1 Introduction

The Sulawesi Island of Indonesia was the site of a large earthquake (Mw 7.5) on 28 September 2018 which was followed by a deadly tsunami. The United States Geological Survey (USGS) located the epicenter at 0.178oS and 119.840oE occurring at 10:02:43 UTC at the depth of 10.0 km (Fig. 1). The USGS focal mechanism solution identified a dominant strike-slip mechanism with strike, dip and rake angles of the most likely fault plane as 350o, 67o and − 17o, respectively (red mechanism in Fig. 1). The fault plane from the gCMT (global CMT: http://www.globalcmt.org) were: 348o, 40o and − 9o, respectively. Based on media reports and results of preliminary field surveys (Figure 2), the Sulawesi tsunami reached a maximum height of approximately 6−11 m along the coast of Palu within the Palu Bay (Fig. 1) (Muhari et al. 2018). As of 10 October 2018, the reported number of deaths has been 1763, making the Sulawesi event as the deadliest event in Indonesia since the December 2004 Sumatra-Andaman earthquake and tsunami. It is likely that the number of deaths will increase in the following weeks. Indonesia has experienced several deadly tsunamis since the December 2004 tragedy (> 130,000 deaths; Synolakis and Kong, 2006) including the tsunamis of October 2010 Mentawai (408 deaths) (Satake et al. 2013), the 2006 West Java (668 deaths) (Fujii and Satake, 2006), and the March 2005 Nias-Simeulu (> 915 deaths, mostly from earthquake) (Borrero et al. 2011).

Fig. 1
figure 1

a The epicenter of the 28 September 2018 Sulawesi earthquake (red star) along with those of past large tsunamigenic earthquakes in the region (colored stars). The locations of tide gauges used in this study are shown by green solid squares. The focal mechanisms for the 1996 and 2018 events are from the USGS catalog. Abbreviations are: NST, North Sulawesi Trench; EST, East Sangihe Thrust; PKF, Palu-Koro Fault; MF, Matano Fault; SUN, Sunda Plate; PHP, Philippines Sea Plate; AUS, Australian Plate; PP, Pacific Plate. b Sea level records of the tsunami as registered on three tide gauge stations in the region. c De-tided sea level records showing clear tsunami records for the Pantoloan and Mamuju but no tsunami signal is apparent for the Lahat Datu station

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Fig. 2
figure 2

Photos of tsunami damage and inundation in Sulawesi. The dashed contour line at the bottom-right panel shows the water depth in meters. Photos belong to the authors

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From a tectonic point of view, the epicentral area around the Sulawesi Island is located within one of the most complicated tectonic zones of the world where four major tectonic plates meet: Pacific plate from the east, the Philippine Sea plate from north, the Australian plate from south and the Sunda plate from the east (Fig. 1). The Palu-Koro strike-slip fault system (PKF) runs through the epicentral area (Fig. 1a). The Sulawesi region experienced at least three other lethal tsunamis in past hundred years (Fig. 1) in 1927 (M6.3, tsunami height of 15 m), in 1968 (M7.4, tsunami height of 8−10 m, 392 deaths) and in 1996 (M7.7−7.8, tsunami height of 3.4 m, 9 deaths) (Latief et al. 2000; Pelinovsky et al. 1997).

The 28 September 2018 Sulawesi event has been considered as a tsunami mystery because strike-slip earthquakes are usually unable to produce large tsunamis (Synolakis, 2003; Heidarzadeh et al. 2017) while the 2018 Sulawesi tsunami was 6−11 m in height along the coast. Strike-slip ruptures do not usually produce large vertical uplift/subsidence on the seafloor because of the dominant horizontal movements of the fault; thus, they are usually unable to produce destructive tsunamis. For example, the Mw 7.8 Wharton Basin earthquake in SW Sumatra, with a dominant strike-slip mechanism, generated tsunami amplitudes of less than 10 cm at tide gauges (Heidarzadeh et al. 2017). In addition, the size of the earthquake was Mw 7.5 which is relatively small in terms of tsunami generation. Therefore, it has been speculated that the large waves of the 2018 Sulawesi tsunami were the results of secondary sources triggered by the main shock. Potential secondary sources are splay faulting, submarine landslides, bay oscillations and funneling effects of the Palu Bay (Fig. 1).

In this research, we present the observed waveforms of the tsunami and conduct analysis to explore the spectral contents of the waveforms. Numerical modeling of the tsunami is performed using the tectonic source of the tsunami in order to examine whether the tsunami could be generated by the purely-tectonic source or not. Results from spectral analysis are combined with numerical simulations to infer potential sources of the tsunami.

2 The Earthquake Fault and Local Bathymetry

The Palu-Koro strike-slip fault system (PKF) was most likely responsible for the Mw 7.5 Sulawesi earthquake (Fig. 1, 3). According to Bellier et al. (2001), the left-lateral and north-south striking PKF system accommodates a horizontal slip rate of 35 ± 8 mm/yr. Preliminary crustal displacement analysis using satellite images revealed up to several meters of horizontal displacement along the PKF system (http://www.gsi.go.jp/common/000205265.png). Most of the tsunami deaths were reported for the coast of Palu Bay which is a semi-enclosed basin with length and width of approximately 35 and 8 km, respectively. The maximum water depth of the bay is approximately 300 m based on the coarse bathymetry data from the GEBCO digital atlas (Weatherall et al. 2015) (Fig. 3a). We note GEBCO bathymetry data may not be accurate enough for coastal and shallow areas such as the Palu Bay. The bathymetry data from BIG (Badan Informasi Geospasial, Indonesia) indicates a maximum water depth of ~ 700 m (Fig. 3b) as a deep narrow channel in the middle of the bay.

Fig. 3
figure 3

Bathymetry of the Palu Bay from GEBCO (a) and BIG (Badan Informasi Geospasial, Indonesia) (b) bathymetry data

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3 Data and Methods

We analyzed three tide gauge records in Mamuju (Indonesia), Pantoloan (Indonesia) and Lahat Datu (Malaysia). All records have sampling intervals of 1 min. The Lahat Datu data was provided by the Intergovernmental Oceanographic Commission of UNESCO/UN at http://www.ioc-sealevelmonitoring.org/ while the other two records were obtained and processed by the Agency for Geo-spatial Information, Indonesia (BIG) (http://tides.big.go.id). Sea level data were de-tided by predicting the tidal signals using a least squares method of harmonic analysis and then removing the tidal signals from the original tide gauge records. For spectral analysis, we followed the Welch algorithm (Welch, 1967) with half-window overlaps (e.g., Rabinovich et al. 2011; Heidarzadeh and Satake, 2013). Duration of high-energy tsunami waves were calculated by the Averaged-Root-Mean-Square (ARMS) diagrams for the tsunami waveforms (Heidarzadeh and Satake, 2014) using a moving time window with length of 20 min (i.e., 20 data points). The duration of high-energy tsunami wave is the time that the ARMS level of the waveform is above that for the background wave (i.e., before the arrival of the tsunami).

For tsunami simulations, we applied the COMCOT package (Cornell Multi-grid Coupled Tsunami Model) (Liu et al. 1998; Wang and Liu, 2006). COMCOT solves linear and nonlinear Shallow Water Equations on both Cartesian and Spherical coordinates. COMCOT adapts a numerical scheme to mimic physical dispersion following the method by Imamura et al. (1988). A two-level nested bathymetric grid was created with resolutions of 30 and 5 arc-sec from the GEBCO-2014 (The General Bathymetric Chart of the Oceans) data (Weatherall et al. 2015) (Fig. 1a). The higher-resolution grid (i.e., level 2) was interpolated from the original GEBCO 30 arc-sec bathymetry and topography data. We applied linear simulations for the larger grid and nonlinear simulations for the smaller ones. Runup calculations were not included in our numerical simulations, as it requires high-resolution nearshore bathymetry and topography. Simulations were conducted for a total time of 11 h with time step of 0.5 s. The second version of the USGS source model has been used in this study for tsunami generation which has dimensions of 200 km (length) × 30 km (width) with maximum slip of 9 m occurring within the Palu Bay (https://earthquake.usgs.gov/earthquakes/eventpage/us1000h3p4/finite-fault). The initial tsunami wave field was calculated using the co-seismic seafloor displacements obtained from the Okada’s (1985) analytical method. Both vertical co-seismic displacement (\( D_{z} \)) and the vertical water displacement due to steep slopes (\( D_{h} \)) were considered following the approach proposed by Tanioka and Satake (1996):

$$ D_{h} = D_{x} \frac{dH}{dx} + D_{y} \frac{dH}{dy} $$
(1)

in which, \( D_{x} \) and \( D_{y} \) are the E-W and N-S components of co-seismic seafloor displacement, \( H \) is water depth (positive downward), \( D_{h} \) is the vertical displacement of water due to the horizontal movement of the slope. The combined vertical displacement of water is the sum of \( D_{z} \) and \( D_{h} \).

4 Results of Tide Gauge Data Analysis and Physical Properties of the Tsunami

The Lahat Datu tide gauge did not record any clear tsunami signal (Fig. 1b) which can be attributed to the relatively large noise level (± 8 cm) and small size of the tsunami. The maximum trough-to-crest wave height recorded at two stations of Pantolaon (inside the Palu Bay) and Mamuju (outside the Palu Bay) are 380 and 24 cm, respectively (Table 1, Figure 1c). The Pantoloan record is 16 times larger than that of the Mamuju. The respective arrival times are 5 and 19 min (Table 1). Our numerical simulations, however, indicate an arrival time of ~45 min for the Mamuju record. Therefore, either the timing of the tide gauge was problematic or maybe a different mechanism was responsible for the early tsunami observed in Mamuju. Assuming that the latter holds true, the relatively short tsunami arrival time in Mamuju may indicate that other sources nearby were responsible for the tsunami in Mamuju.

Table 1 Parameters of the Sulawesi tsunami of 28 September 2018 recorded by local tide gauges (Main shock, Mw = 7.5 at 10:02:43 UTC)
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In addition to such a significant difference in tsunami heights between Pantoloan and Mamuju, the two records are significantly different in terms of wave periods: their respective dominant periods are 3−4 and 10−12 min from inspection of the waveforms (Fig. 1c, Table 1). The dominant period of the Pantoloan waves are ~3 times longer than those of Mamuju. The sampling interval of 1 min appears to be insufficient to properly capture the short-period tsunami oscillations in Pantoloan; thus, the actual extrema of the waves are possibly higher than the values shown in Table 1. The ARMS diagrams (Fig. 4) show that the high-energy waves at the Pantoloan last for 5.5 h while they last for at least 14 h in Mamuju.

Fig. 4
figure 4

a The sea level records of the 28 September 2018 Sulawesi tsunami in Pantoloan and Mamuju. b Respective Averaged-Root-Mean-Square (ARMS) diagrams

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Tide gauge data analysis indicates that, in terms of physical properties of the waves, the Pantoloan and Mamuju tsunami waves are significantly different: the Pantoloan waves are significantly larger in height and are dominated by shorter-period waves and shorter duration in comparison to the waves at the Mamuju station. It appears that the two waveforms are possibly generated by two completely different sources or mechanisms. Usually different tide gauge records of the same tsunami contain the same or similar wave periods for at least the first few cycles (e.g., Heidarzadeh and Satake, 2013).

5 Results of Spectral Analysis

Spectral analyses (Fig. 5) reveal dominant tsunami period bands. For the Pantolaon station, the tsunami period band is 2.8−6.7 min while it is 4.0−18.3 min for Mamuju. The respective dominant tsunami periods are 3.6−4.4 and 10.0 min (Fig. 5). Tsunami source dimensions can be estimated from the tsunami dominant periods using the following equation (Heidarzadeh and Satake 2015b):

Fig. 5
figure 5

Spectral analysis for the sea level records of the 28 September 2018 Sulawesi tsunami in Pantoloan and Mamuju

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$$ L = \frac{T}{2}\sqrt {gH} $$
(2)

in which, \( L \) is source length, \( H \) is average water depth, \( g \) is gravitational acceleration and \( T \) is tsunami dominant periods. We note that Equation (2) is applicable for wave periods (\( T \)) extracted from first few cycles of the tsunami, which is usually free from bay oscillations and other bathymetric effects. By assuming average water depth of ~100 m for inside the Palu Bay (Fig. 2) and ~1200 m for outside the bay (Fig. 1), Eq. (2) results in tsunami source dimensions of approximately 3−4 and 32−38 km for inside and outside the Palu Bay, respectively. We note that the average water depth of the Palu Bay could be slightly different considering the BIG bathymetry data in Fig. 3b. It is possible that these two sources are different parts of the same tectonic source because the isolated segment of the tectonic source located inside the Palu Bay may act independently towards tsunami generation within the bay.

6 Results of Numerical Simulations

Results of numerical simulations are shown in Figs. 6−11. Two different initial conditions for the 2018 Sulawesi tsunami were considered: the co-seismic vertical crustal displacement (Fig. 6c, \( D_{z} \)), and the combination of the vertical component (\( D_{z} \)) and the additional vertical water displacement due to the horizontal movement of the seafloor slope (\( D_{h} \)) (Fig. 6d, the component \( D_{z} + D_{h} \)). It can be seen that these two initial conditions are similar to each other with small differences (Fig. 6). Our calculations yield up to ~3 and ~1 m of co-seismic horizontal N-S (Fig. 6a) and E-W (Fig. 6b) crustal displacement. The maximum co-seismic vertical displacement is ~1 m (Fig. 6c, d).

Fig. 6
figure 6

Co-seismic crustal displacement due to 28 September 2018 Sulawesi earthquake calculated using the revised source model on USGS. a The N-S component (\( D_{y} \)). b the E-W component (\( D_{x} \)). c the vertical component (\( D_{z} \)). d combination of vertical component (\( D_{z} \)) and the effect of steep bathymetry (\( D_{h} \)) based on the methodology proposed by Tanioka and Satake (1996)

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Snapshots of tsunami simulations at different times for two large and small grids are shown in Figs. 7, 8 indicating a similar pattern of tsunami propagation from our two initial sources (i.e., \( D_{z} \) and \( D_{z} + D_{h} ) \). Several nodes (i.e., points with zero amplitude) appear in the tsunami snapshots within the Palu Bay (Figs 7, 8, right panels) indicating patterns of bay oscillations. Based on the snapshots in grid-1 (i.e., the largest grid), the first negative wave arrives in Mamuju ~45 min after the earthquake origin time while the observation waves show an arrival time of ~20 min (Fig. 1c). This may indicate that the timing of the Mamuju tide gauge station is not correct or possibly a different local source was responsible for the early tsunami in Mamuju. As the periods and amplitudes of the simulated and observed waves agree well at the Mamuju station, it is most likely that there was a clock error with the tide gauge. The simulated waves at the locations of the two tide gauges agree well with those of observations (Fig. 9, blue waveforms), at least for the first cycle of the waves. We note that the observation waveform in Mamuju is delayed 45 min in Fig. 9 to match the timing of the simulations. Tsunami simulations are usually aimed at reproducing the first wave cycle because later cycles are mixed with reflected/refracted waves as well as nonlinear bathymetry effects; hence, high-resolution bathymetry/topography data along with dispersive modeling would be necessary to fully reproduce late cycles. In such a context, the simulation results shown in Fig. 9 are successful in reproducing most of the features of the two observed tide gauge records.

Fig. 7
figure 7

Snapshots of tsunami simulations in grid-1 (left) and grid-2 (right) at different times due to the 28 September 2018 Sulawesi tsunami. These snapshots are from the simulations based on the vertical co-seismic displacement (\( D_{z} \))

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Fig. 8
figure 8

Snapshots of tsunami simulations in grid-1 (left) and grid-2 (right) at different times due to the 28 September 2018 Sulawesi tsunami. These snapshots are from the simulations based on the combination of the vertical co-seismic displacement and the vertical water displacement due to steep bathymetry (\( D_{z} + D_{h} \))

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Fig. 9
figure 9

Comparison of observed (black) and simulated (red) waveforms of the 2018 Sulawesi tsunami. a Simulations are based on the vertical co-seismic displacement (\( D_{z} \)). b Same as “a” but for simulations based on the combination of the vertical co-seismic displacement (\( D_{z} \)) and the vertical water displacement due to steep bathymetry (\( D_{h} \)). Observation waveforms (Obs.) are shifted 45 min to match with the simulations. Obs. stands for observations

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Oscillations of tsunami waves at various locations within the Palu Bay are plotted in Fig. 10 based on our numerical simulations. A long period of ~85 min is seen in all of the numerical wave gauges within the Palu Bay which can be attributed to the fundamental periods of the bay. According to Rabinovich (2010), the fundamental periods of a semi-enclosed long basin (i.e., length is significantly larger than the width) is given by the following equation:

Fig. 10
figure 10

Tsunami simulations of the 28 September 2018 Sulawesi tsunami for various points within the Palu Bay revealing long-period waves with periods of ~85 min due to Bay oscillations. The red-dotted line indicates the origin time of the earthquake

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$$ T = \frac{4L}{(2n + 1)}\frac{1}{{\sqrt {gH} }} $$
(3)

in which, \( T \) is the fundamental mode of the bay, \( L \) is the length of the bay, \( H \) is average water depth, \( g \) is gravitational acceleration and \( n = 0, 1, 2, \ldots \) which gives various fundamental modes. By assuming a length of 35 km (\( L \)) and an average water depth of ~100 m (\( H \)), the few first fundamental periods are 75, 25, 15 and 10.7 min. The longest fundamental period of 75 min is close to the value of ~85 min seen on the simulated waveforms in Fig. 10.

The maximum tsunami wave amplitudes during the entire time of tsunami simulations are shown in Fig. 11 for both initial conditions. Figure 11, which does not include runup stage, yields maximum amplitude of ~1.5 m for the Sulawesi tsunami. Previous studies have shown that maximum coastal wave amplitudes are rough estimates of wave runup. Obviously, this value is much smaller than the reported runup of 6−11 m by tsunami survey teams (Muhari et al. 2018). Based on Fig. 11, maximum wave amplitudes are concentrated at the southern tip of the Palu Bay as well as around the Pantoloan tide gauge station.

Fig. 11
figure 11

a Maximum tsunami amplitudes after 11 h of tsunami simulations based on the vertical co-seismic displacement (\( D_{z} \)). b same as “a” but for simulations based on the combination of the vertical co-seismic displacement and the vertical water displacement due to steep bathymetry (\( D_{z} + D_{h} \))

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7 Insights on the Source Mechanism and Potential Landslide Location

Numerical modeling and spectral analysis conducted in this study help to comment on the type of the tsunami source. Based on the spectral analysis, the tide gauge stations located inside and outside of the Palu Bay generated tsunami waves with significantly-different dominating periods of 4.0 and 10.0 min, respectively. Numerical modeling proved that a purely-tectonic source of the tsunami is able to generate both types of the shorter- and longer-period waves inside and outside of the bay. However, the simulated maximum tsunami amplitudes (1.5 m) are smaller than the surveyed runup heights of 6−11 m inside of the Palu Bay. Therefore, it may be concluded that an additional secondary source has contributed to the tectonic source of the tsunami. We provide evidence in the next section that such a secondary source most likely was a submarine landslide within the Palu Bay.

To shed light on the location of a potential secondary landslide source, a backward tsunami ray tracing is conducted whose result is shown in Fig. 12. For this analysis, a hypothetical tsunami source is placed at the location of the Pantoloan tide gauge station and propagation of the tsunami is modelled up to 5 min, which is the arrival time of the 2018 Sulawesi tsunami at this tide gauge station (Table 1). The edges of tsunami travel distances after 5 min in both directions (north and south) determine potential landslide locations (i.e., the two dashed boxes in the bottom-right panel in Fig. 12). The field survey by Muhari et al. (2018) revealed that the largest runup heights were concentrated at the southern part of the Palu Bay around the latitude of -0.82oS. Therefore, the bottom dashed rectangle at the latitude of − 0.82oS (Fig. 12) is more likely to be the location of a potential landslide.

Fig. 12
figure 12

Results of backward tsunami ray tracing by placing a point tsunami source at the location of the Pantoloan tide gauge (top-left panel) and propagating the synthetic tsunami for 5 min. The edges of tsunami travel distances after 5 min in both directions (north and south) determine potential landslide locations (i.e., the two dashed boxes in the bottom-right panel). The bottom dashed rectangle at the latitude of − 0.82oS is more likely to be the location of a potential landslide because largest runup heights of the 2018 Sulawesi tsunami were concentrated around this area

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8 Discussion

Our purely-tectonic source model for the 2018 Sulawesi tsunami reproduces fairly well both tide gauge records in Pantoloan and Mamuju; except for the arrival time of the Mamuju record. The agreement between our simulations with observations includes both wave periods and wave amplitudes. In other words, the purely-tectonic source model explains the sharp difference between wave amplitudes (i.e., a ratio of ~16) and wave periods (i.e., a ratio of ~3) of the Pantoloan and Mamuju tide gauge records. However, the maximum simulated coastal amplitudes from our source model is ~1.5 m which are far less than the reported wave heights of 6−11 m. As of 20 October 2018, preliminary tsunami field surveys have been conducted and the data on the runup are yet to be analyzed. It has been reported that the extreme wave height of 11 m was the splash height and perhaps the flow depth on the land was ~3 m (Muhari et al. 2018). If we assume that these speculations hold true, then our source model could be capable of reproducing runup heights of ~ 3 m given high-resolution bathymetry/topography. Long-wave runup significantly depends on the actual nearshore bathymetry/topography, and particularly on the last coastal slope on which runup occurs (Kanoglu and Synolakis 1998).

In early days following the Sulawesi disaster, the potential involvement of a secondary source such as a submarine landslide (e.g., Synolakis et al. 2002) or a splay fault (e.g., Plafker, 1972) was mentioned. Both phenomena have been responsible for extremely large tsunamis following moderate earthquakes in the past. The 15-m large tsunami waves in July 1998 in Papua New Guinea were generated by a landslide tsunami following an Mw 7.0 earthquake (Tappin et al. 2001; Synolakis et al. 2002; Heidarzadeh and Satake, 2015a). Splay fault have been reported to double tsunami heights compared to cases without a splay component (Heidarzadeh et al. 2009). Both splay faults and landslides are local phenomena with limited source dimensions (e.g. a few kilometers). The dimensions of the 1998 PNG landslide were ~ 4 km in both length and width. For the 2018 Sulawsi event, a video recording of the sea surface of the Palu Bay shortly after the earthquake, captured onboard an aircraft, shows several local sea surface disturbances (Fig. 13). Another 4-min eyewitness video from onboard a boat also recorded at least three subaerial landslides within the Palu Bay following the earthquake (Fig. 14). Due to the small size of these sea surface disturbances and landslides in the eyewitness videos (Figs. 13, 14), they may not necessarily be of the sizes capable of producing significant tsunamis. It appears that the area is susceptible to subaerial and submarine landslides; therefore, it could be possible that a large submarine landslide along the submerged slopes was responsible for the 6−11 m tsunami waves. Potential contribution of such secondary sources (i.e., co-seismic landslides) could be examined by acquisition and interpretations of marine geological data from the seafloor within the Palu Bay.

Fig. 13
figure 13

Photo captures indicating sea surface disturbances taken from onboard an aircraft flying over the Palu Bay shortly after the 28 September 2018 Sulawesi earthquake origin time (source of the video: https://www.instagram.com/p/BoRttnsn5po/?taken-by=icoze_ricochet)

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Fig. 14
figure 14

Photo captures showing the generation and propagation of a subaerial landslide taken from onboard a boat within the Palu Bay shortly after the origin time of the 28 September 2018 Sulawesi earthquake (source of the video: https://www.youtube.com/watch?time_continue=2&v=61ItBglP-YM)

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Ideas of the existence of a tsunami generation mechanism other than the strike-slip fault might be strengthened by findings from field surveys (Muhari et al. 2018) which revealed that maximum inundation of the tsunami was limited to the areas within 400 m from the shoreline. Due to their short-period waves, landslide-generated waves are not capable of producing long inundations. From the hydrodynamics point of view, inundation distance strongly depends on the period of the waves: the longer the period of the waves, the longer the inundation distance. The short-period waves inside the bay (Pantoloan, Fig. 1b) and rapid arrival time onshore may indicate that tsunami might have been generated inside the bay by a relatively small source. This wave severely impacted on infrastructures and buildings at the front row near by the coastline (Fig. 2), however, the waves were not strong enough to penetrate further inland as the inundation line was found not more than 400 m landward.

A main challenge for the source studies of the Sulawesi tsunami is the lack of enough sea level observations. Only two tide gauge records are available; i.e., Pantoloan and Mamuju. For inside the Palu Bay, where the extreme tsunami waves of 6–11 m were observed, only one sea level record is available (i.e., Pantoloan). The water waves from local phenomena such as submarine landslides usually travel short distances and decay rapidly (Fritz et al. 2004; McFall and Fritz, 2016; Heidarzadeh and Satake, 2017a,b); hence, even if we assume that a submarine landslide was involved, it is uncertain whether the single sea level record has captured such short-period and short-lasting waves or not.

A combination of spectral analysis, numerical simulations and field data may lead us to two different sources/mechanisms for the tsunamis recorded in Pantoloan and Mamuju. For the Pantoloan record, the inferred source dimension of 3−4 km (Table 2) could be from a small submarine landslide; approximately with the same size as that of the 1998 PNG landslide tsunami. The larger source dimension of 32.5 km (Table 2) inferred from the Mamuju record is in agreement with the size of the initial co-seismic crustal displacement shown in Fig. 6c, d.

Table 2 Estimates of tsunami source dimensions using the tsunami dominating periods
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9 Conclusions

The 28 September 2018 Sulawesi tsunami was analyzed using sea level data and numerical modeling of tsunami. Main findings are:

  1. 1.

    The maximum tsunami wave height at two tide gauge stations of Pantoloan (within the Palu Bay) and Mamuju (outside the Bay) were 380 and 24 cm, respectively. The respective dominant wave periods were 3.6−4.4 and 10.0 min. The high-energy waves at Pantoloan lasted for 5.5 h while they lasted for at least 14 h in Mamuju. The two observed waveforms were significantly different with wave amplitude and period ratios of ~16 and ~3, respectively.

  2. 2.

    Based on the results of spectral analyses of the tsunamis recorded inside (i.e., Pantoloan) and outside (i.e., Mamuju) of the Palu Bay, the dimensions of the tsunami sources are estimated at 3.4–4.1 km and 32.5 km, for inside and outside of the Palu Bay, respectively.

  3. 3.

    Numerical simulations of the tsunami using a purely-tectonic source model based on USGS were capable of fairly well reproducing both observation tide gauge records in Pantoloan and Mamuju; except for arrival time in Mamuju. Our simulations (excluding runup calculations) resulted in maximum coastal amplitudes of ~1.5 m which is far less than the observed runup of 6–11 m. After acquiring high-resolution bathymetry/topography data and having a full understanding of runup field data, the model needs to be re-run.

  4. 4.

    Evidence may indicate the occurrences of submarine landslides following the Sulawesi event which potentially contributed to and intensified the main tectonic tsunami; such as the actual sea surface disturbances captured by video recordings from onboard an airplane and a boat within the Palu Bay. Submarine landslides could be responsible for extreme local runup heights; however, marine geological data need to be acquired from the Palu Bay to confirm such hypotheses. We identify the southern part of the Palu Bay, around the latitude of -0.82oS, as the most likely location of a potential landslide based our backward tsunami ray tracing analysis.