# Extreme tsunami inundation in Hawai‘i from Aleutian–Alaska subduction zone earthquakes

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## Abstract

The 2011 Tohoku earthquake and tsunami motivated an analysis of the potential for great tsunamis in Hawai‘i that significantly exceed the historical record. The largest potential tsunamis that may impact the state from distant, Mw 9 earthquakes—as forecast by two independent tsunami models—originate in the Eastern Aleutian Islands. This analysis is the basis for creating an extreme tsunami evacuation zone, updating prior zones based only on historical tsunami inundation. We first validate the methodology by corroborating that the largest historical tsunami in 1946 is consistent with the seismologically determined earthquake source and observed historical tsunami amplitudes in Hawai‘i. Using prior source characteristics of Mw 9 earthquakes (fault area, slip, and distribution), we analyze parametrically the range of Aleutian–Alaska earthquake sources that produce the most extreme tsunami events in Hawai‘i. Key findings include: (1) An Mw 8.6 ± 0.1 1946 Aleutian earthquake source fits Hawai‘i tsunami run-up/inundation observations, (2) for the 40 scenarios considered here, maximal tsunami inundations everywhere in the Hawaiian Islands cannot be generated by a single large earthquake, (3) depending on location, the largest inundations may occur for either earthquakes with the largest slip at the trench, or those with broad faulting over an extended area, (4) these extremes are shown to correlate with the frequency content (wavelength) of the tsunami, (5) highly variable slip along the fault strike has only a minor influence on inundation at these tele-tsunami distances, and (6) for a given maximum average fault slip, increasing the fault area does not generally produce greater run-up, as the additional wave energy enhances longer wavelengths, with a modest effect on inundation.

## Keywords

Tsunami modeling 1946 tsunami Earthquake source mechanisms Tsunami inundation North Pacific, Aleutian Islands, and Hawai‘i## 1 Introduction

The March 11, 2011, great Tohoku earthquake and tsunami in Japan served as a wake-up call to coastal communities in the Pacific, re-emphasizing the lesson learned in the Indian Ocean in 2004: the potential for a giant Mw 9 earthquake to inflict a devastating tsunami both locally and across the ocean. The State of Hawaii was largely spared great damage ($30.6M, National Centers for Environmental Information 2016) from the Tohoku tsunami, and statewide evacuation zones were sufficient. However, as TV showed in real time, the tsunami waves approaching the Japanese coast, overtopping the carefully planned and constructed system of seawalls, inundating cities and the countryside, and severely damaging a nuclear power plant, the question posed by Butler (2012) is whether Hawai‘i is prepared for a worst-case scenario like Tohoku.

The bases for the danger to Hawai‘i from the Aleutians are threefold: tectonics, proximity, and geometry. The Aleutian subduction zone is very seismogenically active, with three Mw ≥ 8.6 earthquakes since 1946. The tsunami propagation time from there to Hawai‘i is a short, 4.5 h—imparting the minimum warning time for all non-local tele-tsunamis. Finally, the arcuate Aleutians are geometrically situated to focus tsunami energy toward Hawai‘i (e.g., Titov et al. 1999, 2001; Tang et al. 2006). These points are illustrated in Fig. 2, where the observed tsunami energy from the 1946 and 1957 events skirted the Hawaiian Islands, propagating to the east and west of the Islands, respectively. Between these two epicenters lies the possibility for an extreme Mw ~9 event (Butler 2012) that would be far more devastating than either the 1946 or 1957 tsunamis.

In order to meet this threat, the Hawaii State Civil Defense (now Emergency Management Agency) engaged with the lead author (R.B.) to work with the Pacific Tsunami Warning Center and the Hawai‘i Mapping Project to formulate the maximum credible tsunamigenic earthquake(s) threatening the Hawai‘i coast. After “appropriate and prudent” review by the U.S. Geological Survey looking at Hawaii’s risk, these extreme earthquakes were to be used as the basis for updated tsunami evacuation maps for the state.

Several guiding principles were established. From the outset, the focus is on tele-tsunamis, and not directly on local Hawaiian sources, or meteor impact origins (although both were obliquely considered). We consider the Aleutian–Alaska subduction zone the most dangerous source region (other zones were found to yield smaller tsunamis than comparable Aleutian earthquakes; i.e., even though there is a significant threat from Kamchatka—see Figs. 14 and 15 in “Appendix”—the potential threat from credible Aleutian tsunamis is larger still). We consider ‘credible’ to mean that the physical parameters of the earthquake (faulting and slip) have been observed—or inferred from analysis—in prior Mw 9+ earthquakes (see Butler et al. 2016 for probabilistic analysis). Since the largest tsunami experienced in Hawai‘i is the 1946 event, we first validated our tsunami model forecasts with 1946 data, to link and corroborate knowledge of the earthquake with observed tsunami effects. We then model candidate Aleutian earthquake scenarios using two different tsunami codes to independently validate results—these methods comprise the NOAA operational code, SIFT, and the University of Hawai‘i research code, NEOWAVE (see “Appendix” for details). The effects of varying key parameters are explored to ascertain effects on tsunami amplitudes: fault areas, shallow and deep faulting, laterally varying distribution of slip on the faults, location along the arc, and earthquake seismic moment magnitude, Mw.

## 2 Earthquakes

### 2.1 The Aleutian tsunami of 1946

Butler (2012) reviewed the main characteristics of the 1946 Aleutian earthquake, for which the magnitude has been variously estimated from 7.1 to 9.3 (e.g., Johnson and Satake (1997). López and Okal (2006) derived a seismic moment of 8.5 × 10^{21} N-m from surface waves, equivalent to Mw = 8.6 with uncertainty ≥±0.1. Length and width were determined from relocation of 1 year of aftershocks. The very slow rupture of the 1946 earthquake and limited instrumentation at the time preclude further resolution beyond average fault properties (López and Okal 2006). The fault length is stated as a conservative minimum, and the authors indicate that it could be 250 km; a width of 120 km was used in subsequent tsunami modeling (Okal and Hébert 2007) of 1946 tsunami data from the South Pacific. Johnson and Satake (1997) use a fault width of 145 km to model tide gauge data, but find little slip contribution in the deepest 50-km section. Tanioka and Seno (2001) modeled the event with a 40- to 60-km width in the shallowest section.

*M*

_{0}or moment magnitude Mw of an earthquake does not uniquely define the fault, but rather determines the product of area

*A*and displacement (slip)

*D*on the fault though the formulae,

*M*

_{0}=

*μ*AD and \(M_{\text{w}} = \frac{2}{3}\log_{10} \left( {M_{0} } \right) - 10.7\) (e.g., Aki 1966; Kanamori 1977), where

*μ*is the rigid strength of the rock. For a given fault area, the tsunami amplitude scales directly with the slip (Okada 1985). Considering the uncertain trade-off between fault area and slip, we must consider a range of possible models for the 1946 event keyed to the magnitude Mw. This serves as a proxy for the real situation, where the first alert of a great tsunami comes from seismic data in the form of the moment magnitude. We consider a range of earthquake faults and slips for the 1946 event using the subfault framework of SIFT/SIM (see “Appendix”), as illustrated in Figs. 4, 16, 17, and 18. Tsunami amplitudes measured at eight sites in the Hawaiian Islands, 12 sites along the west coast of North America, and two sites in Samoa were compared with SIFT/SIM forecast model results. By calculating the geometric mean over the forecast/observed tsunami amplitude ratios for the data set, the fit to an Mw 8.6 earthquake can be judged. Table 1 summarizes fits for the various scenarios. As recognized in prior studies (e.g., Johnson and Satake 1997; Tanioka and Seno 2001), a preponderance of shallow faulting improves the overall fit to the data. These results were replicated using NEOWAVE for northwest O‘ahu data with similar conclusions. The Hawai‘i data are consistent with the Okal and Hébert (2007) South Pacific data set and the López and Okal (2006) seismic data. The results indicate that a moment magnitude of Mw 8.6 ± 0.1 is consistent with both the Hawai‘i and west coast data from 1946. This validation of consistency between the 1946 earthquake moment and the tsunami record is also corroborated by earthquake and tsunami data for the recent 2010 Chile (Mw 8.8) and 2011 Tohoku (Mw 9.1) events (see “Appendix”).

Fault area | ALL | Center | West | East | Center shallow | West shallow | East shallow |
---|---|---|---|---|---|---|---|

Segments | |||||||

All | 0.7 | 1.0 | 0.8 | 0.8 | 1.6 | 1.0 | 1.1 |

Hawaii | 0.6 | 0.7 | 0.7 | 0.7 | 1.5 | 1.3 | 1.4 |

Non-Hawaii | 0.7 | 1.2 | 0.9 | 0.9 | 1.7 | 0.9 | 0.9 |

### 2.2 Aleutian model parameterization

We cannot simply define the earthquake capable of generating the largest tsunami by choosing an arbitrarily large seismic moment. Both the extent and distribution of faulting, and the amount and distribution of displacement at the seafloor need to be physically realizable. In determining these bounds, we use prior Mw 9.0+ events of the past 100 years as a guide.

The 1960 Chile earthquake (Mw 9.55) exhibited the largest average fault displacement overall, though estimates vary. Kanamori and Cipar (1974) estimated about 24-m slip using a larger rigidity of 7 (in units 10^{10} Pa), appropriate for deeper rupture than acknowledged today for these shallow megathrust events (Kanamori personal communication 2011). Using a rigidity of 4.4 appropriate for the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson 1981), a slip of 38 m is derived. Trade-offs in uncertainties in fault dip, depth, and area suggest a fault slip between 26 and 44 m, again assuming a standard rigidity of 4.4 rather than 6 (e.g., Cifuentes 1989). Geodetic methods, which account for only about one-fifth of the observed seismic moment, yield smaller values for the slip (Barrientos and Ward 1990). However, even for the smallest overall estimates for this earthquake, about 35 m of slip was observed in a segment of the earthquake equivalent to a Mw 9.0 event (Moreno et al. 2009). The value of 36 m in Butler (2012) is an average of several studies—35 to 38 m (Kanamori and Cipar 1974; Cifuentes 1989; Henry and Das 2001). Larger values of seismic moment for the main Chilean earthquake reported by Cifuentes and Silver (1989) are associated with greater uncertainty. The value ~35 m is used here, with an estimated uncertainty of about 5 m.

The 2004 Sumatra–Andaman earthquake (Mw 9.3) has the longest fault rupture recorded at about 1450 km (e.g., Lay et al. 2005; Ammon et al. 2005). The 2011 Tohoku earthquake (Mw 9.1) was characterized by relatively short overall rupture and large 50-m shallow displacement near the trench (e.g., Lay et al. 2011; Yamazaki et al. 2011b, c). The 1964 Alaska earthquake (Mw 9.2) was notable in laterally varying slip characterized by alternating large and small displacement patches on the fault (e.g., Ichinose et al. 2007), whereas the 1952 Kamchatka earthquake was characterized by small shallow displacement near the trench, increasing with depth (Johnson and Satake 1999). The large, deeper fault displacement characteristic of Kamchatka has smaller seafloor effects, and the resultant tsunami is smaller. In selecting features to generalize the maximum credible earthquake, we assume that in an extreme case 2 of the 3 major influences—large average slip (35 m), long fault length (up to 1500 km), and large slip (50 m) near trench—may interact together to create credible, physically realizable earthquakes.

## 3 Tsunami scenarios

### 3.1 Aleutian models

The two regions adjacent to the 1946 earthquake (Fig. 1) have not experienced significant seismic slip historically (Butler 2012). Westward is a ~700-km segment of the Eastern Aleutian subduction zone between the 1946 and 1957 tsunamigenic earthquakes (Fig. 2). The second lies east of the 1946 earthquake in the Shumagin Islands and west of the rupture of the great 1964 Alaska earthquake (Figs. 14, 15). This second region is comprised of a ~600-km segment of the subduction zone including the area of the 1938 earthquake, which, though large (Mw 8.3), averaged only 2 m or less of slip (Butler 2012). The Shumagin-1938 region has a greater tsunami impact on the west coast of North America than in Hawai‘i (e.g., Kirby et al. 2013). However, for a comparable magnitude and fault size, the tsunami forecast modeling herein shows that an Eastern Aleutian scenario produces run-ups in Hawaii up to 5 times larger than the Shumagin-1938 segment, attributable to the geometry of the subduction zone with respect to Hawai‘i.

Faulting parameters are shown for earthquakes discussed

Earthquake Mw | Uniform fault slip (m) | Region | SIFT subfaults, fault length, and area |
---|---|---|---|

Mw 9.25 | 35 | East Aleutians | ac18–23ab 600 km, 60,000 km |

Mw 9.25 | 35 | Alaska Peninsula | ac26–31ab 600 km, 60,000 km |

Mw 9.25 | 35 | Quasi-1957 | ac12–17ab 600 km, 60,000 km |

Mw 9.25 | 35 | Quasi-Kamchatka | ki2–7ab 600 km, 60,000 km |

Mw 9.25ab (50–20 m) | 50 (b), 20 (a) 35 average | East Aleutians | ac18–23ab 600 km, 60,000 km |

Mw 9.29ab (50–20 m) | 50 (b), 20 (a) 35 average | East Aleutians | ac18–24ab 700 km, 70,000 km |

Mw 9.43 | 35 | 1957, East Aleutians, 1946, Shumagin | ac16–26ab 1100 km, 110,000 km |

Mw 9.45 | 35 | 1957, East Aleutians | ac13–24ab 1200 km, 120,000 km |

Mw 9.6 | 35 | East Aleutian, 1946, Shumagin, 1938 | ac18–31ab, ac21–31z 1400 km, 195,000 km |

### 3.2 Tsunami model validations

A quantitative measure for comparing NEOWAVE and SIFT/SIM is the maximum run-up forecast in a harbor. This value is easily measured and specific to each harbor. The extent of inundation area, however, is the desired outcome related more directly to tsunami evacuation maps. Although qualitative maps are produced by the SIFT/SIM codes, specific measures of inundation area are not readily available from the operational codes accessed at PTWC. Further, the local small-scale grids are not identical between SIFT/SIM and NEOWAVE. Whereas this can still accommodate measuring maximum run-up, measures of inundation area become qualitative comparisons of maps. Therefore, the initial validation focused quantitatively on maximum run-up, and qualitatively on comparing maps.

The SIFT/SIM and NEOWAVE forecasts for maximum run-ups in 7 Hawaiian harbors are compared in Fig. 6. The comparison between SIFT/SIM and NEOWAVE is generally good and consistent with a clear trend along the line representing the same outcome. Large run-ups and smaller run-ups are similarly and consistently expressed by both NEOWAVE and SIFT. Nonetheless, for individual values there are significant excursions from unity. For instance, SIFT/SIMs show run-ups of 30–35 m where NEOWAVE has values of about 25 m. SIFT/SIM shows generally larger run-ups (more data lie to the right of the line). NEOWAVE gives generally larger run-ups for the Mw 9.25ab earthquake. The overall variation expressed as the root-mean-squared difference is 5 m. Therefore, overall the SIFT/SIM maximum run-ups vary by about 5 m from the NEOWAVE run-ups, for these very large earthquakes as forecast in Hawai‘i.

Maximum run-up results are compared by harbor region in Fig. 7, together with the observed maximum run-ups from the 1946 tsunami, which are dwarfed by 2–10 times larger forecasts for Mw 9+ events. The overall comparison between NEOWAVE and SIFT/SIM is qualitatively very good. Largest run-ups are observed at Hilo, Kahului, and Haleiwa, where harbor embayment resonance amplifies the tsunami (e.g., Munger and Cheung 2008). The largest differences are observed in Haleiwa, where SIFT/SIM forecasts significantly larger run-ups. For the other harbors, the two forecast methods give similar results. Nonetheless, the trend observed in Fig. 7 is again apparent—the Mw 9.25ab event with 50-m slip near the trench stands out for NEOWAVE. This is significant. For SIFT/SIM, there are diverse earthquake scenarios that give comparable maximum run-ups. However, the NEOWAVE forecasts indicate that the large slip near the trench is a critical factor influencing the maximum run-ups in Hawai‘i and gives direction for reviewing maximum inundation scenarios.

The lack of a trend in Fig. 7 is striking: Earthquakes with larger fault areas do not systematically produce larger tsunamis. Although the earthquake magnitude and fault area vary by more than a factor of three, the maximum run-up remains relatively constant. For a uniform 35 m of slip at the earthquake source, the same initial deformation of the seafloor sets the initial tsunami amplitude (e.g., Okada 1985). For these very large events (≥600 km length), increasing the fault area qualitatively extends the breadth of the tsunami, but does not substantially affect its initial height. In fact, for harbors shown in Fig. 7 with the largest run-ups (Hilo, Kahului, Haleiwa) a 9.6 magnitude earthquake with uniform 35-m slip produces smaller run-up than do 9.25, 9.43, and 9.45 magnitude earthquakes with similar 35-m slip. The explanation for this effective maximum tsunami amplitude is explored in Sect. 3.5.

### 3.3 Tsunami inundations for the earthquake scenarios

In the initial analysis, the maximum run-up—from anywhere within each harbor grid—served as the principal quantitative measure, with qualitative estimates of inundation based on maps. For NEOWAVE, we have access to the output inundation data and can define the inundation area within a grid resolution of about 9 m. Since the inundation forecast has the greatest merit for differentiating earthquake scenarios, inundation area was measured for each site–scenario pair, for direct comparison of different earthquake scenarios at a common site. The earthquake scenarios were then tested at 8 additional coastal locations (Fig. 3) in the Islands—Hanalei and Po‘ipu, Kaua‘i; Nanakuli, Kaneohe, Kailua, and East Honolulu, O‘ahu; Lahaina, Maui; and Kona, Hawai‘i—to confirm the tsunami forecast trends observed previously. For each of these sites, all five earthquake scenarios were considered to strengthen the case for the largest Aleutian tsunami that may impact the Islands. Two scenarios emerged giving the largest tsunami forecasts: An earthquake contained within the Eastern Aleutians with largest slip near the subduction trench (Mw 9.25ab) and a larger event (Mw 9.6) with uniform faulting extending 1400 km northeast toward Kodiak Island.

Hanalei on Kaua‘i experienced among the largest run-ups during the 1946 tsunami. The forecast for Hanalei showed the largest run-up for sites considered in the Hawaiian Islands from the Mw 9.25 Eastern Aleutian earthquake source—more than 40 m on a steep cliff west of Hanalei. However, other forecast scenarios could not be successfully completed for Hanalei, as the steepness of the gradient at the cliff face required fine tuning of the time-step in the computation not attempted in this analysis.

In parallel with this study, Butler et al. (2014) analyzed and dated the paleotsunami site in the Makauwahi sinkhole on the southeastern coast of Kaua‘i between Po‘ipu and Nawiliwili harbor (orange star in Fig. 3), positing evidence for a great tsunami there in the sixteenth century. At this site, which is 100 m from the beach and at an elevation of 7.2 m, tsunami forecast modeling was employed using NEOWAVE and high-resolution LiDAR data. This analysis utilized the same set of earthquake sources as this study, augmented with additional sites in Kamchatka, Western Aleutians, and the Alaska Peninsula regions. Results indicate that an Eastern Aleutian earthquake of Mw 9.25 or greater is necessary to inundate the site. See Butler et al. (2014) for details and further discussion.

The normalized inundation for each of the 15 sites (7 initial + 7 new, excluding Hanalei) is plotted in Fig. 8. Inundation at each site is scaled by the mean of the inundations forecast from the five scenarios. Note that largest inundations flooding the harbor valleys do *not* necessarily correspond with maximum run-up, which often occur at steeper slopes. For most of the sites in Hawai‘i, the Mw 9.25ab event produces the largest inundations. However, for Kahului, Maui and Honolulu/Ewa, O‘ahu, the Mw 9.6 scenario produces larger inundations (with inundations from the 1100-km-long Mw 9.43 event comparable in Honolulu). Nonetheless, examples wherein a larger earthquake does not lead to larger inundations are also evident in Fig. 8. This effect is most conspicuous for Lahaina, Maui, Haleiwa, O‘ahu, and Hilo, Hawai‘i, but is a general observation in the inundations forecast among many of the events. Nonetheless, some incremental adjustments in the fault area do not follow this same trend. For example, increasing the eastward length *and* width of the East Aleutian fault does not yield greater inundations in Hilo, but increasing the fault length alone does (see next section).

Finally, for the O‘ahu communities of Kailua and Hawai‘i Kai, the tsunami inundations from these great tsunamis would top the barrier sandbars at the beachfront, flooding the interior villages—a disaster not experienced historically. It may be noted that O‘ahu’s main power plant is located at Kahe Point within the Nanakuli grid. Its current elevation is about 7.3 m, which is about double the prior local run-ups observed from the 1946 tsunami (3.7 m) and 1957 tsunami (3.4 m). For the Mw 9.25ab event shown in Fig. 5, run-ups exceed 15 m and the site is inundated. The other scenarios show smaller run-ups that reach or exceed the power plant’s elevation, and threaten significant inundation.

### 3.4 Effects of lateral variation in forcing

*not*in general increase the tsunami inundation and can decrease the maximum run-up. Rather, adding width changes the breadth of the tsunami but not its initial amplitude. By contrast, extending the Eastern Aleutian fault length from 600 to 700 km (extending eastward) and keeping the width at 100 km (Mw 9.29ab) does increase the inundation forecast at Hilo (Fig. 10). However, as Hilo is the most eastward harbor in Hawai‘i the eastward increase in the fault length also reduces the proximal tsunami propagation distance, which might contribute to the increased inundation forecast. Careful reflection on the earthquake faulting factors contributing to inundations—area, width, slip, depth of faulting, water depth, and the geometry of the tsunamigenesis—must be considered in assessing potential tsunamigenic inundation.

### 3.5 Tsunami wavelength

The wavelength of the tsunami clearly has an effect on the resulting coastal inundation. The size of the earthquake source (fault area) has a direct influence on the wavelength of the tsunami. Resonance phenomena observed in tsunami amplitudes in Hawaiian harbors have been related to coastal response characteristics depending on the geometry, shape, and bathymetry profile (e.g., Munger and Cheung 2008) and its interaction with the spectral content of the tsunami. In the present analysis, it is clear that the tsunami wavelength has an influence on the run-up and inundation, and must be a consideration in determining the extent of evacuation zones. The key phenomenon observed in the joint forecasts is that increasing earthquake magnitude does not, by itself, lead to a larger tsunami. Rather, both the amount of slip and the fault area contribute in different measures. By the Okada (1985) elastic relations, tsunami amplitudes are related directly to slip on the fault. However, doubling the fault area does *not* necessarily lead to tsunami amplitude increase, but does increase the amplitude of longer wavelength components of the tsunami. Since coastal resonances are excited by the spectral characteristic of the tsunami, to gain a more complete understanding of the range of inundations/run-up it is necessary to include *both* longer and shorter wavelength tsunamis, derived from the setting and characteristics of the earthquake.

*both*longer and shorter wavelength tsunamis in our analysis.

### 3.6 Tsunamigenesis of maximum credible earthquakes

## 4 Discussion

The State of Hawaii has experienced 225 deaths due to tsunamis since 1900 (National Centers for Environmental Information, NOAA 2016). All 49 other states combined have experienced 160 tsunami-related deaths since 1900. In Alaska alone, the local tsunami from the 1964 Alaska earthquake caused 106 deaths. However, nearly all Hawaiian deaths were due to earthquakes more than 3500 km distant from the Islands. This is a unique situation, quite different from the local devastation of the 2011 Tohoku event. All of Hawai‘i’s coastline, population, and coastal infrastructure are vulnerable in a way not seen elsewhere in the USA.

The results of the analysis show that Mw 9.0+ earthquakes in the Aleutians have forecast tsunamis in Hawai‘i that substantially exceed current tsunami evacuation maps (ca. 2010) in 14 of the 15 coastal zones considered, the sole exception being the west (Kona) coast of the Big Island. Figure 10 shows the worst-case scenario for Hilo, which has been devastated by the historical tsunamis of 1946 and 1960 that had served as the basis for existing tsunami evacuation maps. The potential inundation zone for an extreme Aleutian tsunami could more than double historic flooding. Significantly enhanced inundations are forecast on O‘ahu in Kailua and Hawaii Kai—where overtopping of the beach sand bar leads to extensive flooding—and at the Kaneohe Marine Base and the Kahe Power Plant. All of these effects are encompassed by the two earthquake scenarios that together produce the largest tsunami forecasts. These scenarios have been submitted to and accepted by Hawaii State Civil Defense for deriving new, extended ‘extreme’ tsunami evacuation zone maps for the State of Hawaii. Further, although this is a theoretical analysis, paleotsunami evidence on Kaua‘i corroborates the reality of such events in Hawai‘i’s past (Butler et al. 2014).

In as much as the focus of this analysis is to determine the largest Aleutian tsunami that may potentially impact Hawai‘i, could even larger earthquakes cause larger inundations? In principle, yes. However, a larger earthquake implies a larger seismic moment (greater energy), which in turn implies larger fault area and/or slip. We have seen that incrementally increasing the fault area can lead to increasing the tsunami run-up or inundation (e.g., Fig. 10), but that large increases in the length and width of the faulting do *not* correspondingly increase run-up/inundation (Figs. 7, 8). We have considered scenarios where there are extremes of 50-m slip, limited to near the shallow trench or along lateral portions of the fault length. However, in each case 35 m of average slip was maintained to be consistent with the greatest average slip observed in seismic data for the great Mw 9.55 Chilean earthquake of 1960—the largest earthquake ever recorded. Increasing the average slip along the entire fault to 40 or 50 m would increase tsunami amplitudes. Since sea floor deformation is directly proportional to slip on the fault (Okada 1985), increasing the average slip along the entire fault to 40 or 50 m would effectively increase the tsunami amplitudes at the source by about 15 or 45%, respectively. Although nonlinear effects must be considered, larger tsunamis in Hawai‘i would result. However, to make this assumption we must presume that the largest slip (~50 m for the 2011 Tohoku Japan earthquake) ever observed on a *portion* of a fault could occur as the average over the *entire* fault surface. Such an assumption is not yet warranted.

### 4.1 Summary

A detailed analysis is presented for determining the maximum credible earthquakes forecasting extreme tsunami run-up and inundation in the Hawaiian Islands. The purpose of the study is to provide guidance to the Hawaii Emergency Management Agency for new tsunami evacuation maps being re-drawn following the 2011 Tohoku disaster. Only tele-tsunami sources are considered, and after review the Aleutians pose the greatest threat to Hawai‘i. Hawaiian data are first modeled for the great 1946 tsunami to validate our ability to characterize the tsunami source, propagation, and response by the Hawaiian coasts. Two state-of-the-art tsunami forecast methods are jointly employed to validate the results. Wave diffraction and refraction effects create hazards on all coasts. Earthquake sources are parameterized by physical faulting characteristics observed in prior Mw ≥ 9 earthquakes: utilizing extensive investigation of source locations, faulting areas, shallow-vs-deep and laterally varying distributions of fault slip, coastal resonance influences, and wavelength-dependent coastal responses. This methodology is focused primarily on distant tele-tsunamis impacting Hawai‘i.

## Notes

### Acknowledgements

The work has greatly benefited by collaboration with the Pacific Tsunami Warning Center (PTWC). In particular, RB thanks PTWC for access to their SIFT/SIM tsunami codes for the analysis work. For their insightful discussions of tsunamis, we thank Gerard Fryer and Chip McCreery at PTWC and Yefei Bai, Kwok Fai Cheung, and Yoshiki Yamazaki at the Hawai‘i Tsunami Mapping Project (HTMP) at the University of Hawai‘i (UH). We thank Yefei Bai and HTMP for providing access and expert assistance in using the NEOWAVE tsunami code for high-resolution tsunami forecast simulations. This work was supported in part by the Hawaii State Civil Defense (now Emergency Management Agency) and by the UH School of Ocean and Earth Science and Technology (SOEST). SOEST Contribution No. 9853, HIGP Contribution No. 2235.

### Data statement

Tsunami run-up and inundation data from the 1946 event are from the National Centers for Environmental Information, last accessed April 2016: (https://www.ngdc.noaa.gov/nndc/struts/form?t=101650&s=166&d=166). Earthquake parameters and subfault details used in this analysis are listed in Table 2. Digital bathymetry and topography data used in the tsunami forecasts are discussed and referenced in “Appendix.” Extensive inundation maps for Hawaiian harbors are found in Butler (2014).

## Glossary

Amount of fault motion in meters same as Slip

The deeper region of the dipping fault

Fault parameters including area, strike, dip, rake, displacement, rock rigidity, area

Great earthquake with thrust mechanism, also a fault capable of a great earthquake

Magnitude of earthquake derived from its seismic moment

University of Hawai‘i tsunami code

National Oceanic and Atmospheric Administration

Pre-historic tsunami

Preliminary reference earth model

Pacific Tsunami Warning Center

Historical magnitude scale no longer used, see Mw

NOAA tsunami code

Amount of fault motion, in meters, same as displacement

100 km × 50 km fault unit

Tsunami that travels from a great distance, i.e., not locally generated

Tsunami producing

Open-ocean sites (within model framework) where the tsunami is measured

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