement
field as the tsunami source.
To capture the physics of the interaction of the Palu
earthquake and tsunami we utilize a physics-based, cou-
pled earthquake-tsunami model. The dynamic earth-
quake rupture model incorporates spatial variation in
subsurface material properties, spontaneously develop-
ing slip on a complex, non-planar system of 3D faults, off-
fault plastic deformation, and the non-linear interaction
of frictional failure with seismic waves. The coseismic de-
formation of the crust generates time-dependent seafloor
displacements, which we translate into bathymetry per-
turbations to source the tsunami. The tsunami model
solves for non-linear wave propagation and inundation
at the coast.
Using this coupled approach, we evaluate the in-
fluence of coseismic deformation during the strike-slip
Sulawesi earthquake on generating the observed tsunami
waves. The physics-based model reveals that the rup-
ture of a fault crossing Palu Bay with a moderate but
wide-spread component of normal fault slip produces
vertical deformation, which can explain the observed
tsunami wave amplitudes and wave run-up heights.
2 The 2018 Palu, Sulawesi earthquake and
tsunami
2.1 Tectonic setting
The Indonesian island of Sulawesi is located at the
triple junction between the Sunda plate, the Australian
plate and the Philippine Sea plate (Bellier et al, 2006;
Socquet et al, 2006, 2019) (Fig. 1a). Convergence of
the Philippine and Australian plates toward the Sunda
plate is accommodated by subduction and rotation of
the Molucca Sea, Banda Sea and Timor plates, leading
to complicated patterns of faulting (Fig. 1a).
In central Sulawesi, the NNW-striking Palu-Koro
fault (PKF) and the WNW-striking Matano faults (MF)
(Fig. 1a) comprise the Central Sulawesi Fault System.
The Palu-Koro fault runs off-shore to the north of Su-
lawesi through the narrow Palu Bay and is the fault
that hosted the earthquake that occurred on 28 Septem-
ber 2018. With a relatively high slip rate of 40 mm/yr
inferred from recent geodetic measurements (Socquet
et al, 2006; Walpersdorf et al, 1998) and clear evidence
for Quaternary activity (Watkinson and Hall, 2017), the
Palu-Koro fault was presumed to pose a threat to the
region (Watkinson and Hall, 2017). In addition, four
tsunamis associated with earthquakes on the Palu-Koro
fault have struck the northwest coast of Sulawesi in the
3
Fig. 1
(a) Tectonic setting of the September 28, 2018
Mw
7.5 Sulawesi earthquake (epicenter indicated by yellow star). Black
lines indicate plate boundaries based on Bird (2003); Argus et al (2011). Abbreviations: BH – Bird’s Head plate; BS – Banda
Sea plate; MF – Matano fault zone; PKF – Palu-Koro fault zone; MS – Molucca Sea plate and TI – Timor plate. Arrows
indicate the far-field plate velocities with respect to Eurasia (Socquet et al, 2006). The red box corresponds to the zoom-in
region displayed in (b). (b) A zoom of the region of interest. The site of the harbor tide gauge of Pantoloan is indicated as well
as the city of Palu. Locations of the GPS stations at which we provide synthetic ground displacement time series (see Appendix
Sec.8.2) are indicated by the red triangles. Focal mechanisms and epicenters of the September 28, 2018 Palu earthquake (USGS
(2018a), top), October 1, 2018 Palu aftershock (middle), and January 23, 2005 Sulawesi earthquake (bottom) are shown. These
later two events provide constraints on the dip angles of individual segments of the fault network. Individual fault segments of
the Palu-Koro fault used in the dynamic rupture model are coloured. (c), (d) and (e) 3D model of the fault network viewed
from top, SW and S.
4
past century (1927, 1938, 1968 and 1996) (Pelinovsky
et al, 1997; Prasetya et al, 2001).
The complex regional tectonics subject northwestern
Sulawesi to transtensional strain (Socquet et al, 2006).
Transtension promotes some component of dip-slip fault-
ing on the predominantly strike-slipping Palu-Koro fault
(Bellier et al, 2006; Watkinson and Hall, 2017) and leads
to more complicated surface deformation than is ex-
pected from slip along a fault hosting purely strike-slip
motion.
2.2 The 2018 Palu, Sulawesi earthquake
The
Mw
7.5 Sulawesi earthquake that occurred on Septem-
ber 28, 2018 ruptured a 180 km long section of Palu-
Koro fault (Socquet et al, 2019). It nucleated 70 km
north of the city of Palu at shallow depth, with inferred
hypocentral depths varying between 10 km and 22 km
(Valkaniotis et al, 2018). The rupture propagated pre-
dominantly southward, passing under Palu Bay and the
city of Palu. It arrested after a total rupture time of
30–40 seconds (Socquet et al, 2019; Okuwaki et al, 2018;
Bao et al, 2019).
The earthquake appears to have propagated at a
supershear rupture speed, i.e., faster than the shear
waves produced by the earthquake are able to travel
through the surrounding rock (e.g., Socquet et al, 2019;
Bao et al, 2019; Mai, 2019). Socquet et al (2019) note
that the characteristics of the relatively straight, clear
rupture trace to the south of the Bay, with few after-
shocks, match those for which supershear rupture speeds
have been inferred in other earthquakes. Using back-
projection analysis, which maps the location and timing
of earthquake energy from the waves recorded on distant
seismic arrays, Bao et al (2019) do not resolve any por-
tion of the rupture as traveling at sub-Rayleigh speeds.
The authors conclude that this fast rupture velocity
began at, or soon after, earthquake nucleation and was
sustained for the length of the rupture. Surprisingly, Bao
et al (2019) infer supershear rupture speeds at the lower
end considered theoretically stable, possibly due to the
influence of widespread, pre-existing damage around
the fault. While the actual speed, point of onset, and
underlying mechanics of this event’s supershear rupture
propagation remain to be studied further, it will initiate
re-assessment of hazard associated with strike-slip faults
worldwide with respect to the potential intensification
of supershear shaking.
2.3 The induced tsunami
The Palu earthquake triggered a local but powerful
tsunami that devastated the coastal area of the Palu
Bay quickly after the earthquake. Inundation depths of
over 6 m and run-up heights of over 9 m were recorded at
specific locations (e.g. Yalciner et al, 2018). At the only
tide gauge with available data, located at Pantoloan
harbor, a trough-to-peak wave amplitude of almost 4 m
was recorded just five minutes after the rupture (Muhari
et al, 2018). In Ngapa (Wani), on the northeastern shore
of Palu Bay, CCTV coverage show the arrival of the
tsunami wave after only 3 minutes.
Coseismic subsidence and uplift, as well as submarine
and coastal landsliding, have been suggested as causes of
the tsunami in Palu Bay (Heidarzadeh et al, 2018). Both
displacements and landsliding are documented on land
(Valkaniotis et al, 2018; Løvholt et al, 2018; Sassa and
Takagawa, 2019), and also at coastal slopes (Yalciner
et al, 2018).
Tsunami models of the Sulawesi event performed
using Okada’s solution in combination with the USGS fi-
nite fault model (USGS, 2018b) do not generate tsunami
amplitudes large enough to agree with observations (Hei-
darzadeh et al, 2018; Sepulveda et al, 2018; Liu et al,
2018; van Dongeren et al, 2018). Liu et al (2018) and
Sepulveda et al (2018) perform Okada-based tsunami
modeling with earthquake sources generated by invert-
ing satellite data, but also produce wave amplitudes that
are too small. Reasonable tsunami waves are produced
by combining tectonic and hypothetical landslide sources
(van Dongeren et al, 2018; Liu et al, 2018). However, the
predominantly short wavelengths associated with the
observed small scale, localized landsliding (Yalciner et al,
2018) appears to be incompatible with the observed long
period tsunami waves (Løvholt et al, 2018).
3 Physical and Computational Models
3.1
Earthquake-tsunami modeling within the ASCETE
framework
The ASCETE framework (Advanced Simulation of Cou-
pled Earthquake and Tsunami Events; see Gabriel et al,
2018) establishes methods for coupling physics-based
models of geodynamic subduction zone processes, seis-
mic cycling, dynamic earthquake rupture, and tsunami
propagation and inundation. Here, we apply part of the
framework to model the coupling between a single dy-
namic earthquake rupture and the resulting occurrence
of a tsunami.
Since the earthquake and tsunami communities use
different vocabulary, we specify the terminology used
5
throughout this manuscript. We call the complete phys-
ical setup, including, e.g., the bathymetry dataset, fault
structure and the governing equations for an earthquake
or tsunami, a ‘physical model’. Furthermore, a com-
puter program discretizing the equations and implement-
ing the numerical workflow is termed a ‘computational
model’. The result of a computation for a specific event
achieved with a computational model and according to
a specific physical model will be called a ‘scenario’. We
use ‘model’ where the use of the term as either physical
or computational model is unambiguous.
The computational model used to produce the earth-
quake scenario is SeisSol (Dumbser and Käser, 2006;
Pelties et al, 2014; Uphoff et al, 2017), which solves the
elastodynamic wave equation. Seissol solves for sponta-
neous dynamic rupture and seismic wave propagation
to determine the temporal and spatial evolution of slip
on predefined frictional interfaces, and the stress and
velocity fields throughout the modeling domain. With
this approach, the earthquake source is not predeter-
mined, but evolves spontaneously as a consequence of
the model’s initial conditions and of the time-dependent,
non-linear processes occurring during the earthquake.
Initial conditions include the geometry and frictional
strength of the fault(s), the tectonic stress state, and
the regional lithological structure. Fault slip evolves as
frictional shear failure according to an assigned friction
law that controls how the fault yields and slides. Model
outputs include spatial and temporal evolution of the
earthquake rupture front(s), off-fault plastic strain, sur-
face displacements, and the ground shaking caused by
the radiated seismic waves.
SeisSol uses the Arbitrary high-order accurate DE-
Rivative Discontinuous Galerkin method (ADER-DG).
It employs fully non-uniform, unstructured tetrahedral
meshes to combine geometrically complex 3D geological
structures, nonlinear rheologies, and high-order accurate
propagation of seismic waves. Fast time to solution is
achieved thanks to end-to-end computational optimiza-
tion (Breuer et al, 2014; Heinecke et al, 2014; Retten-
berger et al, 2016) and an efficient local time-stepping
algorithm (Uphoff et al, 2017). To this end, dynamic
rupture simulations can reach high spatial and tempo-
ral resolution of increasingly complex geometrical and
physical modelling components (e.g. Bauer et al, 2017;
Wollherr et al, 2018a). SeisSol is verified with a wide
range of community benchmarks, including strike-slip,
dipping and branching fault geometries, laboratory de-
rived friction laws, as well as heterogeneous on-fault
initial stresses and material properties (de la Puente
et al, 2009; Pelties et al, 2012, 2013, 2014; Wollherr et al,
2018b) in line with the SCEC/USGS Dynamic Rupture
Code Verification exercises (Harris et al, 2011, 2018).
SeisSol is freely available (SeisSol website, 2019; SeisSol
github, 2019).
The computational model to generate the tsunami
scenario is StormFlash2D, which solves the nonlinear
shallow water equations using an explicit Runge-Kutta
discontinuous Galerkin discretization combined with a
sophisticated wetting and drying treatment for the inun-
dation at the coast (Vater and Behrens, 2014; Vater et al,
2015, 2017). A tsunami is triggered by a (possibly time-
dependent) perturbation of the discrete bathymetry.
StormFlash2D allows for stable and accurate simula-
tion of large-scale wave propagation in deep sea, as
well as small-scale wave shoaling and inundation at the
shore, thanks to a multi-resolution adaptive mesh refine-
ment approach based on a triangular refinement strategy
(Behrens et al, 2005; Behrens and Bader, 2009). Bottom
friction is parameterized through Manning friction by a
split-implicit discretization (Liang and Marche, 2009).
The model’s applicability for tsunami events has been
validated by a number of test cases (Vater et al, 2018),
which are standard for the evaluation of operational
tsunami codes (Synolakis et al, 2007).
Coupling between the earthquake and tsunami mod-
els is realized through the time-dependent coseismic 3D
seafloor displacement field computed in the dynamic
earthquake rupture scenario, which is translated into
2D bathymetry perturbations of the tsunami model.
3.2 Earthquake model
The 3D dynamic rupture model of the Sulawesi earth-
quake requires initial assumptions related to the struc-
ture of the Earth, the structure of the fault system, the
stress state, and the frictional strength of the faults.
These input parameters are constrained by a variety of
independent near-source and far-field data sets. Most
importantly, we aim to ensure mechanical viability by a
systematic approach integrating the observed regional
stress state and frictional parameters and including state-
of-the-art earthquake physics and fracture mechanics
concepts in the model (Ulrich et al, 2019).
3.2.1 Earth structure
The earthquake model incorporates topography and
bathymetry data and state-of-the-art information about
the subsurface structure in the Palu region. Local topog-
raphy and bathymetry are honored at a resolution of
about 900 m (GEBCO, 2015; Weatherall et al, 2015). At
depth, 3D heterogeneous media are included by combin-
ing two subsurface velocity data sets. A local model by
Awaliah et al (2018), which is built from ambient noise
tomography, covers the model domain down to 40 km
6
depth. The Global Earth Model (Fichtner et al, 2018)
is used to cover the model domain down to 150 km.
3.2.2 Fault structure
For this model, we construct a network of non-planar, in-
tersecting crustal faults that ruptured in this earthquake.
This includes three major fault segments: the Northern
segment, a previously unmapped fault on which the
earthquake nucleated, and the Palu and the Saluki seg-
ments of the Palu-Koro fault (cf. Fig. 1b-e). We map
the fault traces from the horizontal ground displacement
field inferred from correlation of Sentinel-2 optical im-
ages (De Michele, 2018) and from synthetic aperture
radar (SAR) data (Bao et al, 2019), which is discussed
more below. Differential north-south offsets clearly de-
lineate the on-land traces of the Palu and Saluki fault
segments. The trace of the Northern segment is less well-
constrained in both data sets. Nevertheless, we produce
a robust map by honoring the clearest features in both
datasets and smoothing regions of large variance using
QGIS v2.14 (Quantum, 2013).
Beneath the Bay, we adopt a relatively simple fault
geometry motivated by the on land fault strikes, the
homogeneous pattern of horizontal ground deformation
east of the Bay (De Michele, 2018), which suggests
slip on a straight, continuous fault under the Bay, and
the absence of direct information available to constrain
the rupture’s path. We extend the Northern segment
southward as a straight line from the point where it
enters the Bay to the point where the Palu segment
enters the Bay. We extend the Palu segment northward,
adopting the same strike that it displays on land to the
south of the Bay. This trace deviates a few km from the
mapping reported in Bellier et al (2006, their Fig. 2),
both on and off land. South of the Bay, the modeled
segment mostly aligns with the fault as mapped by
Watkinson and Hall (2017, their Fig. 5).
We constrain the 3D structure of these faults using
focal mechanisms and geodetic data. We assume that
the Northern and Palu segments both dip 65
East,
as suggested by the mainshock focal mechanisms (67
,
USGS (2018a) and 69
, IPGP (2018), Fig. 1b) and
the focal mechanism of the 2018, October 1st
Mw
5.3
aftershock (67
, BMKG solution, Fig. 1b). This also
is consistent with pronounced asymmetric patterns of
ground deformation suggesting slip on dipping faults
around the city of Palu and the Northern fault segment
in both the optical De Michele (2018) and SAR data. In
addition, the eastward dip of the Palu segment on land
is consistent with the analysis of Bellier et al (2006).
The southern end of the Palu segment bends towards
the Saluki segment and features a dip of 60
to the
northeast, as constrained by the source mechanism of
the 2005
Mw
6.3 event (see Fig. 1b). In contrast, we
assume that the Saluki segment is vertical. The assigned
dip of 90
acknowledges the inferred ground deformation
of comparable amplitude and extent on both sides of
this fault segment (De Michele, 2018). All faults reach
a depth of 20 km.
3.2.3 Stress state
The fault system is subject to a laterally homogeneous
regional stress field, systematic constraints based on
seismo-tectonic observations, fault fluid pressurization
and the Mohr-Coulomb theory of frictional failure fol-
lowing Ulrich et al (2019). This is motivated by the
fact that tractions on and strength of natural faults
are difficult to quantify. With this approach, only four
parameters must be specified to fully describe the state
of stress and strength governing the fault system, as fur-
ther detailed in the appendix (Sec. 8.3). This systematic
approach facilitates rapid modeling of an earthquake.
Using static considerations and few trial dynamic
simulations, we identify an optimal stress configuration
for this scenario that simultaneously (i) maximizes the
ratio of shear over normal stress all across the fault
system; (ii) determines shear traction orientations that
predict surface deformation compatible with the mea-
sured ground deformation and focal mechanisms; and
(iii) allows dynamic rupture across the fault system’s
geometric complexities.
The resulting physical model is characterized by a
stress regime acknowledging transtension, high fluid
pressure, and relatively well oriented, apparently weak
faults. The effective confining stress increases with depth
by a gradient of 5.5 MPa/km. From 11–15 km depth,
we taper the deviatoric stresses to zero, to represent
the transition from a brittle to a ductile deformation
regime. The depth range is consistent with the 12 km
interseismic locking depth estimated by Vigny et al
(2002).
3.2.4 Earthquake nucleation and fault friction
Failure is initiated within a highly overstressed circular
patch with a radius of 1.5 km situated at a depth of
10 km. This depth is at the shallow end of the range
of inferred hypocentral depths (Valkaniotis et al, 2018)
and shallower than the modeled brittle-ductile transition
mimicking the lower end of the seismogenic zone.
Slip evolves on the fault according to a rapid velocity-
weakening friction formulation, which is motivated by
laboratory experiments that show strong dynamic weak-
ening at coseismic slip rates (e.g., Di Toro et al, 2011).
7
This formulation reproduces realistic rupture charac-
teristics, such as reactivation and pulse-like behavior,
without imposing small-scale heterogeneities (e.g., Dun-
ham et al, 2011; Gabriel et al, 2012). We here use a form
of fast-velocity weakening friction proposed in the com-
munity benchmark problem TPV104 of the Southern
California Earthquake Center (Harris et al, 2018) and
as parameterized by Ulrich et al (2019). Friction drops
rapidly from a steady-state, low-velocity friction coeffi-
cient, here 0.6, to a fully weakened friction coefficient,
here 0.1 (see Sec. 8.4).
3.2.5 Model resolution
A high resolution computational model is crucial in
order to accurately resolve the full dynamic complexity
of our earthquake scenario. The required high numerical
accuracy is achieved by combining a numerical scheme
that is accurate to high-orders and a mesh that is locally
refined around the fault network.
The earthquake model domain is discretized into an
unstructured computational mesh of 8 million tetrahe-
dral elements. The shortest element edge lengths are
200 m close to faults. The static mesh resolution is coars-
ened away from the fault system. Simulating 50 s of
this event using 4th order accuracy in space and time
requires about 2.5 hours on 560 Haswell cores of phase
2 of the SuperMUC supercomputer of the Leibniz Su-
percomputing Centre in Garching, Germany. We point
out that running hundreds of such simulations is well
within the scope of resources available to typical users
of supercomputing centres.
3.3 Tsunami model
The bathymetry and topography for the tsunami model
is composed with the high-resolution data set BAT-
NAS (v1.0), provided by the Indonesian Geospatial Data
Agency (DEMNAS, 2018). This data set has a horizon-
tal resolution of 6 arc seconds (or approximately 190 m),
and it allows for sufficiently accurate representation of
bathymetric features, but is certainly relatively inaccu-
rate with respect to inundation treatment.
The coupling between the earthquake and tsunami
models is enforced by adding a perturbation derived
from the 3D coseismic seafloor displacement from the dy-
namic rupture scenario to the initial 2D bathymetry and
topography of the tsunami model. These time-dependent
displacement fields are given by the three-dimensional
vector (
∆x, ∆y, ∆z
). Additionally to the vertical dis-
placement
∆z
, we incorporate the horizontal compo-
nents
∆x
and
∆y
into the tsunami source by applying
the method proposed by Tanioka and Satake (1996).
Fig. 2
Setup of the tsunami model including high-resolution
bathymetry and topography data overlain by the initial adap-
tive triangular mesh refined near the coast.
This is motivated by the potential influence of Palu
Bay’s steep seafloor slopes (more than 50%). The ground
displacement of the earthquake model is translated into
the tsunami generating bathymetry perturbation by
∆b =∆z ∆x ∂b
∂x ∆y b
∂y ,(1)
where
b
=
b
(
x, y
)is the bathymetry (increasing in the
upward direction).
∆b
is time-dependent, since
∆x
,
∆y
and
∆z
are time-dependent (cf. Fig. S2). The tsunami is
sourced by adding
∆b
to the initial bathymetry and to-
pography of the tsunami model. It should be noted that
a comparative scenario using only
∆z
as bathymetry
perturbation (see appendix, Sec. 8.5) did not result in
large deviations with regards to the preferred model.
The domain of the computational tsunami model
(latitudes ranging from
1
to 0
, longitudes ranging
from 119
to 120
, see Fig. 2) encompasses Palu Bay
and its near surroundings in the Makassar Strait, since
we here focus on the wave behavior within the Bay of
Palu. The tsunami model is initialized as an ocean at
rest, for which (at
t
= 0) the initial fluid depth is set in
such manner that the sea surface height (ssh, deviation
from mean sea level) is equal to zero everywhere in
the model domain. Additionally, the fluid velocity is
set to zero. This defined initial steady state is then
altered by the time-dependent bathymetry perturbation
throughout the simulation, which triggers the tsunami.
The simulation is run for 40 min (simulation time),
which needs 13 487 time steps.
The triangle-based computational grid is initially re-
fined near the coast, where the highest resolution within
Palu Bay is about 3 arc seconds (or 80 m). This results
8
in an initial mesh of 153 346 cells, which expands to
more than 300 000 cells during the dynamically adaptive
computation. The refinement strategy is based on the
gradient in sea surface height (ssh).
The parametrization of bottom friction includes the
Manning’s roughness coefficient
n
. We assume
n
= 0
.
03,
which is a typical value for tsunami simulations (Harig
et al, 2008).
4 Results
In the following, we present a well-constrained, physics-
based, coupled earthquake and tsunami model scenario
explaining local and far-field seismic and tsunami obser-
vations.
4.1 The dynamic earthquake rupture scenario:
sustained supershear rupture and normal slip
component within Palu Bay
Based on a systematic derivation of initial conditions
(Sec. 3.2), we find that early and persistent supershear
rupture is required to reproduce seismological data,
geodetic data, as well as field observations in the near-
and far-field. The model produces moderate vertical dis-
placements beneath Palu Bay due to oblique slip on a
dipping fault, even though it does not feature significant
submarine geometric complexities.
4.1.1 Earthquake rupture
The dynamic earthquake scenario is characterized by
an unilateral southward rupture (Fig. 3). The rupture
nucleates at the northern tip of the Northern segment,
then transfers to the Palu segment at the southern end
of Palu Bay, on which it propagates also unilaterally
southward. Additionally, a shallow portion of the Palu-
Koro fault beneath the Bay ruptures from North to
South (see inset of Fig. 4a). This segment is dynamically
unclamped (due to reduced normal stress) while the
rupture of the Northern segment passes. The rupture
passes from the Palu segment onto the Saluki segment
through a restraining bend at a latitude of -1.2
. In
total, 195 km of faults are ruptured leading to a
Mw
7.6
earthquake scenario.
4.1.2 Fault slip
The modeled slip distributions and orientations (Fig. 4)
are modulated by the geometric complexities of the fault
system. On the northern part of the Northern segment,
slip is lower than elsewhere along the fault due to a
restraining fault bend near -0.35
latitude (Fig. 4a).
South of this small bend, the slip magnitude increases
and remains mostly homogeneous, ranging between 6
and 8 m. Peak slip occurs on the Palu segment.
Over most of the fault network, the faulting mech-
anism is predominantly strike-slip, but does include a
small to moderate normal slip component (Fig. 4b). This
dip-slip component varies as a function of fault orienta-
tion with respect to the regional stress field. It increases
at the junction between the Northern and Palu segment
just south of Palu Bay, and at the big bend between the
Palu and Saluki fault segments, where dip-slip reaches
a maximum of approx. 4 m. Pure strike-slip faulting
is modeled on the southern part of the vertical Saluki
segment (Fig. 4b). The dip-slip component along the
rupture shown in Fig. 4b produces subsidence above the
hanging wall (east of the fault traces) and uplift above
the foot wall (west of the fault traces). The resulting
seafloor displacements are further discussed in Sec. 4.2.
4.1.3 Earthquake rupture speed
The earthquake scenario features an early and persis-
tent supershear rupture velocity (Fig. 4d). This means
that the rupture speed exceeds the seismic shear wave
velocity (
Vs
) of 2.5 to 3.1 km/s in the vicinity of the
fault network from the onset of the event. This agrees
with the inferences for supershear rupture by Bao et al
(2019) from back-projection analyses and by Socquet
et al (2019) from satellite data analyses. However, we
here infer supershear propagation faster than Eshelby
speed (
2Vs
), and thus faster than Bao et al (2019), well
within the stable supershear rupture regime (Burridge,
1973).
4.1.4
Teleseismic waves, focal mechanism, and moment
release rate
The dynamic rupture scenario satisfactorily reproduces
the teleseismic surface waves (Fig. 5a) and body waves
(Fig. 5b). Synthetics are generated at 5 teleseismic sta-
tions around the event (Fig. 5c). Following Ulrich et al
(2019), we translate the dynamic fault slip time histories
of the dynamic rupture scenario into a subset of 40 dou-
ble couple point sources (20 along strike times 2 along
depth). From these sources, broadband seismograms are
calculated from a Green
'
s function database using Insta-
seis (Krischer et al, 2017) and the PREM model for a
maximum period of 2 s and including anisotropic effects.
Our synthetics agree well with the observed teleseis-
mic signals in terms of both the dominant, long-period
surface waves and the body wave signatures.
9
Shear mach front
a)
b)
2s
9s
13s
23s
28s
North
Parcle velocity (m/s)
Absolute Slip rate (m/s)
Absolute slip rate (m/s)
Supershear rupture
Interface wave reected
from the free surface
rupture
branching
Rupture terminaon
Fig. 3
(a) Snapshot of the wavefield (absolute particle velocity in m/s) and the slip rate (in m/s) across the fault network at a
rupture time of 15 s. (b) Overview of the simulated rupture propagation. Snapshots of the absolute slip rate are shown at a
rupture time of 2, 9, 13, 23 and 28 s. Labels indicate noteworthy features of the rupture.
The focal mechanism of the modeled source is com-
patible with the one inferred by USGS (compare Fig. 1b
and Fig. 5c). The nodal plane characterizing this model
features strike/dip/rake angles of 354
/69
/
14
, which
is very close to the 350
/67
/
17
focal plane inferred
by USGS.
The dynamically released moment rate is in agree-
ment with source time functions inferred from tele-
seismic data (Fig 5d). Our scenario yields a relatively
smooth, roughly box-car shaped moment release rate
spanning the full rupture duration. This is consistent
with Okuwaki et al (2018)’s inference and consistent
with the smooth inferred fault slip reported by Socquet
et al (2019). Interestingly, we can identify a pronounced
effect of the rupture slowing down at the geometrical
complexity posed by the Northern segment restraining
bend at -0.35
latitude. This resembles the moment rate
solutions by USGS and SCARDEC at
5 s rupture
time. The transfer of the rupture from the Palu segment
to the Saluki segment at 23 s produces a transient de-
crease in the moment release rate in our model. This
feature is discernible in observations as well.
4.1.5 Earthquake surface displacements
We use observations from optical and radar satellites,
both sensitive to the horizontal coseismic surface dis-
placements, to validate the outcomes of the earthquake
scenario.
The patterns and magnitudes of the final horizon-
tal surface displacements in two dimensions (black ar-
rows in Fig. 6a) are inferred from subpixel correlation
of coseismic optical images acquired by the Coperni-
cus Sentinel-2 satellites by the European Space Agency
(ESA) (De Michele, 2018). We use both, east-west and
north-south components from optical image correlation.
We also infer coseismic surface displacements by in-
coherent cross correlation of synthetic aperture radar
(SAR) images acquired by the Japan Aerospace Ex-
ploration Agency (JAXA) Advanced Land Observation
Satellite-2 (ALOS-2). SAR can measure surface displace-
ments horizontally in the along-track direction and in the
slant direction between the satellite and the ground that
is a combination of vertical and horizontal displacement.
Here, we use the along-track horizontal displacements
(Fig. 6c) that are nearly parallel to the strike of the fault.
Further details about our data processing approach and
the dataset used can be found in appendix Sec. 8.6.
The use of two independent but partially coinciding
datasets provides additional insight on data quality. We
compare the SAR data and the optical data by project-
ing the optical data into the along-track direction of the
SAR data. This allows for identification of the robust fea-
tures in the imaged surface displacements. Along most
of the rupture, fault displacements are sharp and linear,
highlighting smooth and straight fault orientations with
some bends. Both datasets appear to be consistent to
first order (
±
1
m
) in a 30 km wide area centered on the
10
a) b)
c)
fault slip (m)
rake
rupture velocity (m/s)
119.5°E
120.0°E
0.5°S
1.0°S
Vs
Vp
Supershear rupture
Subshear rupture
rake<0
rake>0
119.5°E
120.0°E
0.5°S
1.0°S
119.5°E
120.0°E
0.5°S
1.0°S
119.5°E
120.0°E
0.5°S
1.0°S
d)
Slip along dip (m)
Fig. 4
Kinematic and dynamic source properties of the dynamic rupture scenario. (a) Final slip magnitude. The inset shows
the slip magnitude on the main Palu-Koro-fault within the Bay. (b) Dip-slip component. (c) Final rake angle. (b) and (c) both
illustrate a moderate normal slip component. (d) Maximum rupture velocity indicating pervasive supershear rupture.
fault and south of
0
.
6
latitude, as identified in Fig.
6a. North of the Bay, the optical displacements are large
in magnitude relative to the SAR measurements. Such
large displacements continue north of the inferred rup-
ture trace, suggesting a bias in the optical data in this
region. These large apparent displacements may be due
to partial cloud cover in the optical images or to image
misalignment. The EW component seems unaffected by
this problem. Significant differences between inferences
from SAR and optical data are furthermore observed
in the area near the Palu-Saluki bend. Thus, deviations
between model synthetics and observational data in the
the affected areas North of the Bay will be analyzed
with caution.
Overall, the earthquake dynamic rupture scenario
matches observed ground displacements well. East of
the Palu segment, a good agreement between synthetic
displacements and observations is achieved. Horizontal
surface displacement vectors predicted by the model are
well aligned with and of comparable amplitude to optical
observations (Fig. 6a). West of the Palu segment, the
modeled amplitudes are in good agreement with the SAR
and optical data, however the synthetic orientations
point to the southwest, whereas the optical data are
oriented to the southeast. While surface displacement
orientations around the Saluki segment are reproduced
well, amplitudes may be overestimated by about 1 m on
the eastern side of the fault (Fig. 6d). North of the Bay,
the modeled amplitudes are exceed SAR measurements
by about 2 m. Nevertheless, the subtle eastward rotation
of the horizontal displacement vectors near the Northern
11
a)
b)
c) d)
PaluSaluki bend
(1.2° latude)
restraining bend
(0.35° latude)
Fig. 5
(a) and (b): Comparison of modeled (blue) and observed (black) teleseismic displacement waveforms. A 10-450 s
band-pass filter is applied to all traces. (a) Full seismograms dominated by surface waves. (b) Zoom in to body wave arrivals.
Synthetics are generated using Instaseis (Krischer et al, 2017) and the PREM model including anisotropic effects and a maximum
period of 2 s. (c) Moment-tensor representation of the dynamic rupture scenario and locations at which synthetic data are
compared with observed records. (d) Synthetic moment rate release function compared with those observationally inferred from
teleseismic data by Okuwaki et al (2018), USGS and by the SCARDEC method (optimal solution, Vallée et al, 2011)
.
segment bend (at
0
.
35
latitude) is captured well by
the scenario.
4.2 Tsunami propagation and inundation: an
earthquake-induced tsunami
The surface displacements induced by the earthquake
result in a bathymetry perturbation
∆b
(as defined in
Eq.
(1)
), which is visualized after 50 s simulation time
(equal to earthquake rupture time) in Fig. 7a. In general,
the bathymetry perturbation shows subsidence east of
the faults and uplift west of the faults. The additional
bathymetry effect present through the approach of Tan-
ioka and Satake (1996) locally modulates the smooth
displacement fields from the earthquake rupture scenario
(cf. Fig. S5). Four cross-sections of the final perturbation
in W–E direction are shown in Fig. 7b which capture
the area of Palu Bay and clearly show the step induced
by the normal slip component. The variation along the
fault is displayed in Fig. 7c. The step varies between
0.8 m and 2.8 m, with an average of 1.5 m. Note, that
this step is essentially defined as fault throw in struc-
tural geology. However, here we explicitly incorporate
effects of bathymetry and thus refer to the resulting
seafloor perturbation.
The tsunami generated in this scenario is mostly
localized in Palu Bay, which is illustrated in snapshots
of the dynamically adaptive tsunami simulation after
20 s and 600 s simulation time in Fig. 8. This is expected
as the modeled fault system is offshore only within
the Bay. At 20 s, the seafloor displacement due to the
earthquake is clearly visible in the sea surface height
(ssh) within Palu Bay. Additionally, the effect of a small
uplift is visible along the coast north of the Bay.The
local behavior within Palu Bay is displayed in Fig. 9
12
Opcal SAR SAR SAR
Modeled displacement (m)
Measured displacement (m)
Residual displacement (m)
Track RMS 0.52 m
a) b) c) d)
Fig. 6
(a) Comparison of the modeled and inferred horizontal surface displacements from subpixel correlation of Sentinel-2
optical images by De Michele (2018). Some parts of large inferred displacements, e.g., north of
0
.
5
latitude, are probably
artifacts, because they are not visible in SAR data. The area inside the black polygon highlights where an at least first order
agreement between SAR and optical data is achieved. Our (b) modeled and (c) measured ground displacements in the SAR
satellite along-track direction (see text). (d) residual =(c) (b).
119.75 119.80 119.85 119.90
longitude
1
0
1
b[m]
b)
step across fault
0.85 0.80 0.75 0.70
latitude
0
1
2
3
step across fault [m]
c)
Fig. 7
(a) Snapshot of the computed bathymetry perturbation
∆b
used as input for the tsunami model. The snapshot
corresponds to a 50 s simulation time at the end of the earthquake scenario. (b) W–E cross-sections of the bathymetry
perturbation at 0.85(blue), 0.8(orange), 0.75(green), 0.7(red) latitude showing the induced step in bathymetry
perturbation across the fault. (c) step in bathymetry perturbation (as indicated in panel (b)) as function of latitude. Grey
dashed line shows the average.
13
at 20 s, 180 s and 300 s. The local extrema along the
coast reveal the complex wave reflections and refractions
within the Bay caused by complex, shallow bathymetry
as well as funnel effects.
We compare the tsunami modeling results with ob-
servational data based mainly on the comprehensive
overview of run-up data, inundation data, and arrival
times of tsunami waves around the shores of the Palu
Bay compiled by Yalciner et al (2018). In view of the
available, relatively low resolution topography data, we
conduct a macro-scale comparison between the scenario
and the inundation data, rather than point-wise compar-
ison. Additionally, we compare the synthetic time series
of the Pantoloan harbor tide gauge at (119
.
856155
E,
0
.
71114
S) to the observational gauge data, which has
a 1-minute sampling rate. The observational time series
was detided by a low-pass filter eliminating wave periods
above 2 hours.
The Pantoloan tide gauge is the only tide gauge with
available data in Palu Bay. The instrument is installed
on a pier in Pantoloan harbor and thus records the
change of water height with respect to a pier moving
synchronous with the land. It recorded the tsunami with
a leading trough arriving five minutes after the earth-
quake onset time (Fig. 10). The first and highest wave
arrived approximately eight minutes after the earth-
quake rupture time. The difference between trough and
cusp amounts to almost 4 m. A second wave arrived
after approximately 13 minutes with a preceding trough
at 12 minutes.
The corresponding synthetic time series derived from
the tsunami scenario is also shown in Fig. 10. Although
a leading wave trough is not present in the scenario re-
sults, the magnitude of the wave is well captured. Note,
that the initial negative shift of approx. -80 cm within
the first minute of the scenario is a modeling artefact
that we explain hereafter in Sec. 5.3. It cannot be easily
filtered out, due to re-adjustments throughout the com-
putation to the background mean sea level. After 5 min
of simulated time, the model mareogram resembles the
measured wave behavior, characterized by a dominant
wave period of about 4 min. The scenario exposes a
clear resonating wave behavior due to the narrow geom-
etry of the Bay. We note that these wave amplitudes
are reproduced due to displacements resulting from the
earthquake, without any contribution from landsliding.
Fig. 11 displays the maximum run-up obtained from
the tsunami scenario at locations where observations
have been reported around the Bay. We consider only
those points on land that are reached by water in the sce-
nario. A quantitative view comparing these same results
with observations is shown in Fig. 12. The overall agree-
ment is quite remarkable, with some overestimation of
the run-up in the northern margins of the bay and some
slight underestimation in the southern part near Grand-
mall Palu City. In general, errors are lower than 10%.
What we can conclude is that large misfit in the run-up
heights are more or less randomly distributed, suggest-
ing local amplification effects that cannot be captured in
the scenario due to insufficient bathymetry/topography
resolution. Fig. 13 shows maximum inundation depths
computed from the tsunami scenario near Palu City.
Qualitatively, the results from the scenario agree quite
well with observations, as the largest inundation depths
are close to the Grandmall area, where vast damage due
to the tsunami was reported.
In summary, the tsunami scenario sourced by coseis-
mic displacements from the dynamic earthquake rupture
scenario yields results that are qualitatively compara-
ble to available observations. Wave amplitudes match
well, as do the run-up distribution and the inundation
distances, given the limited quality of the available to-
pography data.
5 Discussion
The Palu, Sulawesi tsunami was as unexpected as it
was devastating. While the Palu-Koro fault system
was known as a very active strike-slip plate boundary
tsunamis from strike-slip events are generally not antic-
ipated. Fears arise that other regions, currently not ex-
pected to sustain tsunami-triggering ruptures, are at risk.
The here presented physics-based, coupled earthquake-
tsunami model shows that a submarine strike-slip fault
can produce a tsunami, if a component of dip-slip fault-
ing occurs. In the following, we discuss advantages and
limitations of physics-based models of tsunamigenesis
as well as of the earthquake and tsunami model indi-
vidually. We then focus on the broader implications of
rapid coupled scenarios for seismic hazard mitigation
and response. Finally, we look ahead to improving the
here presented coupled model in light of newly available
information and data.
5.1
Success and limitation of the physics-based tsunami
source
We constrain the initial conditions for our coupled model
according to the available earthquake data and physi-
cal constraints provided by previous studies, including
those reporting regional transtension (Walpersdorf et al,
1998; Socquet et al, 2006; Bellier et al, 2006). A stress
field characterized by transtension induces a normal
component of slip on the dipping faults in the earth-
quake scenario. The here assumed degree of transtension
14
Fig. 8
Snapshots of the tsunami simulation at 20 s (left) and 600 s (right), showing the dynamic mesh adaptivity of the
simulation.
Fig. 9 Snapshots of the tsunami simulation at 20 s, 180 s and 300 s (left to right), showing only the area of Palu Bay.
translates into a fault slip rake of about 15
on the 65
dipping modeled faults (Fig. 4c), which is consistent
with the earthquake focal mechanism (USGS, 2018a).
The such induced normal slip component results in
widespread uplift and subsidence. Fault surface ruptur-
ing generates a step in the bathymetry across the fault
of 1.5 m in average within Palu Bay, which translates
into a step in the bathymetry perturbation of similar
magnitude. (Fig. 7c). This is sufficient for triggering
a realistic tsunami that reproduces the observational
data quite well. In particular it is enough to obtain the
observed wave amplitude at the Pantoloan harbor wave
gauge and the recorded run-up heights.
However, we point out that transtension is not an
indispensable condition to generate oblique faulting in
such a fault network. From static considerations, we
indeed infer that specific alternative stress orientations
can equally induce a considerable dip-slip component in
biaxial stress regimes (Fig. S3).
The coupled earthquake model performs well at re-
producing observations from a macroscopic perspective
and suggests that additional sources of tsunami gener-
ation are not needed to explain the tsunami. However,
it does not constrain the small-scale features of the
tsunami source and thus does not allow to completely
15
Fig. 10
Time series from the wave gauge at Pantoloan port.
Blue dashed: measurements, orange: output from the model
scenario.
119.75 119.80 119.85 119.90
0.90
0.85
0.80
0.75
0.70
0.65
0.60
Panggang
Primkopal
Grandmall
Kampung
Pantoloan
Bulu Kadia
2
4
6
8
10
12
max. runup [m]
Fig. 11
Maximum simulated run-up at different locations
around Palu Bay, where observations have been recorded.
rule out other, potentially additional, sources of tsunami
generation.
For example, despite the overall consistency of the
earthquake scenario results with data, the fault within
the Bay may have hosted a different or more compli-
cated slip profile than this scenario produces. The fault
geometry underneath the Bay is not known. We here
choose a simple geometry that honors the information
at hand (see Sec. 3.2.2). However, complex faulting may
also exist there, as observed south of the Bay where slip
partitioning between minor dip-slip fault strands and
the primary rupture occurred (Socquet et al, 2019). Fur-
thermore, a less smooth fault geometry in the Northern
region, closely fitting inferred fault traces, may allow
reducing fault slip locally, and therefore better fitting
ground displacement observations in the North.
Finally, incorporating the effect of landslides is likely
to be necessary to capture local features of the tsunami
wave and inundation patterns. Constraining these sources
is very difficult without pre- and post-event high-resolution
bathymetric charts. Our study suggests that these sources
play a secondary role in explaining the overall tsunami
magnitude and wave patterns, since these can be gen-
erated by strike-slip faulting with a normal slip compo-
nent.
5.2 The Sulawesi earthquake scenario
The speed of this earthquake is of utmost interest, al-
though it does not provide an important contribution
to the tsunami generation in this scenario. We review
our results here and note avenues for additional mod-
eling. The initial stress state and lithology included in
the physical earthquake model are areas that could be
improved with more in-depth study and better available
data.
The dynamic earthquake model requires supershear
rupture velocities to produce results that agree with the
teleseismic data and moment rate function. This scenario
also provides new perspectives on the possible timing
and mechanism of this supershear rupture. Bao et al
(2019) infer an average rupture velocity of about 4 km/s
from back-projection. This speed corresponds to a barely
stable mechanical regime, which is interpreted as being
promoted by a damage zone around the mature Palu-
Koro fault that formed during previous earthquakes.
In contrast, our earthquake scenario features an early
and persistent rupture velocity of 5 km/s on average,
close to P-wave speed. Supershear rupture speed is en-
abled in our model by a relatively low fault strength
and triggered immediately at rupture onset by a highly
overstressed nucleation patch. Supershear transition is
enabled and enhanced by high background stresses (or
more generally, low ratios of strength excess over stress
drop) (Andrews, 1976). The so called transition distance,
the rupture propagation distance at which supershear
rupture starts to occur, also depends on nucleation
energy (Dunham, 2007; Gabriel et al, 2012, 2013). Ob-
servational support for the existence of a highly stressed
nucleation region arises from the series of foreshocks
that occurred nearby in the days before the mainshock,
including a Mw6.1 on the same day of the mainshock.
We conducted numerical experiments reducing the
level of overstress within the nucleation patch, reach-
ing a critical overstress level at which supershear is not
anymore triggered immediately at rupture onset. These
16
Panggang Primkopal Grandmall Kampung Pantoloan Bulu Kadia
0
2
4
6
8
10
12
max. runup [m]
Fig. 12
Maximum run-up from observations (blue) and simulation (orange) at different locations around Palu Bay (left to
right: around the Bay from the northwest to the south to the northeast, see Fig. 11 for locations).
119.82 119.83 119.84 119.85 119.86 119.87 119.88
0.89
0.88
0.87
0.86
0.85
0.0
0.5
1.0
1.5
2.0
maximum inundation [m]
Fig. 13
Maximum inundation computed from the tsunami
scenario near Palu City.
alternative models initiate at subshear rupture speeds
and never transition to supershear. Importantly, these
slower earthquake scenarios do not reproduce our obser-
vational constraints, specifically teleseismic waveforms
and moment release rate.
Stress and/or strength variations due, for example,
to variations in tectonic loading, stress release by pre-
vious earthquakes, or local material heterogeneities are
expected, but poorly constrained and therefore not in-
cluded in our dynamic rupture model. Accounting for
such features in relation to long term deformation can
distinctly influence the stress field and lithological con-
trasts (e.g., van Dinther et al, 2013; Dal Zilio et al, 2018,
2019; Preuss et al, 2019; D’Acquisto et al, 2018; van
Zelst et al, 2019). Realistic initial conditions in terms
of stress and lithology are shown to significantly influ-
ence the dynamics of individual ruptures (Lotto et al,
2017a; van Zelst et al, 2019). Specifically, different fault
stress states for the Palu and the Northern fault seg-
ments are possible, since the Palu-Koro fault acts as
the regional plate-bounding fault that likely experiences
increased tectonic loading (Fig. 1a). The introduction of
self-consistent, physics-based stress and strength states
could be obtained by coupling this earthquake-tsunami
framework to geodynamic seismic cycle models (e.g.,
van Dinther et al, 2013, 2014), as done in Gabriel et al
(2018). However, in light of an absence of data or models
justifying the introduction of complexity, we here use
the simplest option with a laterally homogeneous stress
field that honors the regional scale transtension.
We also note that the earthquake scenario is depen-
dent on the subsurface structure model (e.g., Lotto et al,
2017a; van Zelst et al, 2019). The local velocity model
of Awaliah et al (2018) is of limited resolution within
the Palu area, since only one of the used stations allows
illuminating this region. Despite the strong effects of
data regularization, this is to our knowledge the most
detailed data set characterizing the subsurface in the
area of study.
5.3 The Sulawesi tsunami scenario
Overall, the tsunami model shows good agreement with
available key observations. Wave amplitudes and peri-
ods at the only available tide gauge station in the Bay
match well. Run-up and inundation data from our model
show satisfactory agreement with the observations by
international survey teams (Yalciner et al, 2018).
Apart from the above discussed earthquake model
limitations that may influence the tsunami characteris-
tics, the following additional reasons may cause devia-
tions to tsunami observations: (a) insufficiently accurate
bathymetry/topography data; (b) simplified coupling
between earthquake rupture and tsunami scenarios; (c)
approximation by hydrostatic shallow water wave theory.
In the following we will briefly discuss these topics.
17
The insufficient resolution of the bathymetry and
topography datasets may prevent us from properly cap-
turing local effects, which may dominate some tsunami
and inundation observations. In fact, subtle features
such as a wall or dam, a small inlet of a few meters
width, rocks or submarine obstacles can strongly mod-
ulate the water wave locally. These effects cannot be
accounted for in our computation based on a relatively
coarse bathymetry/topography data set of about 190 m
resolution.
The accuracy of the tsunami model may also be af-
fected by the simplification underlying the shallow water
equations. In particular, a near-field tsunami within a
narrow bay may be affected by large bathymetry gradi-
ents. In the shallow-water framework, all three spatial
components of the ground displacements generated by
the earthquake model cannot be properly accounted for.
In fact, a direct application of a horizontal displacement
to the hydrostatic (single layer) shallow water model
would lead to unrealistic momentum in the whole water
column. Additionally, all bottom movements are immedi-
ately and directly transferred to the whole water column,
since we model the water wave by (essentially 2D) shal-
low water theory. In reality, an adjustment process takes
place. The large bathymetry gradients may also lead
to non-hydrostatic effects in the water column, which
cannot be neglected. Suitable numerical discretizations
are underway (e.g., Jeschke et al, 2017), and should be
tested to quantify the influence of such effects in realistic
situations such as the Sulawesi event.
We account for the effect of the horizontal seafloor
displacements by applying the method proposed by Tan-
ioka and Satake (1996). We observe only minor differ-
ences in the modeled water waves when including the
effect of the horizontal ground displacements (see Fig. 9,
13, S7 and S8). We thus conclude that vertical ground
displacements are the primary cause of the tsunami.
A modeling artefact is visible in the synthetic mare-
ogram at Pantaloan wave gauge, directly after the earth-
quake (Fig. 10). About 80 cm of ground subsidence is
imprinted on the synthetic data, but not visible in the
observed signal. This is the direct effect of the subsidence
at Pantoloan (cf. Fig. 7 and Fig. S2). We cannot remove
this shift from the time series, since the tsunami model
includes a background mean sea level, to which it read-
justs throughout the computation. On the other hand,
the tide gauge at Pantaloan is not sensitive to a possible
uplift or subsidence at that site. In fact, the instrument
and the water surface are displaced jointly during an
earthquake, and therefore the distance between them
remains fixed.
5.4 Advantages and outcome of a physics-based
coupled model
By capturing dynamic slip evolution that is consistent
with the fault geometry and the regional stress field, the
dynamic rupture model produces mechanically consis-
tent ground deformation, even in submarine areas where
space borne imaging techniques are blind. These seafloor
displacement time-histories, which include the influence
of seismic waves, in nature contribute to source the
tsunami and are utilized as such in this coupled frame-
work. However, the earthquake-tsunami coupling is not
physically seamless. For example, as noted above, seis-
mic waves cannot be captured using the shallow water
approach, but rather require a non-hydrostatic water
body (e.g. Lotto et al, 2018). However, the coupled sys-
tem remains mechanically consistent to the order of
the typical spatio-temporal scales governing tsunami
modeling. Thus, a physics-based, coupled model is well-
posed to shed light on the mechanisms and competing
hypotheses governing earthquake-tsunami sequences as
puzzling as the Sulawesi event.
The use of a dynamic rupture earthquake source
has distinct contributions relative to the standard finite-
fault inversion source approach, which is typically used
in tsunami models. The latter enables close fitting of
observations through the use of a large number of free
parameters. Despite recent advances (e.g., Shimizu et al,
2019), kinematic models typically need to pre-define
fault geometries. Naive first-order finite-fault sources
are automatically determined after an earthquake and
this can be done quickly (e.g. by USGS or GFZ German
Research Centre for Geoscience), which is a great advan-
tage. Models can be improved later on by including new
data and more complexity. However, kinematic models
are characterized by inherent non-uniqueness and do not
ensure mechanical consistency of the source (e.g., Mai
et al, 2016). The physics-based model also suffers from
non-uniqueness, but this is reduced, since it excludes
scenarios that are not mechanically viable.
These advantages and the demonstrated progress
potentially make physics-based, coupled earthquake-
tsunami modeling an important tool for seismic haz-
ard mitigation and rapid earthquake response. We fa-
cilitate rapid modeling of the earthquake scenario by
systematically defining a suitable parameterization for
the regional and fault-specific characteristics. We use
a pre-established, efficient algorithm, based on phys-
ical relationships between parameters, to assign the
ill-constrained stress state and strength on the fault
using a few trial simulations (Ulrich et al, 2019). This
limits the required input parameters to subsurface struc-
ture, fault structure, and four parameters governing the
18
stress state and fault conditions. This enables rapid re-
sponse in delivering physics-driven interpretations that
can be integrated synergistically with established data-
driven efforts within the first days and weeks after an
earthquake.
5.5 Looking forward
The coupled model presented here produces a realistic
scenario that agrees with key characteristics of available
earthquake and tsunami data. However, future efforts
will be directed toward improving our model as new
information on fault structure or displacements within
the Bay or additional tide gauge measurements become
available.
In addition, different earthquake models varying in
their fault geometry or in the physical laws governing on-
and off-fault behavior can be utilized in further studies
of the influence of earthquake characteristics on tsunami
generation and impact.
Our model provides high resolution synthetics of, e.g.,
ground deformation in space and time. These predictions
can be readily compared to observational data yet to be
made available to the scientific community. We provide
this in Appendix Sec. 8.2.
Spatial variations of regional stress and fault strength
could be constrained in the future by tectonic seismic
cycle modeling capable of handling complex fault geome-
tries. Future dynamic earthquake rupture modeling may
additionally explore how varying levels of preexisting
and coseismic off-fault damage affect the rupture speed
specifically and rupture dynamics in general.
Future research should also be directed towards an
even more realistic coupling strategy together with an ex-
tended sensitivity analysis on the effects of such coupling.
This, e.g., requires the integration of non-hydrostatic
extensions for the tsunami modeling part (Jeschke et al,
2017) into the ASCETE coupling framework .
6 Conclusions
We present a coupled, physics-based scenario of the
2018 Palu, Sulawesi earthquake and tsunami, which
is constrained by rapidly available observations. We
demonstrate that coseismic oblique-slip on a dipping
strike-slip fault produces a vertical step across the sub-
marine fault segment of 1.5 m on average in the tsunami
source. This is sufficient to produce reasonable tsunami
amplitude and wave run-up. The critical normal-faulting
component results from transtension, prevailing in this
region, and the fault system geometry.
The fully dynamic earthquake model captures im-
portant features, including the timing and speed of the
rupture, 3D geometric complexities of the faults, and
the influence of seismic waves on the rupture propaga-
tion. We find that an early-onset of supershear rupture
speed, sustained for the duration of the rupture across
geometric complexities, is required to match a range of
far-field and near-fault observations.
The modelled tsunami amplitudes and wave run-ups
agree with observations within the range of modeling
uncertainties dominated by the available bathymetry
and topography data.We conclude that the primary
tsunami source may have been coseismically generated
vertical displacements. However, in a holistic approach
aiming to match high-frequency tsunami features, local
effects such as landsliding, non-hydrostatic wave effects,
and high resolution topographical features should be
included.
The coupling of physics-based models, as tackled
within the ASCETE framework, is specifically useful
to assess tsunami hazard in tectonic settings currently
underrepresented in operational hazard assessment. We
demonstrate that high-performance computing empow-
ered dynamic rupture modeling produces well-constrained
studies integrating source observations and earthquake
physics very quickly after an event occurs. In the future,
such physics-based earthquake-tsunami response can
complement both on-going hazard mitigation and the
established urgent response tool set.
7 Acknowledgements
We thank Taufiqurrahman for helping us accessing data
on Indonesian websites, and for putting us in contact
with Indonesian researchers. We thank Dr. T. Yudis-
tira for providing their crustal velocity model of Su-
lawesi and Dr. Andreas Fichtner for providing us a
chunk of their ‘Collaborative seismic earth model’. We
thank Dr. Marcello de Michele for providing his in-
ferred ground-deformations data and for fruitful discus-
sions. The ALOS-2 original data are copyright JAXA
and provided under JAXA RA6 PI projects P3278 and
P3360. Dr. Widodo S. Pranowo provided access to very
early field survey observations. Furthermore, Dr. Abdul
Muhari supported this work by providing 1-minute tide
gauge data for the Pantoloan tide gauge. Finally we
thank the participant of the AGU special session about
the Palu earthquake for interesting discussions.
The work presented in this paper was enabled by
the Volkswagen Foundation (project “ASCETE”, grant
no. 88479).
Computing resources were provided by the Insti-
tute of Geophysics of LMU Munich (Oeser et al, 2006),
19
the Leibniz Supercomputing Centre (LRZ, projects no.
h019z, pr63qo, and pr45fi on SuperMUC), and the Cen-
ter for Earth System Research and Sustainability (CEN)
at University of Hamburg.
T.U., E.H.M. and A.-A.G. acknowledge support by
the German Research Foundation (DFG) (projects no.
KA 2281/4-1, GA 2465/2-1, GA 2465/3-1), by BaCaTec
(project no. A4) and BayLat, by KONWIHR – the Bavar-
ian Competence Network for Technical and Scientific
High Performance Computing (project NewWave), by
KAUST-CRG (GAST, grant no. ORS-2016-CRG5-3027
and FRAGEN, grant no. ORS-2017-CRG6 3389.02),
by the European Union’s Horizon 2020 research and
innovation program (ExaHyPE, grant no. 671698 and
ChEESE, grant no. 823844).
S.V. acknowledges support by Einstein Stiftung Ber-
lin through grant EVF-2017-358(FU).
Part of this research was performed at the Jet Propul-
sion Laboratory, California Institute of Technology un-
der contract with the National Aeronautics and Space
Administration (NASA) by Earth Surface and Interior
focus area and NISAR Science Team.
References
Andrews D (1976) Rupture velocity of plane strain shear
cracks. Journal of Geophysical Research 81(32):5679–5687,
DOI 10.1029/JB081i032p05679
Aochi H, Madariaga R (2003) The 1999 Izmit, Turkey, earth-
quake: Nonplanar fault structure, dynamic rupture process,
and strong ground motion. Bulletin of the Seismological So-
ciety of America 93(3):1249–1266, DOI 10.1785/0120020167
Argus DF, Gordon RG, DeMets C (2011) Geologically current
motion of 56 plates relative to the no-net-rotation reference
frame. Geochemistry, Geophysics, Geosystems 12(11), DOI
10.1029/2011GC003751
Awaliah WO, Yudistira T, Nugraha AD (2018) Identifi-
cation of 3-d shear wave velocity structure beneath
sulawesi island using ambient noise tomography
method. In: 10th ACES International Workshop,
URL http://quaketm.bosai.go.jp/~shiqing/ACES2018/
abstracts/aces_abstract_awaliah.pdf
Bao H, Ampuero JP, Meng L, Fielding EJ, Liang C, Milliner
CWD, Feng T, Huang H (2019) Early and persistent super-
shear rupture of the 2018 magnitude 7.5 Palu earthquake.
Nature Geoscience DOI 10.1038/s41561-018-0297-z
Bauer A, Scheipl F, Küchenhoff H, Gabriel AA (2017) Model-
ing spatio-temporal earthquake dynamics using generalized
functional additive regression. In: Proceedings of the 32nd
International Workshop on Statistical Modelling, vol 2, pp
146–149
Behrens J, Bader M (2009) Efficiency considerations in tri-
angular adaptive mesh refinement. Phil Trans R Soc A
367(1907):4577–4589, DOI 10.1098/rsta.2009.0175
Behrens J, Rakowsky N, Hiller W, Handorf D, Läuter
M, Päpke J, Dethloff K (2005) amatos: Parallel
adaptive mesh generator for atmospheric and oceanic
simulation. Ocean Modelling 10(1–2):171–183, DOI
10.1016/j.ocemod.2004.06.003
Bellier O, Sébrier M, Seward D, Beaudouin T, Villeneuve M,
Putranto E (2006) Fission track and fault kinematics anal-
yses for new insight into the Late Cenozoic tectonic regime
changes in West-Central Sulawesi (Indonesia). Tectono-
physics 413(3-4):201–220, DOI 10.1016/j.tecto.2005.10.036
Bird P (2003) An updated digital model of plate boundaries.
Geochemistry, Geophysics, Geosystems 4(3)
Borrero JC, Legg MR, Synolakis CE (2004) Tsunami sources in
the southern California bight. Geophysical Research Letters
31:L13,211, DOI 10.1029/2004GL020078
Breuer A, Heinecke A, Rettenberger S, Bader M, Gabriel
AA, Pelties C (2014) Sustained Petascale Performance of
Seismic Simulations with SeisSol on SuperMUC. In: Super-
computing. ISC 2014. Lecture Notes in Computer Science,
vol 8488, Springer, Cham, pp 1–18, DOI 10.1007/978-3-319-
07518-1_1
Burridge R (1973) Admissible speeds for plane-strain self-
similar shear cracks with friction but lacking cohesion.
Geophysical Journal of the Royal Astronomical Society
35(4):439–455
D’Acquisto M, Dal Zilio L, van Dinther Y, Molinari I, Gerya
T, Kissling E (2018) Modelling tectonics and seismicity due
to slab retreat along the northern apennines thrust belt.
In: AGU Fall Meeting 2018, URL https://agu.confex.com/
agu/fm18/meetingapp.cgi/Paper/431867
Dal Zilio L, van Dinther Y, Gerya T, Pranger C (2018) Seismic
behaviour of mountain belts controlled by plate convergence
rate. Earth and Planetary Science Letters 482:81–92
Dal Zilio L, van Dinther Y, Gerya T, Avouac J (2019) Bimodal
seismicity in the Himalaya controlled by fault friction and
geometry. Nature Communications 10:48
De Michele M (2018) URL https://www.esa.int/
spaceinimages/Images/2018/10/Indonesia_earthquake_
displacement_data
DEMNAS (2018) DEMNAS – seamless digital elevation model
(DEM) dan batimetri nasional. Badan Informasi Geospasial,
URL http://tides.big.go.id/DEMNAS
Di Toro G, Han R, Hirose T, De Paola N, Nielsen S, Mizoguchi
K, Ferri F, Cocco M, Shimamoto T (2011) Fault lubrica-
tion during earthquakes. Nature 471(7339):494–498, DOI
10.1038/nature09838
van Dinther Y, Gerya T, Dalguer L, Mai P, Morra G, Giardini
D (2013) The seismic cycle at subduction thrusts: insights
from seismo-thermo-mechanical models. Journal Geophysi-
cal Research 118:6183–6202, DOI 10.1002/2013JB010380
van Dinther Y, Mai PM, Dalguer LA, Gerya TV (2014) Mod-
eling the seismic cycle in subduction zones: the role and
spatiotemporal occurrence of off-megathrust events. Geo-
physical Research Letters 41(4):1194–1201
van Dongeren A, Vatvani D, van Ormondt M (2018) Simu-
lation of 2018 tsunami along the coastal areas in the palu
bay. In: AGU Fall Meeting 2018, URL https://agu.confex.
com/agu/fm18/meetingapp.cgi/Session/66627
Dumbser M, Käser M (2006) An arbitrary high-order dis-
continuous Galerkin method for elastic waves on unstruc-
tured meshes – II. the three-dimensional isotropic case.
Geophysical Journal International 167(1):319–336, DOI
10.1111/j.1365-246X.2006.03120.x
Dunham EM (2007) Conditions governing the occurrence of
supershear ruptures under slip-weakening friction. Journal
of Geophysical Research: Solid Earth 112(B7)
Dunham EM, Belanger D, Cong L, Kozdon JE (2011) Earth-
quake Ruptures with Strongly Rate-Weakening Friction and
Off-Fault Plasticity, Part 1: Planar Faults. Bulletin of the
Seismological Society of America 101(5):2296–2307, DOI
10.1785/0120100075, URL https://pubs.geoscienceworld.
20
org/bssa/article/101/5/2296-2307/326473
Fichtner A, van Herwaarden DP, Afanasiev M, Simute S,
Krischer L, Cubuk-Sabuncu Y, Taymaz T, Colli L, Saygin
E, Villasenor A, Trampert J, Cupillard P, Bunge HP, Igel
H (2018) The Collaborative Seismic Earth Model: Genera-
tion 1. Geophysical Research Letters 45(9):4007–4016, DOI
10.1029/2018GL077338
Gabriel AA, Ampuero JP, Dalguer LA, Mai PM (2012) The
transition of dynamic rupture styles in elastic media un-
der velocity-weakening friction. Journal of Geophysical Re-
search: Solid Earth 117(B9)
Gabriel AA, Ampuero JP, Dalguer LA, Mai PM (2013) Source
properties of dynamic rupture pulses with off-fault plasticity.
Journal of Geophysical Research: Solid Earth 118(8):4117–
4126, DOI 10.1002/jgrb.50213, URL http://onlinelibrary.
wiley.com/doi/10.1002/jgrb.50213/abstract
Gabriel AA, Behrens J, Bader M, van Dinther Y, Gunawan
T, Madden EH, Rannabauer L, Rettenberger S, Ulrich T,
Uphoff C, Vater S, Wollherr S, van Zelst I (2018) S21E-
0492: Coupled seismic cycle - Earthquake dynamic rupture
- Tsunami models. In: AGU Fall Meeting 2018, Washington,
D.C., URL https://agu.confex.com/agu/fm18/meetingapp.
cgi/Paper/453669
GEBCO (2015) The GEBCO_2014 Grid, version 20150318
Harig S, Chaeroni, Pranowo WS, Behrens J (2008) Tsunami
simulations on several scales: Comparison of approaches
with unstructured meshes and nested grids. Ocean Dynam-
ics 58:429–440
Harris RA, Barall M, Andrews D, Duan B, Ma S, Dunham E,
Gabriel AA, Kaneko Y, Kase Y, Aagaard B, et al (2011)
Verifying a computational method for predicting extreme
ground motion. Seismological Research Letters 82(5):638–
644
Harris RA, Barall M, Aagaard B, Ma S, Roten D, Olsen K,
Duan B, Liu D, Luo B, Bai K, et al (2018) A suite of
exercises for verifying dynamic earthquake rupture codes.
Seismological Research Letters 89(3):1146–1162
Heidarzadeh M, Muhari A, Wijanarto AB (2018) Insights
on the source of the 28 september 2018 sulawesi tsunami,
indonesia based on spectral analyses and numerical simula-
tions. Pure and Applied Geophysics DOI 10.1007/s00024-
018-2065-9
Heidbach O, Rajabi M, Cui X, Fuchs K, Müller B, Reinecker J,
Reiter K, Tingay M, Wenzel F, Xie F, Ziegler MO, Zoback
ML, Zoback M (2018) The World Stress Map database
release 2016: Crustal stress pattern across scales. Tectono-
physics 744:484–498, DOI 10.1016/J.TECTO.2018.07.007
Heinecke A, Breuer A, Rettenberger S, Bader M, Gabriel
AA, Pelties C, Bode A, Barth W, Liao XK, Vaidyanathan
K, Smelyanskiy M, Dubey P (2014) Petascale high order
dynamic rupture earthquake simulations on heterogeneous
supercomputers. In: SC14: International conference for high
performance computing, networking, atorage and analysis,
IEEE, pp 3–14, DOI 10.1109/SC.2014.6
IPGP (2018) URL http://geoscope.ipgp.fr/index.php/en/
catalog/earthquake-description?seis=us1000h3p4
Jeschke A, Pedersen GK, Vater S, Behrens J (2017) Depth-
averaged non-hydrostatic extension for shallow water equa-
tions with quadratic vertical pressure profile: Equiva-
lence to Boussinesq-type equations. International Jour-
nal for Numerical Methods in Fluids 84(10):569–583, DOI
10.1002/fld.4361
Krischer L, Hutko AR, van Driel M, Stähler S, Bahavar M,
Trabant C, Nissen-Meyer T (2017) On-demand custom
broadband synthetic seismograms. Seismological Research
Letters 88(4):1127–1140, DOI 10.1785/0220160210
Legg MR, Borrero JC (2001) Tsunami potential of major
restraining bends along submarine strike-slip faults. In:
Proceedings of the International Tsunami Symposium 2001,
NOAA/PMEL, 1, pp 331–342
Legg MR, Borrero JC, Synolakis CE (2003) Tsunami haz-
ards from strike-slip earthquakes. American Geophysical
Union, Fall Meeting 2003, abstract id OS21D-06 URL
http://adsabs.harvard.edu/abs/2003AGUFMOS21D..06L
Liang C, Fielding EJ (2017) Interferometry with ALOS-2 full-
aperture ScanSAR data. IEEE Transactions on Geoscience
and Remote Sensing 55(5):2739–2750
Liang Q, Marche F (2009) Numerical resolution of well-
balanced shallow water equations with complex source
terms. Advances in Water Resources 32:873–884, DOI
10.1016/j.advwatres.2009.02.010
Liu PLF, Barranco I, Fritz HM, Haase JS, Prasetya GS, Qiu
Q, Sepulveda I, Synolakis C, Xu X (2018) What we do and
don’t know about the 2018 Palu Tsunami – A future plan.
In: AGU Fall Meeting 2018, URL https://agu.confex.com/
agu/fm18/meetingapp.cgi/Paper/476669
Lotto GC, Dunham EM, Jeppson TN, Tobin HJ (2017a) The
effect of compliant prisms on subduction zone earthquakes
and tsunamis. Earth and Planetary Science Letters 458:213–
222
Lotto GC, Nava G, Dunham EM (2017b) Should tsunami
simulations include a nonzero initial horizontal velocity?
Earth, Planets and Space 69(1):117
Lotto GC, Jeppson TN, Dunham EM (2018) Fully coupled
simulations of megathrust earthquakes and tsunamis in the
japan trench, nankai trough, and cascadia subduction zone.
Pure and Applied Geophysics pp 1–33
Løvholt F, Hasan H, Lorito S, Romano F, Brizuela B, Piatanesi
A, Pedersen GK (2018) Multiple source sensitivity study to
model the 28 September Sulawesi tsunami – landslide and
strike slip sources. In: AGU Fall Meeting 2018, Washington,
DC, URL https://agu.confex.com/agu/fm18/meetingapp.
cgi/Paper/476627
Mai PM (2019) Supershear tsunami disaster. Nature Geo-
science pp 7–8, DOI 10.1038/s41561-019-0308-8
Mai PM, Schorlemmer D, Page M, Ampuero JP, Asano K,
Causse M, Custodio S, Fan W, Festa G, Galis M, et al (2016)
The earthquake-source inversion validation (siv) project.
Seismological Research Letters 87(3):690–708
Mansinha L, Smylie DE (1971) The displacement fields of
inclined faults. Bull Seis Soc Am 61(5):1433–1440
Muhari A, Imamura F, Arikawa T, Hakim AR, , Afriyanto B
(2018) Solving the puzzle of the september 2018 palu, indone-
sia, tsunami mystery: Clues from the tsunami waveform and
the initial field survey data. Journal of Disaster Research
13:sc20181,108, DOI 10.20965/jdr.2018.sc20181108
Oeser J, Bunge HP, Mohr M (2006) Cluster design in the
earth sciences: Tethys. In: International conference on high
performance computing and communications, Springer, pp
31–40
Okada Y (1985) Surface deformation due to shear and tensile
faults in a half-space. Bulletin of the Seismological Society
of America 75(4):1135
Okuwaki R, Yagi Y, Shimizu K (2018)
rokuwaki/2018paluindonesia: v2.0. DOI 10.5281/zen-
odo.1469007
Pelinovsky E, Yuliadi D, Prasetya G, Hidayat R (1997) The
1996 Sulawesi Tsunami. Natural Hazards 16(1):29–38, DOI
10.1023/A:1007904610680
Pelties C, Puente J, Ampuero JP, Brietzke GB, Käser M
(2012) Three-dimensional dynamic rupture simulation with
a high-order discontinuous Galerkin method on unstruc-
21
tured tetrahedral meshes. Journal of Geophysical Research:
Solid Earth 117(B2)
Pelties C, Gabriel AA, Ampuero JP (2013) Verification of
an ader-dg method for complex dynamic rupture problems.
Geoscientific Model Development Discussions 6:5981–6034
Pelties C, Gabriel AA, Ampuero JP (2014) Verification of
an ADER-DG method for complex dynamic rupture prob-
lems. Geoscientific Model Development 7(3):847–866, DOI
10.5194/gmd-7-847-2014
Power W, Clark K, King DN, Borrero J, Howarth J, Lane
EM, Goring D, Goff J, Chagué-Goff C, Williams J, Reid C,
Whittaker C, Mueller C, Williams S, Hughes MW, Hoyle J,
Bind J, Strong D, Litchfield N, Benson A (2017) Tsunami
runup and tide-gauge observations from the 14 november
2016 m7.8 kaik¯oura earthquake, new zealand. Pure and
Applied Geophysics 174(7):2457–2473, DOI 10.1007/s00024-
017-1566-2
Prasetya GS, De Lange WP, Healy TR (2001) The Makassar
Strait Tsunamigenic region, Indonesia. Natural Hazards
24(3):295–307, DOI 10.1023/A:1012297413280
Preuss S, HerrendÃűrfer R, Gerya T, Ampuero J, van Dinther
Y (2019) Seismic and aseismic fault growth lead to different
fault orientations. DOI 10.31223/osf.io/an92e
de la Puente J, Ampuero JP, Käser M (2009) Dynamic rupture
modeling on unstructured meshes using a discontinuous
Galerkin method. Journal of Geophysical Research: Solid
Earth 114(B10)
Quantum G (2013) Development team.(2013). quantum gis
geographic information system. open source geospatial foun-
dation project
Rettenberger S, Meister O, Bader M, Gabriel AA (2016) Asagi:
A parallel server for adaptive geoinformation. In: Proceed-
ings of the Exascale Applications and Software Conference
2016, ACM, New York, NY, USA, EASC ’16, pp 2:1–2:9,
DOI 10.1145/2938615.2938618
Rosen PA, Gurrola E, Sacco GF, Zebker H (2012) The insar
scientific computing environment. In: Synthetic Aperture
Radar, 2012. EUSAR. 9th European Conference on, VDE,
pp 730–733
Ryan KJ, Geist EL, Barall M, Oglesby DD (2015) Dynamic
models of an earthquake and tsunami offshore Ventura,
California. Geophysical Research Letters 42(16):6599–6606,
DOI 10.1002/2015GL064507
Sassa S, Takagawa T (2019) Liquefied gravity flow-induced
tsunami: first evidence and comparison from the 2018 in-
donesia sulawesi earthquake and tsunami disasters. Land-
slides 16(1):195–200, DOI 10.1007/s10346-018-1114-x
SeisSol github (2019) Seissol github. URL https://github.com/
SeisSol/SeisSol
SeisSol website (2019) Seissol website. URL www.seissol.org
Sepulveda I, Haase JS, Liu PLF, Xu X, Carvajal M (2018)
On the contribution of co-seismic displacements to the 2018
palu tsunami. In: AGU Fall Meeting 2018, URL https://
agu.confex.com/agu/fm18/meetingapp.cgi/Paper/476717
Shimizu K, Yagi Y, Okuwaki R, Fukahata Y (2019) Develop-
ment of an inversion method to extract information on fault
geometry from teleseismic data. DOI 10.31223/osf.io/q58t7
Simons WJ, Riva R, Pietrzak J, et al (2018) Tsunami potential
of the 2018 Sulawesi earthquake from GNSS constrained
source mechanism. In: AGU Fall Meeting 2018, Washington,
D.C., URL https://agu.confex.com/agu/fm18/meetingapp.
cgi/Paper/476730
Socquet A, Simons W, Vigny C, McCaffrey R, Subarya C,
Sarsito D, Ambrosius B, Spakman W (2006) Microblock
rotations and fault coupling in SE Asia triple junction
(Sulawesi, Indonesia) from GPS and earthquake slip vector
data. Journal of Geophysical Research: Solid Earth 111(B8)
Socquet A, Hollingsworth J, Pathier E, Bouchon M (2019)
Evidence of supershear during the 2018 magnitude 7.5 Palu
earthquake from space geodesy. Nature Geoscience DOI
10.1038/s41561-018-0296-0
Synolakis CE, Bernard EN, Titov VV, Kânoğlu U, González FI
(2007) Standards, criteria, and procedures for NOAA evalu-
ation of tsunami numerical models. Tech. Rep. NOAA Tech-
nical Memorandum OAR PMEL-135, NOAA/OAR/PMEL
Tanioka Y, Satake K (1996) Tsunami generation by horizon-
tal displacement of ocean bottom. Geophysical Research
Letters 23(8):861–864, DOI 10.1029/96GL00736
Tanioka Y, Yudhicara, Kususose T, Kathiroli S, Nishimura
Y, Iwasaki SI, Satake K (2006) Rupture process of the
2004 great Sumatra-Andaman earthquake estimated from
tsunami waveforms. Earth, Planets and Space 58(2):203–
209, DOI 10.1186/BF03353379
Ulrich T, Gabriel AA, Ampuero JP, Xu W (2019) Dynamic
viability of the 2016 mw 7.8 Kaik¯oura earthquake cascade
on weak crustal faults. DOI 10.31223/osf.io/aed4b, accepted
in Nat. Comm.
Uphoff C, Rettenberger S, Bader M, Madden E, Ulrich T,
Wollherr S, Gabriel AA (2017) Extreme scale multi-physics
simulations of the tsunamigenic 2004 sumatra megathrust
earthquake. In: Proceedings of the International Conference
for High Performance Computing, Networking, Storage and
Analysis, SC 2017, DOI 10.1145/3126908.3126948
USGS (2018a) URL https://earthquake.usgs.gov/earthquakes/
eventpage/us1000h3p4/moment-tensor
USGS (2018b) URL https://earthquake.usgs.gov/
earthquakes/eventpage/us1000h3p4/finite-fault
Valkaniotis S, Ganas A, Tsironi V, Barberopoulou A (2018)
A preliminary report on the M7.5 Palu 2018 earthquake
co-seismic ruptures and landslides using image correla-
tion techniques on optical satellite data. DOI 10.5281/zen-
odo.1467128, report submitted to EMSC
Vallée M, Charléty J, Ferreira AMG, Delouis B, Vergoz J
(2011) SCARDEC: a new technique for the rapid determi-
nation of seismic moment magnitude, focal mechanism and
source time functions for large earthquakes using body-
wave deconvolution. Geophysical Journal International
184(1):338–358, DOI 10.1111/j.1365-246X.2010.04836.x
Vater S, Behrens J (2014) Well-balanced inundation model-
ing for shallow-water flows with Discontinuous Galerkin
schemes. In: Fuhrmann J, Ohlberger M, Rohde C (eds)
Finite Volumes for Complex Applications VII – Elliptic,
Parabolic and Hyperbolic Problems, Springer Proceedings
in Mathematics & Statistics, vol 78, pp 965–973, DOI
10.1007/978-3-319-05591-6_98
Vater S, Beisiegel N, Behrens J (2015) A limiter-based
well-balanced discontinuous galerkin method for shallow-
water flows with wetting and drying: One-dimensional
case. Advances in Water Resources 85:1–13, DOI
10.1016/j.advwatres.2015.08.008
Vater S, Beisiegel N, Behrens J (2017) Comparison of wetting
and drying between a RKDG2 method and classical FV
based second-order hydrostatic reconstruction. In: Cancès
C, Omnes P (eds) Finite Volumes for Complex Applica-
tions VIII - Hyperbolic, Elliptic and Parabolic Problems,
Springer, pp 237–245, DOI 10.1007/978-3-319-57394-6_26
Vater S, Beisiegel N, Behrens J (2018) A limiter-based well-
balanced discontinuous Galerkin method for shallow-water
flows with wetting and drying: Triangular grids. https://
arxiv.org/abs/1811.09505
Vigny C, Perfettini H, Walpersdorf A, Lemoine A, Simons W,
van Loon D, Ambrosius B, Stevens C, McCaffrey R, Morgan
22
P, et al (2002) Migration of seismicity and earthquake
interactions monitored by gps in se asia triple junction:
Sulawesi, indonesia. Journal of Geophysical Research: Solid
Earth 107(B10):ETG–7
Walpersdorf A, Rangin C, Vigny C (1998) GPS compared
to long-term geologic motion of the north arm of Sulawesi.
Earth and Planetary Science Letters 159(1):47–55, DOI
10.1016/S0012-821X(98)00056-9
Watkinson IM, Hall R (2017) Fault systems of the eastern
indonesian triple junction: evaluation of quaternary activity
and implications for seismic hazards. Geological Society,
London, Special Publications 441(1):71–120
Weatherall P, Marks KM, Jakobsson M, Schmitt T, Tani
S, Arndt JE, Rovere M, Chayes D, Ferrini V, Wigley R
(2015) A new digital bathymetric model of the world’s
oceans. Earth and Space Science 2(8):331–345, DOI
10.1002/2015EA000107
Wollherr S, Gabriel AA, Mai PM (2018a) Landers 1992
"reloaded": an integrative dynamic earthquake rupture
model. DOI 10.31223/osf.io/kh6j9, URL eartharxiv.org/
kh6j9
Wollherr S, Gabriel AA, Uphoff C (2018b) Off-fault plas-
ticity in three-dimensional dynamic rupture simulations
using a modal Discontinuous Galerkin method on unstruc-
tured meshes: implementation, verification and application.
Geophysical Journal International 214(3):1556–1584, DOI
10.1093/gji/ggy213
Yalciner AC, Hidayat R, Husrin S, Prasetya G, Annunziato
A, Doˇgan GG, Zaytsev A, Omira R, Proietti C, Probst P,
Paparo MA, Wronna M, Pronin P, Giniyatullin A, Putra PS,
Hartanto D, Ginanjar G, Kongko W, Pelinowski E (2018)
The 28th September 2018 Palu earthquake and tsunami
ITST 07-11 November 2018 post tsunami field survey report
(short). Report, Middle East Technical University (and
others), Ankara, Turkey, URL https://drive.google.com/
open?id=13Y2XRT_ubNTCzvi6uIJbc__iT6O6XQ90
van Zelst I, Wollherr S, Gabriel AA, Madden E, van Dinther
Y (2019) Modelling coupled subduction and earthquake
dynamics. DOI 10.31223/osf.io/f6ng5, URL eartharxiv.org/
f6ng5
23
Fig. S1
Depth dependence of cohesion in the off-fault plastic
yielding criterion
8 Appendix
8.1 Off-fault plasticity
We account for the possibility of off-fault energy dissipa-
tion, by assuming a Drucker-Prager elasto-viscoplastic
rheology (Wollherr et al, 2018b). The model is parame-
terized similarly as in Ulrich et al (2019). The internal
friction coefficient is set equal to the reference fault fric-
tion coefficient (0.6). Similarly, off-fault initial stresses
are set equal to the depth-dependent initial stresses pre-
scribed on the fault. The relaxation time
Tv
is set at
0.05 s. Finally, the cohesion is assumed depth dependent
(see Fig. S1) to account for the tightening of the rock
structure with depth.
8.2 Displacement time histories
Many high-rate GNSS stations have recorded the Palu
event in the near field (Simons et al, 2018). Nevertheless,
these data are not yet available. In Figure S2, we provide
the displacements time histories at a few of these sites.
We hope future access to this data will provide further
constraints to our model.
8.3 Initial stress
In this section, we detail the initial stress parametriza-
tion, presented in general terms in 3.2.
The fault system is loaded by a laterally homoge-
neous regional stress regime. Assuming an Andersonian
stress regime, where
s1> s2> s3
are the principal
stresses and
s2
is vertically oriented, the stress state is
fully characterized by four parameters:
SHmax
,
ν
,
R0
Fig. S2
(a) Locations of known geodetic observation sites for
which we provide synthetic ground displacement time series.
(b) Synthetic unfiltered time-dependent ground displacement
in meters at selected locations.
and
γ
.
SHmax
is the azimuth of the maximum horizontal
compressive stress;
ν
is a stress shape ratio balancing
the principal stress amplitudes;
R0
is a ratio describing
the relative strength of the faults; and
γ
is encapsulating
fluid pressure.
The World Stress Map (Heidbach et al, 2018) con-
strains
SHmax
to the range of 120
±
15
. The stress
shape ratio
ν
= (
s2s3
)
/
(
s1s2
)allows characteriz-
ing the stress regime:
ν
0
.
5indicates pure strike-slip,
ν >
0
.
5indicates transtension and
ν <
0
.
5indicates
transpression. A transtensional regime is suggested by
geodetic studies (Walpersdorf et al, 1998; Socquet et al,
2006), fault kinematic analyses from field data (Bel-
lier et al, 2006), and by the USGS focal mechanism of
the mainshock, which clearly features a normal fault-
ing component. However, the exact value of
ν
is not
constrained.
The fault prestress ratio
R0
describes the closeness
to failure of a virtual, optimally oriented plane according
to Mohr-Coulomb theory (Aochi and Madariaga, 2003).
On this virtual plane, the Coulomb stress is maximized.
Optimally oriented planes are critically loaded when
R0
= 1. Faults are typically not optimally oriented in
reality. In a dynamic rupture scenario, only a small
part of the modeled faults need to reach failure in order
to nucleate sustained rupture. Other parts of the fault
network can break cascadingly even if well below failure
before rupture. The propagating rupture front raises the
local shear tractions to match fault strength locally.
We assume fluid pressure γthroughout the crust is
proportional to the lithostatic stress:
Pf
=
γσc
, where
γ
is the fluid-pressure ratio and
σc
=
ρgz
is the litho-
static pressure. A fluid pressure of
γ
=
ρwater
= 0
.
37
indicates purely hydrostatic pressure. Higher values cor-
respond to overpressurized stress states. Together,
R0
24
and
γ
control the average stress drop
in the dynamic
rupture model as:
(µsµd)R0(1 γ)σc.(2)
The such prescribed average stress drop
is a critical
characteristic of our model, controling the average fault
slip, rupture speed and rupture size.
Following Ulrich et al (2019), we can evaluate dif-
ferent stress and strength initial settings using purely
static considerations. By varying the stress parameters
within their observational constrains we compute the
distribution of the relative prestress ratio
R
and of the
shear traction orientation resolved on the fault system
for each configuration. Ris defined by:
R= (τ0µsσn)/((µsµd)σn),(3)
where
τ0
and
σn
are the initial shear and normal trac-
tions resolved on the fault plane and
µs
and
µd
are the
static and dynamic fault friction assigned in the model.
We can characterize the spatially variable fault
strength in our model by calculating
R
(Eq.
(3)
) at
every point on each fault (Fig. S3 and S4). By definition,
R
is always lower or equal to
R0
, since the faults are
not necessary optimally oriented.
We then select the stress configuration that max-
imizes
R
across the fault system, especially around
rupture transition zones to enable triggering, and that
represents a shear stress orientation compatible with
the inferred ground deformations and the inferred focal
mechanisms.
Our purely static considerations suggest that a trans-
tensional regime is required to achieve a favourable stress
orientation on the fault system. In fact, we see that a
biaxial stress regime (
ν
= 0
.
5) does not resolve sufficient
shear stress simultaneously on the main north-south
striking faults and on the Palu-Saluki bend (see Fig. S3).
Dynamic rupture experiments confirm that the Saluki
fault could not be triggered under such a stress regime.
On the other hand, such optimal configuration can be
achieved by a transtensional stress state, for instance by
choosing
ν
= 0
.
7and
SHmax
in the range 125 to 135
(see fig. S4). We choose
SHmax
= 135
, which allows for
nucleation with less overstress than lower values and
generates ruptures with the expected slip orientations
and magnitudes.
The here assumed fault system does not feature
pronounced geometrical barriers apart from the Palu-
Saluki bend. As a consequence,
R0
is actually poorly
constrained, and trade-offs between
R0
and
γ
are ex-
pected. The preferred, realistic model is characterized
by
R0
= 0
.
7and
γ
= 0
.
79. This results in an effective
confining stress (1
γ
)
σc
that increases with depth by
a gradient of 5.5 MPa/km.
Table S1 Fault frictional properties assumed in this study.
Direct-effect parameter a 0.01
Evolution-effect parameter b 0.014
Reference slip rate V0106m/s
Steady-state low-velocity friction co-
efficient at slip rate V0
f00.6
Characteristic slip distance of state
evolution
L 0.2 m
Weakening slip rate Vw0.1 m/s
Fully weakened friction coefficient fw0.1
Initial slip rate Vini 1016 m/s
8.4 Friction law
We here use a form of fast-velocity weakening friction
proposed in the community benchmark problem TPV104
of the Southern California Earthquake Center (Harris
et al, 2018) and as parameterized by Ulrich et al (2019).
Friction drops rapidly from a steady-state, low-velocity
friction coefficient, here
f0
= 0
.
6, to a fully weakened
friction coefficient, here fw= 0.1(see Table S1).
8.5 Horizontal displacements as additional tsunami
source
For computing the seafloor displacement used as source
for the tsunami model, we apply the method of Tanioka
and Satake (1996) to additionally account for horizontal
displacements, computed from the earthquake simula-
tion. The final states of the three components
∆x
,
∆y
and
∆z
are given in Fig. S5. Applying the approach
of Tanioka and Satake by using Eq.
(1)
the vertical
displacement translates into
∆b
, which is given in Fig. 7.
The difference between
∆z
and
∆b
locally amounts up
to 0.6m as shown in Fig. S6. Although this difference is
quite remarkable and compared to the overall magnitude
more than 30%, it is only very local. Due to the local
bathymetry of Palu bay it also not only amplifies the
displacement, but also diminishes it at some locations.
The local influence of the method by Tanioka and
Satake (1996) can be seen by comparison to the re-
sults section. We have run a similar simulation as de-
scribed in the main part of the paper, but with the
computed seafloor displacement
∆z
as source for the
tsunami model. Snapshots of this scenario in Palu Bay
can be seen in Fig. S7. Compared to the original sce-
nario (cf. Fig. 9) only local effects are visible, especially
at points along the coast. The maximum inundation at
Palu city is given for this alternative scenario in Fig. S8.
Again, only minor differences appear compared to the
25
SHmax=110° SHmax=115°
SHmax=120° SHmax=125°
SHmax=130° SHmax=135°
98°
61°
79°
46°
26° (minimum rake
on the fault bend)
35°
Fault tracon rake Relave prestress rao
ν=0.5
Fig. S3
Magnitude and rake of prestress resolved on the fault system for a range of plausible
SHmax
values, assuming a stress
shape ratio
ν
= 0
.
5(pure-shear). For each stress state , we show the spatial distribution of the pre-stress ratio (left) and the
rake angle of the shear traction (right). Here we assume
R0
= 0
.
7on the optimal plane, which results in
R < R0
for all faults
since these are not optimally oriented. In blue, we label the (out-of-scale) minimum rake angle on the Palu-Saluki bend.
computation which includes horizontal displacements in
the source (cf. Fig. 13). This illustrates that the method
by Tanioka and Satake (1996) might be important to
capture some local effects of the tsunami, but is not
crucial for the general result, which is also confirmed by
other studies (Heidarzadeh et al, 2018).
8.6 Along-track SAR measurements
We here describe our measurements of the final coseismic
surface displacements in along-track direction from SAR
images acquired by the Japan Aerospace Exploration
Agency (JAXA) Advanced Land Observation Satellite-2
(ALOS-2) SAR. We measure along-track pixel offsets
incoherent cross correlation of ALOS-2 stripmap SAR
images acquired along ascending path 126 on 2018/08/17
and 2018/10/12 and ascending path 127 on 2018/08/08
and 2018/10/03. We used modules of the InSAR Scien-
tific Computing Environment (ISCE) (Liang and Field-
ing, 2017; Rosen et al, 2012) for ALOS-2 SAR data
processing.
26
SHmax=110° SHmax=115°
SHmax=120° SHmax=125°
SHmax=130° SHmax=135°
95°
68°
81°
56°
37° (minimum rake
on the fault bend)
46°
Fault tracon rake Relave prestress rao
ν=0.7
Fig. S4 Same as Fig. S3, but assuming a stress shape ratio ν= 0.7(transtension).
Fig. S5 Final horizontal (∆x and ∆y) and vertical (∆z) surface displacements as computed by the earthquake model.
27
Fig. S6
The contribution
∆b∆z
of horizontal displacements
to the final bathymetry perturbation, following Tanioka and
Satake (1996)
28
Fig. S7
Snapshots at 20 s, 180 s, and 300 s of the tsunami scenario using only the vertical displacement
∆z
from the rupture
simulation as source for the tsunami model.
119.82 119.83 119.84 119.85 119.86 119.87 119.88
0.89
0.88
0.87
0.86
0.85
0.0
0.5
1.0
1.5
2.0
maximum inundation [m]
Fig. S8
Computed maximum inundation at Palu City using
only the vertical displacement
∆z
from the rupture simulation
as source for the tsunami model.
... This is likely to be the cause of the tsunami. The physics-based modeling also reveals earthquake displacements are the probable primary source of the tsunami in this earthquake (Ulrich et al., 2019). ...
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