Tsunami Genesis of Strike-Slip Earthquakes Revealed in the 2018 Indonesian Palu Event

The devastating tsunami after the 2018 Indonesian Sulawesi-Palu strike-slip earthquake was a surprise because strike-slip faulting was a known phenomenon of primarily lateral movement of land, while tsunamis were believed to be caused by vertical movements of seafloor or landslides. Here we demonstrated how the strike-slip faulting could have pushed waters from outside and inside the Palu Bay to form a powerful tsunami in the Palu Bay. We constructed three earthquake inversions from seismographs, satellite radar and optical imagery, and used an open-source ocean circulation model to replicate the tsunami. Our experiments revealed that: (1) the southward horizontal displacement of deeper-water slopes along the Makassar coast generated a long-wave tsunami of 40 km, propagating southward into the Palu Bay and consisting with the two distinguished tsunami-peaks in the Pantoloan tide-record, twice higher than the local resonance waves; (2) the two types of tsunamis in the Mamuju tide-record—the “early arrival” tsunami and the late larger tsunami—were originated from the outside and inside sources; and (3) the eyewitness account of the whirlpool circulation in the Palu Bay could be explained by the horizontal strike-slip forcing of the two involved tectonic plates. The east plate was largely responsible for pushing the long-wave tsunami southward that inundated the Palu City and resulted in the devastation. Our findings suggest that the tsunami’s behavior of strike-slip earthquakes is more complex than previously thought and should be considered in future tsunami early warnings.


Introduction
The research community has been puzzled ever since the 28 September 2018 Indonesia Sulawesi-Palu earthquake , which generated a powerful tsunami that killed about 4320 people near the city of Palu. The earthquake occurred on Sulawesi Island, east of the Makassar Strait, close to the Palu-Koro fault within the Indonesian archipelago, at 10:02:43 UTC, with the epicenter at 0.256°S latitude and 119.846°E longitude. After a few minutes of the earthquake, the United States Geological Survey (USGS) and several other agencies determined the earthquake as strike-slip faulting with a magnitude of 7.5 (Jamelot et al., 2019). Strike-slip faulting is in principle unfavorable to generate damaging tsunamis because of insignificant static vertical ground displacement. Previously in 2012 and 2016, two larger strike-slip earthquakes of Mw 8.6 and 7.8 in the Wharton Basin of northeastern Indian Ocean did not generate significant tsunamis (Heidazadeh et al., 2017).
Adding further to the mystery is the early-issued and quickly-canceled tsunami alert by the Indonesian Agency for Meteorology Climatology and Geophysics (BMKG) during the event (Hoffmann et al., 2018;Lacassin et al., 2020). The initial tsunami alert was issued about 20 min after the earthquake at 10:22 UTC, with an advisory of a possible tsunami height of 0.5-3 m. However, later at 10:27 UTC, BMKG received tide-gage measurements from the Mamuju location, about 250 km south of the epicenter, showing a small tsunami of about 3 cm. Based on the Mamuju tide data, BMKG canceled the initial tsunami alert at 10:37 UTC. The cancelation received a lot of criticism from the tsunami community immediately after the tragedy (Lacassin et al., 2020).
Without knowing how tsunamis are generated by earthquakes, it would be difficult to achieve successful early warnings. For a long time, the earthquake-induced vertical elevation of the seafloor has been the conventional theory (hereafter the vertically-forced tsunami theory) to explain the cause of tsunamis (e.g., Abe, 1973;Satake, 1995). It has also been used as the principle in tsunami research and warning systems for decades (Clement & Reymond, 2014). Mathematically, the total vertical displacement (elevation) of seafloor due to faulting has been formulated by Tanioka and Satake (1996): where h is the water depth, D represents a finite fault increment, Dh represents the water depth anomaly due to the seafloor deformation, and h x and h y are the eastward and northward slopes of seafloor topography. E, N, and U are the eastward, northward, and upward components of the seafloor displacement, respectively. Notice that the total seafloor elevation Dh includes contributions from both vertical and horizontal displacements of the seafloor. Because seafloor slopes are small in large-scale, less than 5% for most continental slopes, the horizontal contribution is small and the vertical component is the dominant term. In tsunami modeling, the earthquakeinduced total seafloor elevation Dh is transferred to the sea surface as the initial condition (Satake, 1995). Unfortunately, this vertically-forced theory could not explain the Palu tsunami of strike-slip earthquake satisfactorily because of the expected small vertical ground displacement. For example, Heidazadeh et al. (2019) found that the vertical elevation of the seafloor derived from the widely-used USGS earthquake solution could only explain the tsunami height near Pantoloan, not that near the Palu City, where all the casualties occurred and the waves supposed to be much higher. Jamelot et al. (2019) used three earthquake solutions to simulate the tsunami. Only one of them, assumed a steep dip-strike component under the Palu Bay (their table 3), could produce a wave height comparable to the Pantoloan record. However, both studies could not explain the mysterious ''early arrival'' tsunami at the Mamuju tide-gauge, which recorded an arrival tsunami 18 min after the earthquake. For a tsunami generated within the Palu Bay, it would take at least 47 min to reach the Mamuju station. Such a large discrepancy could not be explained by tsunami travel times (Shokin et al., 1987).
Traditionally, if an earthquake was too small to explain the resultant tsunami, submarine landslides would be assumed as the secondary forcing mechanism (Geist, 2000). In fact, immediately after the 2018 Palu event, landslides were hypothesized as the cause in several publications (e.g., Muhari et al., 2018). For example, Carvajal et al. (2019) and Sepulveda et al. (2020) simulated the tsunami with earthquake-induced seafloor elevation and hypothetical landslides. More detailly, Nakata et al. (2020) simulated 10 hypothetical slumps of submarine landslides and identified that two of them in the northern and southern parts of the bay, with a radius of 0.8 km and 2.0 km, thickness of 40 m and 15 m, and sliding speed of 21 m/s and 19 m/s respectively, were needed to match the observed tsunami at Pantoloan. However, these hypothetical landslides could not explain the Mamuju data either because tsunamis generated within Palu Bay could not reach Mamuju in 18 min. To our knowledge, no evidence of landslides or substantial vertical seafloor motions were reported near Mamuju region to generate the mysterious ''early arrival'' tsunami. Also, land-sliding tsunami has directionality perpendicular to the slope (Geist, 2000). The Palu Bay is so narrow, less than 8 km wide, the land-sliding tsunami should push the water to the opposite coast, but no casualty occurred along the coasts. To the contrary, all casualties occurred at the south end of the Palu Bay that was not facing to those hypothetical land-sliding slopes.
To search for evidence of the hypothetical landslides, we particularly examined the newly available bathymetry data from an Indonesian acoustic survey (Frederik et al., 2019) and compared the Palu Bay bathymetry with that before the earthquake (Supplementary Fig. S1). We found no large size of landslides in the Palu Bay, consistent with the conclusion of the survey team of Frederik et al. (2019), who examined the bathymetry data without comparing with the pre-earthquake bathymetry. They found that the largest scarp was less than 300 m (their line 3b), significantly smaller than the hypothetical landslide with a radius of 0.8 km and 2 km for the tsunami in Nakata et al. (2020). We therefore concluded that these offshore deep-water surveys were inclusive on the submarine land-sliding cause of the tsunami. Besides, three other field-surveys had also been conducted by different national and international teams Muhari et al., 2018;Omira et al., 2019;Pribadi et al., 2018). Some minor landslides and liquefiers along the coast were identified, but it was difficult to determine those coastal landslides or liquefiers as a cause or the consequence of the tsunami (Aránguiz et al., 2020;Sassa & Takagawa, 2019). Liu et al. (2020) simulated the effect of the landslides and concluded that a combination of tectonic and landslide sources was likely the cause of the tsunami. More recently, Heidarzadeh and Mulia (2023) tested the dual earthquake and landslide mechanism for the Palu tsunami. Their results were better than that without land-sliding effect. But the added landslide source did not improve the explanation of the second peak of the tide data at Pantoloan, nor the tsunami travel times at Mamuju (their Figs. 3 and 4).
The rupture speed of the earthquake was also been considered for explaining the tsunami. Most rupture velocities were in the range of 1.5-3 km/s (Riquelme & Fuentes, 2021), while the Palu earthquake was determined to be 4.1 km/s by Bao et al. (2019), consistent with the estimates of 4.3-5.2 km/s by Socquet et al. (2019). To explore the effect of the faster rupture speed on the tsunami, Elbanna et al. (2021) constructed a model by initializing the tsunami along with the rupture speed piece-by-piece, instead of initializing the sea-surface elevation over the whole fault area simultaneously as was done previously (e.g., Tanioka & Satake, 1996;Heidazadeh et al., 2019;Jamelot et al., 2019). Their model generated a wave height of about 2 m. But the modeled tsunami had a very short wave-period of \ 1 min, which was inconsistent with the Pantoloan wave with a period of * 3 min. Ulrich et al. (2019) and Ho et al. (2021) also considered the dynamic rupture process of the earthquake with seismic inversions; both assumed a dip-slip component of 2 m jump across the fault within the Palu Bay. They emphasized that a large dip-slip normal component of 2-4 m was necessary to explain the observed tsunami waves within the bay, but did not provide an explanation for the ''early arrival'' tsunami at Mamuju.
Another mysterious phenomenon was the eyewitness account of whirlpool circulations within the Palu Bay, reported by the survey of Pribadi et al. (2018). The formation of whirlpools after the earthquake was seen on the sea surface based on the testimony of residents in Lolisaluran Beach, Lolipesua and Lolilondo. The phenomenon of whirlpools is the result of oceanic circulation, suggesting ocean gained momentum from the earthquake. This significant evidence of tsunami associated oceanic circulation had not been explained in previous studies. In this study, we use the ''horizontally-forced tsunami theory'' of Song et al. (2008) to reconcile the various observations of the Palu tsunami, previously used in studying the 2004 Indian Ocean tsunami and the 2011 Japanese tsunami, both were caused by subduction earthquakes (Song & Han, 2011;Song et al., 2012Song et al., , 2017Titov et al., 2016). This is the first time of applying the theory to a strike-slip earthquake. Unlocking the mysterious cause of the Palu tsunami will provide inside into the tsunami genesis. It also has practical value for improving tsunami warning systems by knowing how strike-slip earthquakes cause tsunamis.

Earthquake Inversion and Tsunami Source
We have considered three kinds of seismic inversion solutions:

USGS Solution
The USGS has been providing rapid teleseismic earthquake source inversions for most of large earthquakes in the world, widely used by the research community and stakeholders (https://www.usgs.gov/ natural-hazards/earthquake-hazards/earthquakes). The USGS solution and its fault parameters were released without knowing the tsunami conditions, therefore were not modified to fit the tsunami data. It is a fair product to test earthquake inversions for tsunami predictions. Vol. 180, (2023) Tsunami Genesis of Strike-Slip Earthquakes 1911

PAAG Solution
To match the tsunami data, Jamelot et al. (2019) suggested an earthquake inversion by exaggerating the vertical deformation of seafloor in a sub-fault below the Palu Bay, published in Pure and Applied Geophysics (PAAG). We have included their solution in this study for a purpose of cross-comparison.

JPL Solution
Days after the earthquake, both InSAR and optical imagery data from satellites became available. Combined with the teleseismic data, we have also produced an earthquake inversion based on the methodology of Chen et al. (2019). The JPL solution is a joint finite source inversion using teleseismic P waves and InSAR measurements (Supplementary Text S1, Fig. S2-3).
Based on the conventional vertically-forced tsunami theory, the total vertical displacement of seafloor is the main force of tsunamis. The threedimensional seafloor deformation (N, E, U) from the finite source of the earthquake inversion can be used to derive the total vertical displacement, as formulated by Eq. (1) (Tanioka & Satake, 1996). In tsunami modeling, the seafloor elevation is directly transferred into the surface; i:e:; Dg ¼ Dh, where g is the sea surface. In this tsunami formation mechanism, the ocean only gains potential energy (PE), which can be calculated as where D represents a finite fault increment, Dx and Dy is the grid size, g is the gravity acceleration, and q is the water density. The total tsunami energy is the integration of Eq.
(2) over the faulting area and within the rupture period of time (Tang et al., 2012). This vertically-forced theory assumes that the water particles only move vertically over the fault area during the tsunami excitation process because no other force is included. Notice that Eq.
(2) is the maximum PE that the earthquake can generate because the total seafloor elevation is transferred to the sea-surface instantaneously.
In addition to the vertical forcing, Song et al. (2008) argued that the horizontal components of bathymetric slopes could also push the water particles laterally, which adds kinetic energy (KE) to the ocean. The oceanic kinetic energy also powers tsunamis, similar to the potential energy, but with an initial directionality of the moving bathymetric slope. Mathematically, the horizontal movements of the water particles (u b , v b ) in the vicinity of moving bathymetric slopes can be calculated from the seafloor displacement data: Here t is the rise-time of the sub-fault, D represents a finite fault increment, z is the vertical coordinate, and L H is the effective range of the horizontal motion. In this formulation, the ocean gains kinetic energy (KE) from the earthquake, which can be written as where Dz is the vertical grid size in the bottom layer. The total accumulated KE is the integration of Eq. (4) over the whole faulting area and within the period of rupture time. Using wave-making experiments, Song et al. (2017) has further demonstrated that earthquakes can generate equally important KE as the PE. Therefore, both energies should be included in considering earthquake tsunamis. In tsunami modeling, the initial conditions should include both Eq. (1) and Eq. (3a, 3b), rather than Eq. (1) alone as conventionally done. Based on the lab experiments, Song et al. (2017) provided a range of parameters for Eq. (3a, 3b). In the Palu case, we have used L H = 1000 m and rise-time t = 5 s, approximately the maximum depth of the faulting ocean area and the corresponding rupture period, respectively. Based on the formation, we have computed the tsunami source based on the three different earthquake inversions. Figure 1a shows the surface deformation of the USGS inversion, overlaid on the ocean bathymetry. Similar surface deformations from the PAAG and JPL inversions are provided in the online materials ( Supplementary Fig. S4). We use color arrows to highlight the directions of the surface movement due to the two involved tectonic plates. The left plate slipped southward toward the Palu City, represented by the red arrows, while the right plate moved northward, represented by the blue arrows. Figure 1b shows the computed tsunami source or the three-dimensional initial conditions of tsunami, computed from the earthquake inversions. The background color represents the total vertical displacement of the seafloor, computed from Eq. (1); while the arrows are the oceanic depth-averaged velocity (m/s) or horizontal momentum due to the moving bathymetric slopes, computed from Eq. (3a, 3b). Notice that the total vertical displacement of seafloor is very small, in the range of -0.5-0.5 m (background color). The PE caused by the vertical motion is about 1.7e ? 11 J, 2.9e ? 11 J, and 3.3e ? 11 J for the three earthquake inversions, respectively, based on Eq. (2). Similarly, we also computed the KE of the initial ocean velocity, as represented by the arrows, which is 12.7e ? 11 J, 18.0e ? 11 J, and 15.4e ? 11 J, respectively, based on Eq. (4). It can be seen that the KE is about 5-7 times of the corresponding PE. Notice that the velocity depends on the slip distance and the topography, with only a few areas having a velocity of * 1 m/s, which is much less than the hypothetical landslide velocity of * 20 m/s in Nakata et al. (2020). Although the largest velocity area is in the bay, we also see secondary large velocity areas along Earthquake Inversion and tsunami source. a Surface displacement derived from earthquake inversion (USGS solution). Background color is the ocean bathymetry, while arrows represent the slip direction and distance. Red arrows represent the east plate toward south. Blue arrows represent the west plate toward north. White areas represent land. b Three-dimensional tsunami initial conditions derived from the earthquake inversion (USGS solution). Background color is the total vertical displacement of seafloor (Tanioka & Satake, 1996). Arrows represent the horizontal momentum of ocean water due to moving bathymetric slopes (Song et al., 2008) Vol. 180, (2023) Tsunami Genesis of Strike-Slip Earthquakes the Makassar coast, caused by the moving Makassar bathymetric slopes. As will be shown later, these moving deeper-water slopes along the Makassar coast, and outside the bay, are the energy sources to explain the deadly tsunami near Palu City and the ''early arrival'' tsunami recorded by the Mamuju tide gauge.

Validation
We have constructed a three-dimensional tsunami model using the open-source code of the Regional Ocean Modeling System (ROMS), which is available online (www.myroms.org). ROMS is a full hydrodynamic ocean general circulation model, widely used within the oceanography community for various applications (Song & Haidvogel, 1994;Song & Hou 2006). For tsunami simulation, we used the shallowwater equation model with a constant water density, which is equivalent to the depth-averaged shallowwater equation model of Satake (1995). In the vertical direction, we used 12-vertical levels for the water column-a similar setting used in our previous studies of the 2004 Indian Ocean tsunami and the 2011 Japan tsunami (Song et al., 2008(Song et al., , 2012. The three-dimensional model allows simulations of the tsunami either by the vertically-forced [Eq. (1)], the horizontally-forced [Eq. (3a, 3b)], or both vertically and horizontally-forced initial conditions. Palu Bay is a semi-enclosed basin with a width and length of approximately 8 km and 35 km, respectively. The maximum water depth of the bay is about 1100 m. However, the connected Makassar Basin is quite deep, up to 2000 m (Fig. 1a). Our model domain includes the eastern Makassar Basin and Palu Bay, i.e., from 118 to 120°E longitude and from 3°S to 0°latitude. The model domain is divided into 1200 by 3000 grid points, resulting in an average grid size of 125 m and 60 grids across the bay. The bathymetry data is extracted from the BATNAS dataset (https://tanahair.indonesia.go.id/demnas/), which has a 6-arc second resolution.

Horizontally-Forced Tsunami
We first show the model results based on the horizontally-forced tsunami theory [Eq. (3a,3b)] because it provides the dominant energy source [Eq. (4)]. Figure 2 shows the simulated tsunami with the USGS solution in which the color represents the sea level and the red arrows represent the ocean current. After one minute of the earthquake, multiple tsunami sources are formed along the Makassar coast, outside and inside the Palu Bay. The two ellipses highlight those tsunami source regions (Fig. 2a). The red ellipse highlights the main tsunami sources generated outside and inside the Palu Bay. After 3 min of the earthquake, these tsunami sources propagated southward and developed into a long-wave tsunami of about 40 km in the bay, as highlighted by the upper-zoom panel (Fig. 2b). Tsunamis are barotropic waves, i.e., the whole depth of the ocean water is involved. Therefore, tsunamis originated from deep waters have long waves (Pond & Pickard, 1983). Long waves are more dangerous because they keep flooding the coast, resulting in high casualties, and thus dubbed ''killer tsunami''.
The long-wave tsunami has its propagation direction clearly southward to the Palu City, consisting with the slip direction of the east plate. On the other hand, the west plate slipped northward. As a result, the sea-level receded initially near the Palu City, which is consistent with eyewitness accounts (Pribadi et al., 2018). The ocean circulation shows a dominant clockwise eddy in the bay, caused by the horizontal strike-slip forcing of the two involved tectonic plates (Fig. 2B). The eddy is consistent with another eyewitness account of a whirlpool in the bay (Pribadi et al., 2018) (Supplementary Fig. S5). The black ellipse highlights the tsunami source, outside the bay, located along the Makassar southern coast (Fig. 2a). After 3 min of the earthquake, the Makassar coastal tsunami was shown propagating southward towards Mamuju, as highlighted by the lower-zoom panel (Fig. 2b), which was the source of ''early arrival'' tsunami at the Mamuju tide gauge.
To validate the models by the tide-gauge data, we show the tsunami waveforms at Pantoloan, Mamuju, and a virtual tide gauge off the Palu City in Fig. 3. We included four simulation results from the three All four model results show that the Pantoloan tide (Fig. 3a) has a very short wavelength of * 3 min, much shorter than that of previously known tsunamis, but has two distinguished tsunami peaks, significantly higher than the rest crests. To explain the short wavelength of the tsunami, we noticed that the Pantoloan tide-gauge was located in the Pantoloan harbor. The tide data shows a typical seiche wave of the resonance effect of the long-wave tsunami, propagating along the bay. The resonance effect can be determined by the relationship between the harbor geometry and the period T of the wave: , where g is the acceleration due to gravity, and L and h are the length and depth of the harbor (Toffoli & Bitner-Gregersen, 2017). Using the Pantoloan harbor bathymetry data L = 2 km and Although there was no tide gauge near the Palu City, the high fatality indicated the power of the tsunami reaching the shore. To gain insight into the tsunami at this location, we show Fig. 3b as a virtual tide at 119.85°E and 0.88°S off Palu City. All models show a long-wave tsunami with the two distinguished peaks of over 3 m, much higher than the tsunami peaks of Pantoloan. The two dark arrows indicate the tsunami peaks propagated southward, which is the strongest evidence of the deadly tsunami toward the Palu City. The southward propagation of the tsunami is consistent with the slip direction of the tectonic plate, suggesting the tsunami grew destructive after entering the bay. The long-wave tsunamis with high peaks have the potential for higher runup and longer inundation distance, responsible for the high casualties near the Palu City. This result is consistent with an after-event survey, showing that the Palu City coast had the most inundation distance (Pribadi et al., 2018). Figure 3c validates the model results by the Mamuju tide-gauge data. It can be seen that both the data and models show two forms of tsunami: the ''early-arrival'' tsunami arrived at about 18 min after the earthquake, and the late larger tsunami with much higher waves arrived at about 47 min after the earthquake, except the Palu-Bay-only result without the ''early-arrival'' tsunami. These results suggest that all three earthquake solutions, including the PAAG solution which could not explain the ''earlyarrival'' tsunami previously (Jamelot et al., 2019), equally explain the ''early-arrival'' tsunami as long as the horizontally-forced tsunami theory is used. As mentioned above, the Mamuju-recorded tsunamis had been a mystery because it confused BMKG's tsunami warning system. Our study here demonstrated that the large-scale tectonic plate movements can create multiple tsunami sources within and outside the Palu Bay, suggesting a different tsunami formation mechanism of strike-slip earthquakes.

Vertically-Forced Tsunami
As a comparison, Fig. 4 shows the tsunami waveforms using the vertically-forced tsunami mechanism [Eq. (1)]. First, we see that the three earthquake inversions resulted in various waveforms. Ironically, none of them had the feature of the two southward-propagating tsunami peaks from Pantoloan to the Palu City ( Fig. 4a-b). Second, the ''early arrival'' tsunami at Mamuju is too weak, similar to the ''Palu Bay only'' solution (magenta), suggesting that even with the horizontal contribution of Tanioka and Satake (1996) included, the vertically-forced tsunami mechanism could not explain the Mamuju data (Fig. 4c).

Vertically and Horizontally-Forced Tsunami (Three-Dimensional Initial Conditions)
In the final experiment, we also simulated the tsunami with both vertically and horizontally-forced (i.e., three-dimensional) initial conditions, which include the total elevation of sea-surface (Eq. (1)) and the initial momentum of ocean water [Eq. (3a,3b)]. Figure 5 is the corresponding results. Notice that the three-dimensional solutions are slightly Figure 4 Validation by tide gauge (vertically-forced). Same as Fig. 3, but used the vertically-forced tsunami formation mechanism of Tanioka and Satake [1996] [Eq. (1)]. The vertically-forced tsunami models generated inconsistent waveforms: a the models do not match the second peak of the Pantoloan data, b the tsunamis are too weak near Palu city; and c the models do not explain the ''early arrival '' tsunami at Mamuju Vol. 180, (2023) Tsunami Genesis of Strike-Slip Earthquakes 1917 stronger than the horizontally-forced solutions, which is expected. However, the PAAG solution overestimated the tsunami significantly at the Pantoloan and Mamuju tide locations (green lines). The overestimation was due to the PAAG solution that assumed the vertically-force as the only cause of tsunami.
With that assumption, the PAAG inversion had to exaggerate the dip-slip component in the fault model for a tsunami to match the observation (their table 3). Finally, we have also validated the model runups with the survey data in Fig. 6. Immediately after the event, three survey teams visited the Palu area Omira et al., 2019;Pribadi et al., 2018). We have combined all their survey data, as shown by the black bars, where the background colors represent the maximum tsunami height. For the comparison, we derived the model run-ups by the empirical formula of Paprotny et al. (2014). All three earthquake inversion models compare well with the survey data, slightly better than the solutions forced by the horizontally-forced mechanism alone (Fig. 3), suggesting that the vertically-forced factor or landslides might also contribute to the tsunami's power.

Conclusion and Discussions
The 2018 Palu tsunami was apparently a mystery because the triggering earthquake was nearly pure strike-slip faulting and mostly on land. Previous studies had focused on the tsunami source within the Palu Bay based on the vertically-forced or landslideinduced tsunami theory. This study applied the horizontally-forced tsunami theory to the strike-slip faulting scenario of the Sulawesi-Palu earthquake. Our experiments showed that the horizontal displacements of bathymetry slopes, caused by largescale tectonic plate motions, could generate multiple tsunami sources inside and outside the Palu Bay. These inside and outside sources generated a longwave tsunami into the Palu Bay, which was responsible for the devastation at the Palu City. The resultant tsunami was shown to reconcile various observations well, including tsunami's power, waveforms, eyewitness accounts, and travel-times that could not be fully explained previously. Specifically, our modeling experiments and data analyses showed that the southward-slipping east plate created the main momentum into the ocean, in the vicinity of the deep-water slopes along the Makassar coast outside and inside the Palu Bay, excited a long-wave tsunami propagating into the Palu Bay. It propagated southward along the bay and eventually inundated the Palu City at the south end of the Bay, which was likely the cause of the tragedy. The two distinguished wave peaks in the Pantoloan tide-record, different from the local resonance waves, were the strongest evidence of the tsunami formed from sources outside and inside the Palu Bay. The first peak could be explained by the tsunami source within the bay, while the second peak was consistent with tsunami source outside the bay. Their combination formed the powerful tsunami with a wavelength of 40 km, longer than the Palu Bay length of 35 km, before hitting the Palu City. The Mamuju tide-gauge recorded two types of tsunamis: the ''early arrival'' tsunami was originated from the nearby coast while the late larger tsunami was originated from the far-away Palu Bay, which further confirmed the large-scale effects of tectonic plate displacements. In addition, the strike-slip faulting with two oppositemoving plates created the clockwise oceanic circulation in the bay, consistent with the eyewitness account of the after-event survey (Pribadi et al., 2018).
Identifying the cause of the 2018 Palu tsunami has profound implications. Historically, several earthquakes with a similar magnitude had occurred and generated damaging tsunamis in the Indo-Pacific region (Prasetya et al., 2001). Other active seismicity regions, such as the Mediterranean region with a similar geological setting to the Indo-Pacific region, also have earthquakes and tsunamis frequently. Therefore, the demonstrated tsunami formation mechanism for the Palu event may have abroad applications to other regions as well. As mentioned, the two larger strike-slip earthquakes of Mw 8.6 and 7.8 in the Wharton Basin of northeastern Indian Ocean did not generate significant tsunamis (Heidazadeh et al., 2017). Notice that both earthquakes occurred within the Wharton Basin, far away from the continental slope. Bathymetry slope displacement is the necessary condition for the horizontally-forced tsunami (Song et al., 2008). The Wharton Basin has a very different geographic setting from the Palu Bay. It would be interesting to test the tsunami genesis theory for that region as well in future studies.

Figure 6
Validation by tsunami runups (horizontally and vertically-forced). Black bars from all survey data and color dots from models (red, magenta, and green for USGS, JPL, and PAAG solution, respectively). The background color represents the maximum tsunami height within the Bay Vol. 180, (2023) Tsunami Genesis of Strike-Slip Earthquakes So far, we have discussed three competing formation mechanisms, i.e., the vertically-forced, the horizontally-forced, and landslide-induced tsunami theory. In tsunami models, all three mechanisms can generate sizable tsunamis, as mentioned in the Introduction. However, different forcing mechanisms should exhibit different behavioral characteristics of the tsunami, particularly near the source region, which can be distinguished by observations. The distinguished characteristics of the horizontally-forced tsunami are its initial directionality and the large-scale nature caused by the horizontal displacements of the faulting tectonic plates (Oreskes, 2003). Differently, a vertically-forced tsunami does not necessarily have these horizontally-forced characteristics because it is forced vertically. On the other hand, landslide-induced tsunami is local and has the directionality perpendicular to the slope. Note that the land-sliding slope does not necessary perpendicular to the direction of the plate displacement of the earthquake. These distinguished tsunami characteristics through near-field observations are critical evidence to identify the dominant forcing mechanism.
The observational evidence from the Palu event was unprecedented close to the source, which provided the opportunity to identify these tsunami characteristics. Specifically, we carefully examined five types of observational evidence and found that: i) The bathymetry survey of the Palu Bay immediately after the earthquake ( Supplementary Fig. S1) did not find significant seafloor deformation or large-scale landslides, suggesting that other forcing mechanism might play a role in generating the tsunami. ii) Seismic inversions and satellite imageries (Supplementary Fig. S2) confirmed significant horizontal displacements of the seafloor. By using the horizontally-forced mechanism, the three different (USGS, PAAD, JPL) seismic inversions generated a consistent tsunami (Fig. 3). On the other hand, by using the vertically-forced mechanism, the seismic inversions generated inconsistent tsunami waveforms (Fig. 4), suggesting that seismic inversions have better constraint on the horizontal displacement than on the vertical displacement of seafloor.
iii) The two distinguished tsunami-peaks in the Pantoloan tide-record were the key evidence of the tsunami sources originated inside and outside the Palu Bay. Its propagation toward the Palu City was consistent with the faulting east-plate, which slipped southward. iv) The ''early arrival'' tsunami in the Mamuju tidegauge record could be explained by the horizontally-forced mechanism, resulted in multiple tsunami sources outside the Palu Bay due to the large-scale nature of the faulting plates. v) The eyewitness account of the whirlpool circulation in the Palu Bay could be explained by the oceanic momentum transferred by the strike-slip faulting with two opposite-moving plates.
Based on these various observations and model validations, we therefore concluded that the horizontally-forced mechanism might have played a major role in generating the Palu tsunami. The earthquake-induced horizontal displacements and local slopes are the key values in determining the tsunami sources, which can be quantified by observations (Chen et al., 2019;Song, 2007). However, this study does not suggest that the horizontallyforced tsunami formation mechanism was the only cause of the Palu tsunami. Both vertical displacement of seafloor or landslides could also have played a role, but their roles could not be quantified by the seismic inversions, nor by the bathymetry survey. Indeed, any earthquake can have both horizontal and vertical motions of land or landslides. The challenge is to quantify their roles in generating the tsunami. This finding indicates that the tsunami formation mechanism might be more complex than previously thought. Future studies should focus on near-field observations and tsunami's behavior, which are important for identifying the tsunami formation mechanism and for successful early warnings. of Prasetya was funded by The Tsunami Research Foundation of Indonesia and Chen was funded by National Science Foundation of China (Grant No. 42074024). We thank Dwi Susanto for providing the early version of the tide data and Widjo Kongko for the bathymetric data.
Author Contributions YS wrote the main manuscript text. KC conducted the earthquake modeling. GP contributed and examined the tsunami and survey data. All authors were involved in interpreting the results and contributed to improving the manuscript.

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