Local Tsunami Hazards in the Pacific 

Northwest from Cascadia Subduction 

Zone Earthquakes 

Professional Paper 1661-B

U.S. Department of the Interior

U.S. Geological Survey

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Local Tsunami Hazards in the Pacific Northwest from 

Cascadia Subduction Zone Earthquakes 

By Eric L. Geist

Professional Paper 1661-B

U.S. Department of the Interior

U.S. Geological Survey

Earthquake Hazards of the Pacific Northwest Costal and Marine Regions

Robert Kayen, Editor

In estimating the tsunami hazards for the Pacific Northwest posed by major earthquakes 

along the Cascadia subduction zone, it is important to identify uncertainties associated 

with tsunami generation and their effect on near-shore tsunami amplitudes. Earthquake 

parameters, such as width of rupture and distribution of slip, cause significant 

variability in local tsunami estimates. These uncertainties are best incorporated in a 

probabilistic analysis of tsunami hazards.
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

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Produced in the Western Region, Menlo Park, California

Manuscript approved for publication, January 3, 2005

Text edited by Peter Stauffer

Layout and design by Susan Mayfield and Judy Weathers

FRONT COVER

Computer simulation of tsunami wavefield 20 minutes after a hypothetical magnitude 7.8 earthquake on the Cascadia 

subduction zone. Topography and wave heights vertically exaggerated at different scales to illustrate wavefield.
 iii

Contents

Abstract ................................................................................................... 1

Introduction ................................................................................................ 1

Interplate thrust earthquakes ........................................................................... 3

Tsunami physics .......................................................................................... 5

Physics of tsunami generation, propagation, and runup ....................................... 5

Propagation phenomena along the Pacific Northwest continental margin .................. 6

Framework for a local tsunami hazard assessment ................................................ 7

Adaptation of seismic hazard assessment methods .......................................... 7

Sources of uncertainty in probabilistic calculations .......................................... 7

Incorporating uncertainty into probabilistic calculations .................................... 9

Summary ................................................................................................... 12

Acknowledgments ....................................................................................... 12

References ................................................................................................ 12

Figures

1. Map of the Cascadia region, showing bathymetry, plate convergence, 

and possible tsunami sources .................................................................. 2

2. Diagrams showing initial tsunami wave profiles from crack models ........................ 4

3. Map of the Cascadia region, showing projected alongshore distribution of peak 

nearshore tsunami amplitude using a geometry similar to the 

“Long-Wide” geometry of Satake and others (2003) ....................................... 10

4. Map of the Cascadia region, showing projected alongshore distribution of peak 

nearshore tsunami amplitude using a geometry similar to the “Long-Narrow” 

geometry of Satake and others (2003) ......................................................... 11
Local Tsunami Hazards in the Pacific Northwest from

Cascadia Subduction Zone Earthquakes

By Eric L. Geist1 

Abstract

Since the mid-1980s, there has been accumulating 

geologic evidence of large local tsunamis generated by 

earthquakes along the Cascadia subduction zone off the 

Pacific Northwest. Information from recent geophysical and 

geological investigations constrains the potential rupturezone geometry and average repeat time of interplate thrust 

earthquakes. Based on this information, tsunami hazard maps 

have been prepared for coastal communities in the Pacific 

Northwest using sophisticated numerical models to simulate 

tsunami propagation and inundation. In this study, sources of 

uncertainty in tsunami hazard calculations are described and a 

probabilistic hazard analysis for tsunamis, similar to probabilistic seismic hazard analysis (PSHA), is outlined. Though 

probabilistic tsunami hazard analysis (PTHA) shares many 

similarities with PSHA, there are specific issues unique to 

tsunami hazards that need to be accounted for in the probability calculations. For example, the possibility of rupture along 

splay faults from the Cascadia interplate thrust have a large 

effect on tsunami generation, but a relatively small impact on 

peak ground accelerations onshore. The largest sources of 

uncertainty include the average slip and downdip extent of 

rupture. Also, it is demonstrated that significant variations in 

nearshore tsunami amplitude are caused by uncertainty in slip 

distribution patterns. Correct identification of uncertainties 

related to tsunami generation and propagation is critical in performing the probability calculations. PTHA has the potential 

to provide an improved technique for evaluating local tsunami 

hazards in the Pacific Northwest and elsewhere.

Introduction

Before the mid-1980s, the hazard posed by local tsunamis to the Pacific Northwest coast received minimal attention, 

primarily because of that region’s lack of destructive local 

tsunamis in recorded history. Comparative studies of the 

world’s subduction zones by Heaton and Kanamori (1984) and 

later studies by Heaton and Hartzell (1986, 1989) led to the 

recognition of the seismic potential for interplate thrust events 

and associated tsunamis along the Cascadia subduction zone. 

More recent paleoseismologic studies have focused on the 

last large interplate thrust event in 1700 C.E. and recurrence 

intervals from previous events (Atwater, 1987, 1992; Atwater 

and Hemphill-Haley, 1997; Kelsey and others, 2002; Witter 

and others, 2003). Turbidites along the Oregon-Washington 

continental margin also are thought to record the occurrence of 

great Cascadia earthquakes, of which 13 have been recorded 

since the Mount Mazama eruption (approximately 7.7 ka.; 

Adams, 1996; Goldfinger and others, 2003). Independent corroboration of the 1700 C.E. event comes from the investigation 

of Satake and others (1996) and Satake and others (2003), who 

analyzed tsunami records in Japan and deduced that a far-field 

tsunami that struck Japan most likely came from a large magnitude earthquake along the Cascadia subduction zone. These 

geologic investigations prompt a closer look at the hazards 

from local tsunamis in the Pacific Northwest. 

Evidence that the interplate thrust is currently locked 

and not slipping freely comes from the analysis of geodetic 

data (Savage and others, 1991; Hyndman and Wang, 1995; 

Oleskevich and others, 1999; Wang and others, 2003). Significant secular uplift rates (approx. 4 mm/yr, Savage and others, 1991) and horizontal axes of contraction subparallel to the 

plate convergence direction are consistent with deformation 

patterns from an interseismic period in which the interplate 

thrust is locked (Savage and others, 1991; Dragert and others, 

1994; Mitchell and others, 1994; Hyndman and Wang, 1995; 

Wang and others, 2003). Hyndman and Wang (1995) and 

Oleskevich and others (1999) further constrain the width of the 

locked zone from thermal modeling of the subduction zone, 

validated from heat flow measurements (fig. 1). As a possible 

analog to the Cascadia subduction zone, Mazzotti and others 

(2000) analyze data from a dense GPS network in Japan and 

determine that the Nankai and Japan-West Kurile subduction 

zones were fully locked during the period of measurement. 

Placing this result in the context of the abundant seismic history of Japan led Mazotti and others (2000) to conclude that 

heterogeneous slip distribution patterns from past earthquakes 

are in marked contrast to homogeneous interseismic loading 

and that a significant part of the elastic strain along the interplate thrust may be released through slow earthquakes or postseismic slip. (See Dragert and others, 2001, for analysis of a 

recent slow event along the deeper part of the Cascadia subduction zone.) A thorough review of seismicity and geodetic 1 Menlo Park, California
2 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

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Figure 1. Bathymetry 

along the Cascadia subduction zone. Heavy arrow 

shows direction and rate of 

relative plate convergence. 

Possible tsunami sources 

delineated between the 

deformation front and the 

350°C and 450°C isotherms. 

Interseismic locked zone 

along the interplate thrust 

is the region between the 

deformation front and the 

350°C isotherm; transition 

zone is the region between 

the 350°C and 450°C 

isotherms (Hyndman and 

Wang, 1995). 
Interplate Thrust Earthquakes 3

data, interpretation, and arguments for and against seismic and 

aseismic subduction, is given by Rogers and others (1996).

Quantification of the local tsunami hazard typically relies 

on the analysis of past instrumentally recorded events. Unfortunately, there are no recordings of tsunamigenic events along 

the Cascadia subduction zone, except for the 1992 Cape Mendocino earthquake at the southernmost extent of the subduction zone (Oppenheimer and others, 1993; González and others, 1995). Seismicity in the region is primarily located along 

a well-defined Benioff zone and within the North American 

Plate; no earthquakes of any magnitude on the interplate thrust 

of the Washington-Oregon segment of the Cascadia subduction zone have been recorded since 1970 (Ludwin and others, 

1991). In this respect, the Cascadia subduction zone is unlike 

any other subduction zone around the world in which distinctive long-term seismicity patterns are evident (Kanamori, 

1981; Pérez and Scholz, 1997). The lack of interplate seismicity along the Cascadia subduction zone obviously impedes 

quantitative estimation of ground shaking, as well as of tsunami generation from major interplate thrust earthquakes.

Previous studies have estimated tsunami hazards in the 

Pacific Northwest by considering a limited number of different 

earthquake scenarios (Hebenstreit and Murty, 1989; Ng and others, 1990; Whitmore, 1993; Priest and others, 1997, 2000; Preuss and Hebenstreit, 1998; see also review by Mofjeld and others, 1999). Among these studies, several different earthquake 

locations and magnitude were considered, but rupture complexity in terms of nonuniform slip, nonplanar faulting, and heterogeneous elastic structure was not. Geist and Yoshioka (1996) 

examined the effect that variations in earthquake source parameters have on tsunamis generated along the Cascadia subduction 

zone, still from the standpoint of uniform slip, however. In later 

papers, Geist and Dmowska (1999) and Geist (2002) emphasize 

the fundamental importance that distributed slip has on tsunami 

generation. In particular, these papers stress that the initial 

tsunami wavefield calculated using uniform-slip models will 

underestimate both the amplitude and leading-wave steepness 

of the local tsunami (fig. 2A). In producing inundation maps 

for Yaquina Bay, Oregon, Priest and others (1997, 2000) present a thorough review of possible variations of regional source 

parameters and their effect on tsunami generation. A number of 

rupture scenarios were considered in the development of these 

inundation maps, including variations in slip by way of prescribing asperities with higher slip than the surrounding rupture 

area (specified by uniform slip). Tsunami inundation maps for 

the coast of southern Washington were prepared using a similar 

source model for a Cascadia interplate thrust earthquake (Walsh 

and others, 2000) and using a simplified source by Preuss and 

Hebenstreit (1998). In the present paper, sources of uncertainty in assessing tsunami hazards in the Pacific Northwest are 

described and a probabilistic tsunami hazard analysis (PTHA) is 

outlined. Though PTHA can be based on the same earthquake 

source models as used for the National Seismic Hazard maps 

(Frankel and others, 1996, 2002), issues specific to tsunami generation and propagation are described that need to be addressed 

when calculating tsunami probabilities.

Interplate Thrust Earthquakes

As mentioned in the introduction, potential interplate 

thrust events along the Cascadia margin are difficult to define, 

owing to the lack of historical precedents. Paleoseismologic 

data do suggest that slip along the interplate thrust is accommodated by large (M > 8) earthquakes, though not all necessarily rupture the entire subduction zone (Adams, 1996; 

Atwater and Hemphill-Haley, 1997; Kelsey and others, 2002; 

Goldfinger and others, 2003; Witter and others, 2003). In this 

respect, the pattern of rupture occurrence appears more like 

that of characteristic earthquakes than a Gutenberg-Richter 

distribution of earthquake magnitudes (Wesnousky, 1994). 

From the standpoint of constructing a worst-case scenario, it 

is unclear whether tsunami earthquakes (that is, earthquakes 

that generate much larger tsunami amplitudes in comparison 

to other tsunamigenic earthquakes for a given magnitude; 

Kanamori, 1972; Kanamori and Kikuchi, 1993; Polet and 

Kanamori, 2000) may occur along the Cascadia subduction 

zone that could generate local tsunamis larger than the one 

derived from the 1700 event. An appropriate approach is to 

follow the two earthquake recurrence scenarios considered 

by Frankel and others (1996) and Frankel and others (2002) 

for the Cascadia subduction zone: (1) a single M 9 event that 

ruptures the entire subduction zone every 500 years on average 

and (2) a series of M 8.3 events (ruptures 250 km long) that 

collectively fill the entire subduction zone every 500 years.

The locked zone that controls interseismic deformation 

(Savage and others, 1991; Hyndman and Wang, 1995; Flück 

and others, 1997; Oleskevich and others, 1999; Wang and 

others, 2003) provides basic information with which we can 

constrain earthquake rupture (fig. 1). These authors generally 

define a locked seismogenic zone from approximately the base 

of the continental slope to the 350°C isotherm and a transition 

zone where seismic and aseismic slip could occur between the 

350°C and 450°C isotherms (fig. 1). Scholz (1990) indicates 

that large earthquakes frequently transgress upper and lower 

stability boundaries (updip to the sea floor or downdip into 

the transition zone). The upper stability boundary, if it exists, 

is difficult to define (Flück and others, 1997). For a large 

earthquake initiating at depth, it is likely that rupture will 

break through to the sea floor, as suggested by Rudnicki and 

Wu (1995) from the point of view of crack mechanics and as 

suggested by Kanamori and Kikuchi (1993) for some tsunami 

earthquakes. Dmowska and Kostrov (1973) and Rudnicki 

and Wu (1995) demonstrate that a rupture that extends to the 

traction-free sea floor will be associated with substantially 

large slip for a given earthquake moment in comparison to a 

shallow imbedded rupture (that is, one that does not reach the 

sea floor). Geist and Dmowska (1999) show, however, that 

the tsunami size will not increase proportionally with slip for 

a sea-floor rupturing event over an imbedded event, owing to 

characteristic changes in the slip distribution between the two 

types of events. For either an imbedded or a sea-floor rupture, 

the initial tsunami wave profile calculated using heterogeneous 
4 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

0 20 40 60 80 100 120

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Splay

Compound

Rupture

30°

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B

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Distributed slip (crack)

DISTANCE IN KILOMETERS

DISTANCE IN KILOMETERS

VERTICAL DISPLACEMENT, UZ, IN METERS

VERTICAL DISPLACEMENT, UZ,

IN METERS

0

0

0

0

Figure 2. Initial tsunami wave profiles from crack models (Geist and Dmowska, 1999). A, Comparison of initial 

wave profiles from a crack model (thick line) and a uniform slip dislocation model (thin line). Geometry of 

imbedded thrust fault rupture shown below. Rupture is 40 km wide, with an average of 1.16 m of slip. B, Effect 

of splay faulting on tsunami generation. Vertical displacement field for a compound rupture is calculated by 

superimposing the displacement fields for the decollement fault modeled as an imbedded crack and the splay 

fault modeled as a surface-rupture crack. Geometry of compound thrust fault rupture shown below. Rupture on 

main thrust is 40 km wide, with an average of 1.16 m of slip.
Tsunami Physics 5

slip will be significantly different from the profile calculated 

using standard, uniform slip dislocation models (fig. 2A).

The potential interplate rupture zone along the Cascadia 

margin is significantly narrower compared to other subduction 

zones (Zhang and Schwartz, 1992; Tichelaar and Ruff, 1993; 

Flück and others, 1997; Oleskevich and others, 1999; Wang 

and others, 2003). The exceptionally high aspect ratio (rupture length : width ≅ 10:1) for the largest earthquake that could 

occur on the Cascadia subduction zone (Hyndman and Wang, 

1995) is significantly larger than observed aspect ratios from 

other subduction zones (Geller, 1976; for example, the aspect 

ratio of the 1960 Chile earthquake is approximately 4:1). Recent 

work by Nielsen and others (2000) demonstrates the effects 

that rate-and-state friction parameters as well as rupture geometry have on rupture dynamics and periodicity. They indicate 

that two rupture regimes are present: (1) a cracklike regime 

with periodic to quasi-periodic events that rupture the entire 

fault and (2) a self-healing regime in which rupture propagates 

by self-healing pulses that exhibit strong dynamic complexity 

(see also Madariaga and others, 1998; Zheng and Rice, 1998). 

Furthermore, Nielsen and others (2000) indicate that as the 

aspect ratio of the rupture increases, the rupture regime crosses 

over from cracklike to self-healing. Large aspect ratios exhibit 

strong dynamic complexity (that is, strongly heterogeneous 

slip with regard to tsunami generation) and aperiodic recurrence intervals, according to these modeling studies.

Earthquakes with higher than expected tsunami excitation in Cascadia would include nonplanar rupture along 

seaward-vergent splay faults from the interplate thrust (fig. 

2B). Fukao (1979) originally proposed this type of mechanism to explain tsunami earthquakes. Observations of vertical 

displacement following the 1964 Great Alaska earthquake by 

Plafker (1965) provide evidence for secondary rupture along 

splay faults during a major subduction zone earthquake. For a 

given seismic moment, slip on high-angle splay faults results 

in higher amounts of vertical displacement in comparison to 

lower angle interplate thrust events (Geist, 1999; Cummins 

and Kaneda, 2000). Both seaward-vergent and landward-vergent splay faults are imaged along the Cascadia subduction 

zone (MacKay and others, 1992), though only compound 

events involving interplate thrust and seaward-vergent splays 

are likely to result in increased tsunami amplitudes (Geist and 

Yoshioka, 1996). Instead of using simple elastic dislocations 

as in Geist and Yoshioka (1996), a slip distribution is used in 

this study that considers the decollement fault as an imbedded crack and the high-angle splay fault as a surface-rupture 

crack, using the expressions of Dmowska and Kostrov (1973). 

Vertical displacement in figure 2B is calculated as described in 

Geist and Dmowska (1999). For the position of the splay fault 

relative to the decollement as shown in figure 2B, peak vertical 

displacement is enhanced. The central question, however, is 

whether updip rupture along the decollement can propagate to 

a splay fault. This question has been addressed using a static 

analysis (Jeyakumaran and Keer, 1994) and, more recently, 

dynamic simulations (Aochi and others, 2000; Kame and others, 2003). In future studies, heterogeneous slip distributions, 

optimally derived from dynamic rupture simulations, such as 

Aochi and others (2000), or from seismic inversion results, 

should be used to accurately simulate the tsunami wavefield 

derived from compound rupture involving splay faults.

Other tsunami source parameters unique to tsunami 

earthquakes, such as low shear modulus/high slip, shallow rupture depth, and deep water in the source region, can 

result in increased tsunami excitation for an earthquake of 

a given seismic moment (Geist and Dmowska, 1999; Geist 

and Bilek, 2001). It is difficult to assess the likelihood of 

tsunami earthquake occurrence for the Cascadia subduction 

zone. Because of the elevated thermal regime, the region of 

frictional instability (that is, the region for potential rupture) 

is much shallower in Cascadia than in other subduction zones 

(Hyndman and Wang, 1995; Oleskevich and others, 1999). 

Whether or not rupture would transgress the upper frictional 

stability transition and break to the sea floor, producing a 

tsunami earthquake (see Kanamori and Kikuchi, 1993; Geist 

and Dmowska, 1999), is unclear (see also discussion by Priest 

and others, 1997). Because the zone of potential rupture is 

shallow within the solid earth and in relatively deep water, 

tsunami generation is more effective along the Cascadia subduction zone in comparison to other subduction zones for an 

earthquake of a given magnitude.

Tsunami Physics

Physics of Tsunami Generation, Propagation, 

and Runup

Before describing the uncertainties in tsunami hazard 

analysis and the probabilistic method, a summary of how 

tsunamis are generated by earthquakes and how tsunami waves 

propagate is given in this section. For a more complete review 

of tsunami physics, the reader is referred to Kajiura (1963), 

Carrier (1971), Mei (1983), Geist (1999), and Satake (2002).

Tsunamis are generated by earthquakes through the transfer of large-scale elastic deformation associated with earthquake rupture to potential energy within the water column. In 

most cases, the initial tsunami amplitude wavefield mimics 

the static, coseismic vertical displacement field associated 

with the earthquake. In regions of steep bathymetry, Tanioka 

and Satake (1996) demonstrate that the horizontal displacement field from an earthquake also contributes to the vertical 

displacement of the water column. Calculation of coseismic 

displacement field (uk) is derived from expressions relating 

the slip of a dislocation over surface Σ imbedded in an elastic 

medium. The general definition of dislocation is meant in this 

case, where relative displacement is arbitrary along the rupture 

zone (Somigliana dislocation, Rybicki, 1986). The particular 

case of a Volterra dislocation is one where the relative displacement or slip (∆ui

) is constant. Volterra dislocations, most 

often considered in calculating coseismic displacement and 

expressions for specific cases (e.g., Mode I, II, and III frac-
6 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

Wave dynamics become increasingly more complicated 

as tsunamis approach shore. Because modeling tsunami 

runup involves moving boundary conditions and often turbulent flow, it has been difficult to devise a robust procedure 

that would be applicable to realistic shoreline geometries, 

even though theoretical treatments have been derived by, for 

example, Carrier and Greenspan (1958). Recently, however, 

there has been considerable effort toward the development 

of runup and overland flow models (Antunes do Carmo and 

Sebra-Santos, 1996; Sato, 1996; Johnsgard and Pedersen, 

1997; Titov and Synolakis, 1998). Of note, Titov and Synolakis (1998) have developed a procedure where the nonlinear 

shallow-water wave equations (2) are split so that twodimensional runup can be computed. In addition, coseismic 

subsidence and strong tidal fluctuations that can occur in the 

Pacific Northwest (Mofjeld and others, 1997) affect tsunami 

inundation patterns. Continued research in the area of tsunami runup will be critical for the development of accurate 

tsunami hazard maps.

Propagation Phenomena along the Pacific 

Northwest Continental Margin

Tsunamis generated by Cascadia interplate thrust earthquakes will be significantly affected by propagation over the 

broad continental shelf. Using high-order wave theory, Shibata 

(1983) demonstrates that frequency dispersion can have a 

significant effect on the local tsunamis propagating across 

continental shelves. Other studies indicate that the incidence 

angle, period, and shelf slope have a strong influence on 

reflection and transmission at the shelf break and coastline 

(Abe and Ishii, 1980; Carrier and Noiseux, 1983; Koshimura 

and others, 1999).

Tide gauge records of the 1992 Cape Mendocino tsunami demonstrated that edge waves can be excited along the 

Pacific Northwest coast (González and others, 1995). Edge 

waves are trapped coastal waves that occur in distinct modes, 

with an exponential amplitude decay away from shore. Ishii 

and Abe (1980) show how edge-wave excitation is dependent 

on continental margin geometry. Fujima and others (2000) 

demonstrate that when a tsunami source is close to the coastline (that is, a local tsunami), the gravest mode of edge waves 

is generated. For this type of edge wave, Fujima and others 

(2000) note that while a single edge-wave phase may not 

have a large amplitude (in comparison to the direct arrival), 

resonance and interference can cause locally high amplitudes 

at certain locations. As noted by González and others (1995), 

because the phase and group velocities for edge waves are 

much slower than nontrapped modes, large-amplitude arrivals at coastal observation points oblique to the source region 

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tures, Okada, 1985), are derived from the general formulation 

for Volterra dislocations of Steketee (1958):

where, μ is the shear modulus, ω represents the static elastic 

Green’s functions, and ν represents the unit surface-normal 

vectors.

Whereas the characterization of earthquake rupture 

using a single Volterra (uniform slip) dislocation or several 

Volterra dislocations that span the width of the rupture zone 

is common in tsunami modeling (for example, Imamura and 

others, 1995; Satake and Tanioka, 1995; Geist and Yoshioka, 

1996; Piatanesi and others, 1996), Geist and Dmowska (1999) 

demonstrate the fundamental importance that distributed slip 

has on tsunami generation. As originally discussed by Freund 

and Barnett (1976) and later by Rudnicki and Wu (1995), the 

assumption of uniform slip implies that deformation is concentrated at the edges of rupture. In contrast, variable slip in the 

dip direction for a dip-slip fault will concentrate deformation 

near the center of the rupture zone and will result in substantially higher vertical displacements and therefore higher initial 

tsunami amplitudes in comparison to a uniform-slip rupture 

of identical seismic moment (Geist and Dmowska, 1999). 

Rupture in subduction-zone earthquakes is inherently complex, as indicated from seismic inversion results (Beck and 

Ruff, 1989; Thatcher, 1990), leading Geist (2002) to adapt a 

fractal source model of subduction-zone earthquake rupture to 

estimate the range of local tsunami amplitudes possible for a 

given earthquake. Stemming from a lack of knowledge of fault 

plane and rupture heterogeneity, simple dislocation models 

have been proposed for Cascadia subduction zone earthquakes 

(Hebenstreit and Murty, 1989; Whitmore, 1993; Flück and 

others, 1997). It should be recognized, however, that because 

dip variations in slip are not accounted for, these models may 

underestimate coseismic vertical displacement that controls 

initial tsunami amplitude.

Once generated, tsunamis propagate outward from the 

source region and behave according to shallow-water wave 

theory (inviscid), since tsunami wavelength is typically much 

greater than ocean depths. The shallow-water wave equations, 

neglecting bottom friction, are 

where h is the water depth, η is wave elevation, and v is the 

depth-averaged horizontal vector velocity field. For a broad 

range of periods (400 s < T < 10,000 s) in which the shallow-water wave equations are applicable, the phase velocity is 

given by c = √gh (Ward, 1980). In water depths greater than 

~50 m (Shuto, 1991), the shallow-water wave equations can be 

approximated by the linear long-wave equations:

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Framework for a Local Tsunami Hazard Assessment 7

can occur much later than the first arrival (see Carrier, 1995). 

González and others (1995) emphasize that accurate tsunami 

assessments and forecasts need to account for the excitation of 

edge waves, particularly in the Pacific Northwest.

Framework for a Local Tsunami Hazard 

Assessment

Adaptation of Seismic Hazard Assessment 

Methods

Tsunami hazards in the past have primarily been assessed 

using deterministic methods. Typically, this involves the calculation of runup and inundation from (1) an incident design 

wave, not directly linked to a source model, (2) a designated 

maximum credible earthquake, or (3) a series of source scenarios as, for example, employed by Priest and others (1997). 

Probabilistic methods of hazard assessment have an advantage over deterministic methods by including measures of 

uncertainty and of the likelihood of the event occurring, often 

with the specification of risk-tolerance factor. Probabilistic 

methods have been used for analyzing the hazard from distant 

tsunamis based on historical data (for example, Houston and 

others, 1977) and simple seismological models (Lin and Tung, 

1982; Rikitake and Aida, 1988). In a series of recent studies, probabilistic methods for tsunami hazard assessment are 

discussed for earthquakes, asteroid impacts, and landslides 

(Ward, 2000; Ward and Asphaug, 2000; and Ward, 2001, 

respectively). As formulated by Ward (2000), the Poissonian 

probability that a tsunami at a particular location along a 

coastline (r) will exceed a particular risk tolerance (a0) over a 

given time interval (T) is given by 

as in PSHA. In calculating rate term (N) in equation 4 where 

empirical attenuation relationships are used in PSHA, Ward 

(2000) indicates that model-based relationships can instead be 

used for PTHA based on tsunami-generation and wave theory 

and the known bathymetry of the world’s oceans. In applying 

this method for tsunamis produced by asteroid impact, Ward 

and Asphaug (2000) present the results of the probabilistic 

calculations in terms of the probability that a specific site (for 

example, San Francisco) can expect a wave of a specific height 

(for example, 5 m) over a given time period from the present 

(for example, 1,000 years). A similar probabilistic analysis is 

performed for potential submarine landslides in Ward (2001). 

Below, the sources of uncertainty specific to local tsunamis 

generated by Cascadia subduction zone earthquakes are discussed, as well as how these uncertainties may be incorporated 

into probabilistic calculations.

Sources of Uncertainty in Probabilistic 

Calculations

A convenient classification of the sources of uncertainty 

follows the evolution of the tsunami through three stages—

generation, propagation, and runup. The least amount of 

uncertainty is associated with the propagation calculations, in 

which the hydrodynamics are relatively simple. The primary 

component of uncertainty, in this case, is errors in the bathymetry. The hydrodynamics of runup, in contrast, are much more 

complex, involving bottom friction, overland flow, and, in the 

case of breaking waves, turbulent behavior. To model these 

effects accurately, detailed bathymetry and topography are 

needed, but these are often difficult to obtain in the coastal 

zone. The uncertainty associated with runup is analogous to 

the uncertainty associated with site effects in PSHA. Uncertainty related to tsunami generation includes the pattern of 

occurrence for subduction-zone earthquakes (one M 9 earthquake or a series of M 8.3 earthquakes, as discussed previously) and the downdip extent of rupture. Both of these issues 

are addressed by Frankel and others (2002). Uncertainty in the 

shear modulus of rocks in the subduction zone may also be 

important in determining the amount of average slip from an 

earthquake of a given seismic moment (Geist and Bilek, 2001). 

Uncertainty in the average repeat time of these earthquakes 

is addressed in paleoseismological studies (see, particularly, 

Adams, 1996; Atwater and Hemphill-Haley, 1997; Goldfinger 

and others, 2003; and Witter and others, 2003). Variability 

in recurrence intervals indicated by these authors suggest the 

need for a conditional probability model such as the Brownian passage-time model proposed and applied to Cascadia 

events by Ellsworth and others (1999). In this paper, attention 

is drawn to the uncertainty of source parameters, including 

rupture geometry and slip distribution patterns.

To determine the possible range of tsunami amplitudes 

that arise from slip variations during rupture, we first need 

to bracket or isolate the calculations from other sources of 

uncertainty listed above. To exclude the uncertainty associated 

������������������ ��������� (4)

where N is a total rate of exceedance integrated over all possible source locations and parameter space.

A probabilistic method for assessing tsunami hazards 

can be developed based on a similar method that has been in 

use for assessing the ground-motion hazard from earthquakes 

termed probabilistic seismic hazard analysis (PSHA). PSHA 

can be thought of in three steps: (1) specification of seismic 

sources; (2) calculation of ground motion using an empirical 

formula termed the attenuation relationship; and (3) calculation of the probabilities. Details of the PSHA method are 

described by Cornell (1968), National Research Council 

(1988), Ward (1994), Senior Seismic Hazard Analysis Committee (1997), and Anderson and Brune (1999). The PSHA 

method is instrumental in producing the National Seismic 

Hazard Maps (Frankel and others, 1996, 2002). For an 

analogous analysis of tsunami hazards (probabilistic tsunami 

hazard analysis, PTHA), the same specifications of the source 

(location, magnitude, and average repeat time) can be used 
8 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

with the hydrodynamics of runup, propagation calculations 

are stopped at the 50-m isobath. What is analyzed, in this 

case, is termed the peak nearshore tsunami amplitude (PNTA) 

as in Geist (2002). For the source specifications, a M 8.8-

9.0 earthquake with geometric and average slip parameters 

indicated by Satake and others (2003) is analyzed. To explain 

the tsunami observations in Japan from the 1700 Cascadia 

earthquake, Satake and others (2003) consider six source scenarios: three long ruptures that span the length of the Cascadia 

subduction zone and three ruptures of less than 500 km in 

length (labeled “Short-North,” “Short-Central,” and “ShortSouth”). The three long ruptures include “Long-Narrow,” in 

which full slip is imposed downdip to the 350°C isotherm (fig. 

1) and then linearly decreasing to zero at the 450°C isotherm; 

“Long-Splayed,” in which a splay fault (fig. 2) is invoked; 

and “Long-Wide,” in which uniform slip is imposed downdip 

to the 450°C isotherm. Results from their tsunami modeling indicate that the Long-Narrow and Long-Splayed source 

scenarios best fit the tsunami data in Japan and the paleoseismic data in Cascadia. Wang and others (2003) suggest, on 

the basis of analogous events along the Nankai subduction 

zone in Japan, that coseismic rupture occurs within the locked 

zone and linearly decreases to zero at half the width of their 

wide effective transition zone. Rather than using uniform slip 

downdip to the 350°C isotherm, as in past studies, this paper 

uses the stochastic source model of Geist (2002) to produce 

a suite of slip-distribution patterns as described below. Two 

ruputure geometries are analyzed: (1) rupture down to the 

450°C isotherm, as in the Long-Wide model of Satake and 

others (2003), and (2) rupture down to the 350°C isotherm, as 

in the Long-Narrow model of Satake and others (2003), except 

that slip does not continue into the transition zone.

For a given rupture location and geometry, the stochastic source model produces a wide range of slip-distribution 

patterns that are consistent with the high-frequency falloff 

observed in the far-field seismic displacement spectrum 

denoted by ω−γ, as well as the b-value in aftershock sequences 

(Hanks, 1979; Andrews, 1980; Frankel, 1991; Herrero and 

Bernard, 1994; Tsai, 1997). The ω−γ spectral falloff is caused 

by self-similar variations in initial stress or stress drop (Hanks, 

1979; Huang and Turcotte, 1988). The corresponding slip 

distribution follows a fractal scaling relationship in which 

the fractal exponent is linked to γ (Tsai, 1997). Hartzell and 

Heaton (1985) and Polet and Kanamori (2000) indicate that 

the spectral falloff exponent for subduction zone earthquakes 

ranges between 1.0 ≤γ ≤ 2.6. Polet and Kanamori (2000) 

indicate that γ is consistent within a given region and that there 

does not appear to be a difference in γ between tsunami earthquakes and typical subduction zone earthquakes for a given 

region. Because we have no information of the characteristic 

spectral decay for Cascadia subduction zone events, a radialwavenumber slip spectrum that falls off as k-2 is used that corresponds to the generic ω−2 model of Aki (1967). The phase 

of the slip spectrum is randomized to produce slip-distribution 

patterns characterized by a single region of moment release or 

multiple subevents. In this example, each rupture has a nearly 

identical seismic moment (Mw = 9.0). Further details of the 

method are given by Geist (2002).

For a given slip-distribution and rupture geometry, the 

tsunami wavefield is calculated using a standard leap-frog 

finite-difference form of the linear long-wave equations (3). 

A computationally efficient threshold-type model is used to 

model tsunami propagation for a large number of sources, in 

which peak nearshore tsunami amplitude (PNTA) is calculated at the shallowest water depth where the linear long-wave 

equations are valid (approximately 50 m, Shuto, 1991; 20 m 

used in Preuss and Hebenstreit, 1998). The grid spacing in the 

finite-difference calculations is 1.3 km and the time step is 4.5 

seconds. The wave history is modeled for the first 1.5 hours; 

tests indicate that longer times do not significantly effect the 

average or extreme values of the PNTA. 

The variations in PNTA parallel to the Pacific Northwest 

coast are first calculated using 100 different slip-distribution 

patterns and a geometry similar to the Long-Wide model of 

Satake and others (2003) (rupture area shown in light blue in 

figure 3). In addition to the average (red) and maximum and 

minimum (blue) PNTA values along the coast, also shown in 

figure 3 are PNTA histograms for selected locations. These 

histograms illustrate the high degree of scatter (measured by 

the coefficient of variation) and complex distribution of PNTA 

values resulting from the 100 model runs. For all runs using 

the stochastic model, the average amount of slip for a rupture is thought to be consistent with tsunami heights in Japan 

(Satake and others, 2003) and coseismic subsidence (Leonard 

and others, 2004) from the 1700 C.E. event. For the first case, 

the average slip varies between 11.2 and 12.8 m (Mw = 9.0), 

consistent with the results of Sakate and others (2003) for 

conservative tsunami heights in Japan (labeled “Low” tsunami 

heights). The resulting subsidence along the coast is approximately 1.5 to 3 m (depending on the slip distribution), which 

is slightly higher than what is estimated by Leonard and others 

(2004) from paleoseismic evidence in coastal marshes. In 

comparison to previous models of local tsunamis in Cascadia 

(Hebenstreit and Murty, 1989; Whitmore, 1993), the average 

tsunami amplitudes using the Long-Wide model are similar in 

the northern part of the subduction zone (approx. 4-8 m) and 

slightly higher in the southern part of the subduction zone, 

where the downdip width narrows (approx. 8-13 m). Comparing the results in this study at specific sites where previous 

inundation models have been formulated, the range in tsunami 

amplitude offshore Grays Harbor, Washington (2-7 m) is 

slightly lower compared to the offshore amplitudes predicted 

by Preuss and Hebenstreit (1998) (7-8 m). The range in tsunami amplitude at Yaquina Bay, Oregon (5.5-10.5 m) encompasses the runup predicted by Priest and others (1997) using 

an asperity source model (8.5 m). It should be noted that the 

finer grid size used by Priest and others (1997) results in better resolution of small-scale changes in alongshore tsunami 

amplitude than the regional model used in this study.

A second series of simulations was performed by limiting the slip downdip to the 350°C isotherm. The geometry 

is similar to the Long-Narrow rupture of Satake and others 
Framework for a Local Tsunami Hazard Assessment 9

sets of simulations (figs. 3, 4) that results from the interplay 

between propagation path difference and a complex coastal 

response from the irregular bathymetry near Cape Blanco. 

Because tsunami propagation calculations were not made past 

the 50 m isobath, more detailed hydrodynamic studies are 

needed to compute the nearshore site response, particularly in 

estuaries and inland waterways as in Priest and others (1997).

Incorporating Uncertainty into Probabilistic 

Calculations

 In probabilistic hazard analyses, uncertainties are classified as either being epistemic or aleatory. Toro and others 

(1997) define epistemic uncertainty as uncertainty “that is due 

to incomplete knowledge and data about the physics of the 

earthquake process. In principle, epistemic uncertainty can 

be reduced by the collection of additional information.” Toro 

and others (1997) define aleatory uncertainty as uncertainty 

“that is inherent to the unpredictable nature of future events. 

It represents unique details of source, path, and site response 

that cannot be quantified before the earthquake occurs. Aleatory uncertainty cannot be reduced by collection of additional 

information. One may be able, however, to obtain better 

estimates of the aleatory uncertainty by using additional 

data.” Although in some cases it can be difficult to determine 

whether a source of uncertainty is epistemic or aleatory (Panel 

on Seismic Hazard Evaluation, 1997), Anderson and Brune 

(1999) assert that the results of PSHA are critically dependent 

on correct classification of uncertainties. In the calculations 

of exceedance probabilities (equation 4), aleatory uncertainty 

is incorporated into the calculation of the rate term N(r,a0). In 

contrast, epistemic probabilities result in distinct hazard curves 

P(r,T,a0 )that are often aggregated using logic trees (see, for 

example, National Research Council, 1988; Cramer and others, 1996).

Following the definitions given by Toro and others (1997) 

and the examples given by Anderson and Brune (1999), it is 

clear that most uncertainties associated with tsunami propagation calculations are epistemic. That is, the collection of 

bathymetry of higher accuracy and resolution than is presently 

available will lead to a reduction in the uncertainty associated with the propagation path. Similarly, the availability of 

high-resolution nearshore bathymetry and topography reduces 

the uncertainty associated with wave amplification and runup. 

However, turbulent behavior, in particular with breaking 

waves, can be considered as a source of aleatory uncertainty, 

because the collection of additional data does not necessarily 

improve our estimate of turbulent dynamics. Though turbulent dynamics is a topic of active research, in most modeling 

applications it is treated approximately using eddy viscosity 

terms in a turbulent closure scheme (for example, Mellor and 

Yamada, 1974; Blumberg and Mellor, 1987; Sato, 1996). 

For the seismic hazard maps, uncertainties associated with 

the earthquake source (specifically, the characteristic magnitude) are divided into both epistemic and aleatory components 

�u(k)=C��

� L0 k<1L0 (5)

as given by Herrero and Bernard (1994), where ∆r is the mean 

stress drop, μ is the shear modulus, L0 is the characteristic 

rupture length, and C is a geometric factor. In the scenarios 

presented here, for convenience, these parameters were constrained by the average slip from the last earthquake (1700 

C.E.). Although there are scaling laws among these low-order 

earthquake source parameters (Kanamori and Anderson, 1975; 

Geller, 1976; Wyss, 1979; Romanowicz and Rundle, 1993; 

Scholz, 1994; Wells and Coppersmith, 1994) there exists 

significant uncertainty in these empirical relations as indicated 

by the observed data, especially when tsunami earthquakes are 

considered (see Geist, 1999, for mean slip versus M0 specific 

to subduction-zone earthquakes). Comparison of results from 

the simulations shown in figures 3 and 4 demonstrate that, in 

addition to uncertainty in the amount of average slip, there are 

large effects on nearshore tsunami amplitudes from variations 

in slip-distribution patterns and the downdip limit of rupture.

In addition to the source effects described above, spikes 

in the PNTA distribution are caused by localized amplification near headlands and promontories and can be termed site 

response. Because of refraction, bathymetric promontories 

will focus tsunami energy, whereas embayments (in the 

absence of resonance) will defocus tsunami energy. Similar 

site responses along the outer coast were obtained in previous 

modeling studies (Hebenstreit and Murty, 1989; Whitmore, 

1993; Preuss and Hebenstreit, 1998), though the site response 

depends in part on the propagation path from the source to the 

shoreline (Geist, 2002). For example, there is a significant 

difference in site response near latitude 43° N between the two 

(2003), except that in this case slip does not continue into the 

transition zone (rupture area shown in light blue in figure 4). 

It is important to note that in all cases the slip distribution is 

completely described by the stochastic source model; no ad 

hoc taper of slip with depth is imposed as in the studies of 

Priest and others (1997, 2000) and Satake and others (2003). 

The average amount of slip used in this case is 12.5–14.5 m, 

such that Mw = 8.8-8.9 for all 100 earthquakes. This amount 

of slip is consistent with Satake and others (2003) “Medium” 

tsunami heights in Japan and with paleoseismologic estimates 

of subsidence from the 1700 C.E. event. Because slip is 

concentrated at shallow depth beneath the sea floor and under 

relatively deep water, it produces a larger tsunami compared 

to the Long-Wide model (fig. 4). This rupture may be similar 

to what would be expected from a tsunami earthquake (Satake 

and Tanioka, 1999; Geist and Bilek, 2001; Bilek and Lay, 

2002). Whether or not such large amounts of slip can be 

sustained shallow in the subduction zone and over a long fault 

length is not known. Although as much as 10 m of slip was 

estimated from the Mw =7.7 1992 Nicaragua tsunami earthquake (Ihmlé, 1996), tsunami earthquakes greater than Mw

~8.2 are unknown (Bilek and Lay, 2002). 

The low-wavenumber scaling of the stochastic model is 

prescribed by the mean slip along the fault ��u)
10 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

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Figure 3. Alongshore distribution of peak nearshore tsunami amplitude (PNTA) using a geometry similar to the “Long-Wide” 

geometry of Satake and others (2003) and slip distributions from the stochastic source model (average slip 11.2-12.8 m with Mw = 

9.0). Left: Rupture areas used for simulation are shown in light blue. Bathymetry in meters. Right: Average (red) and maximum and 

minimum values (blue) of PNTA using 100 slip distribution patterns. Histograms represent frequency of occurrence for PNTA bins of 

1.0 m at three selected localities. CV is the coefficient of variation.
Framework for a Local Tsunami Hazard Assessment 11

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Figure 4. Alongshore distribution of peak nearshore tsunami amplitude (PNTA) using a geometry similar to the “Long-Narrow” 

geometry of Satake and others (2003) and slip distributions from the stochastic source model (average slip 12.5-14.5 m with Mw = 

8.8-8.9). Left: Rupture areas used for simulation are shown in light blue. Bathymetry in meters. Right: Average (red) and maximum 

and minimum values (blue) of PNTA using 100 slip distribution patterns. Histograms represent frequency of occurrence for PNTA 

bins of 1.0 m at three selected localities. CV is the coefficient of variation.
12 Local Tsunami Hazards in the Pacific Northwest from Cascadia Subduction Zone Earthquakes

(Frankel and others, 2002). Uncertainties in earthquake magnitude and geometry for interplate thrust earthquakes along the 

Cascadia subduction zone are incorporated into the probability 

calculations by defining six source scenarios: two possible 

characteristic magnitudes (M 9 and M 8.3) combined with 

three possible positions of the downdip edge of the rupture 

zone (Frankel and others, 2002). Similarly, for tsunami-hazard 

probability calculations, one should also include a splay fault 

scenario as in Geist and Yoshioka (1996) and Satake and others 

(2003). Uncertainty of the slip distribution is most likely an 

aleatory uncertainty, since it is essentially unpredictable and 

repeated occurrence of a particular earthquake (for example, a 

M 9 Cascadia event) will result in changes in PNTA related to 

changes in the slip distribution (fig. 4). Alternatively (though not 

consistent with the findings of Kelsey and others, 2002), if one 

were to consider Cascadia subduction-zone earthquakes as being 

characteristic sensu stricto (that is, slip distribution and rupture 

area are constant from earthquake to earthquake), then the uncertainty associated with the unknown slip distribution would be 

epistemic, since once the earthquake occurs, the slip distribution 

would be known (see Thought Experiment 2 in Anderson and 

Brune, 1999). Analysis of repeated earthquakes along subduction zones suggest, however, that slip distribution patterns vary 

from event to event (Thatcher, 1990; Boyd and others, 1995) and 

are best described as being a source of aleatory uncertainty.

Summary

Although probabilistic tsunami hazard analysis (PTHA) 

shares many similarities with probabilistic seismic hazard 

analysis (PSHA), there are several issues unique to tsunami 

generation and propagation that need to be resolved before 

routine calculations are performed. For example, tsunami 

generation is sensitive to the possibility of rupture on splay 

faults within the subduction zone such that a splay-fault scenario would have to be added as a separate branch to a logic 

tree, following the approach outlined by Frankel and others 

(2002). In addition, although there is little aleatory uncertainty associated with the propagation calculations, as there is 

with attenuation relations in PSHA, the variation in slip-distribution patterns has a significant effect on nearshore tsunami 

amplitudes and is itself a source of aleatory uncertainty. Using 

rupture geometries specified by Satake and others (2003) for a 

M ~ 9 earthquake, predicted offshore tsunami amplitudes are 

similar to results from previous studies for a wide rupture, but 

slightly larger than previously predicted for a narrow rupture. 

For a given rupture geometry and seismic moment, the coefficient of variation for offshore tsunami amplitudes typically 

ranges between 15 and 25 percent. The overriding uncertainty 

for these calculations, however, is the magnitude and attendant 

first-order source parameters (area, average slip, shear modulus) of a future Cascadia earthquake.

Another issue to be decided is what tsunami hydrodynamic parameter would be mapped under PTHA. Presently, 

tsunami inundation maps show the inundation limit for different source scenarios. In contrast, the tsunami parameter 

analogous to exceedance probabilities of peak ground motion 

or response spectral acceleration in PSHA and of concern to 

engineers is most likely the exceedance probability of peak 

current velocity over the region of inundation. For example, 

one could present a PTHA map along the Cascadia coastline 

for inundation velocities with, for example, a 2-percent probability of exceedance in the next 50 years. Current velocities, 

however, are also most sensitive to errors in nearshore bathymetry and topography. Wave-height exceedence probabilities 

such as calculated by Ward and Asphaug (2000) are more 

tractable, given current technology and available bathymetric/

topographic data in the coastal zone. Though the resolution 

of issues related to PTHA may be difficult, the analysis will 

incorporate scientifically defensible estimates of uncertainties 

and provide an improved technique with which to evaluate 

tsunami hazards.

Acknowledgments

Generic Mapping Tools software from Wessel and Smith 

(1998) was used to produce the maps. The author is grateful 

to Tom Brocher and Hal Mofjeld for suggesting important 

changes to this paper. 

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