NOAA Technical Memorandum ERL PMEL-114

Offshore forecasting of Hawaiian tsunamis

generated in Alaskan-Aleutian Subduction

Zone

Vasily V. Titov, Harold O. Mofjeld, Frank I. Gonz ́alez, and

Jean C. Newman

Pacific Marine Environmental Laboratory

7600 Sand Point Way NE

Seattle, WA 98115

January 1999

Contribution 2049 from NOAA/Pacific Marine Environmental Laboratory
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Contribution No. 2049 from NOAA/Pacific Marine Environmental Laboratory

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ii
Contents iii

Contents

1. Background and Motivation . . . . . . . . . . . . . . . . . . . 1

2. Methodology of This Study . . . . . . . . . . . . . . . . . . . 3

3. Analytical Studies of Cross-Ocean Tsunami Propagation . 4

3.1 Analytic Theory . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 One-Dimensional Monochromatic Model . . . . . . . . . . . . 5

3.3 Model Testing Using Gulf of Alaska Tides . . . . . . . . . . . 5

3.4 AASZ Source Region . . . . . . . . . . . . . . . . . . . . . . . 6

3.5 Deep North Pacific Between the AASZ and Hawaii . . . . . . 6

4. Numerical Study of Tsunami Sensitivity to Source Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1 Sensitivity to Earthquake Location . . . . . . . . . . . . . . . 9

4.2 Sensitivity to Fault Dimensions . . . . . . . . . . . . . . . . . 11

4.3 Sensitivity to Rake and Dip Angles . . . . . . . . . . . . . . . 13

5. Application to Tsunami Database Construction . . . . . . . 13

5.1 Method of Database Construction . . . . . . . . . . . . . . . 15

5.2 User Interface and Real-Time Data Assimilation . . . . . . . 16

6. Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 19

8. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Appendix A: Notes on parallelization of the MOST propagation

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Offshore forecasting of Hawaiian tsunamis

generated in Alaskan-Aleutian Subduction Zone

Vasily V. Titov, Harold O. Mofjeld, Frank I. Gonz ́alez, and

Jean C. Newman

Abstract. This report describes an R&D activity conducted during FY 1998 to develop tsunami

forecasting tools for the Pacific Disaster Center (PDC). The activity included analytical and numerical sensitivity studies of tsunami wave characteristics offshore of Hawaii, for ranges of earthquake source parameters in the Alaska-Aleutian Subduction Zone (AASZ); this region is a major

source of destructive tsunamis that strike Hawaii. A set of tsunami numerical simulation scenarios

was designed to be the basis for the sensitivity analysis, using the 1996 Andreanov Island earthquake/tsunami as a reference. The analysis shows that the first waves are relatively insensitive to

the details of the earthquake fault plane parameters. Simulation results for unit sources have been

stored as an online database with a WWW interface. A database user can quickly obtain a model

prediction of the offshore tsunami wave heights at selected locations for a wide variety of AASZ

earthquake scenarios. This database provides a useful offshore tsunami forecasting tool for hazard

mitigation managers.

1. Background and Motivation

This study has been conducted as part of an effort to provide the Pacific

Disaster Center (PDC) with tsunami forecasting capabilities. PDC is a joint

Department of Defense and State of Hawaii activity, initially established

in February 1996. The purpose of this center is to provide a source of

information and guidance for all disaster-related events. It is currently in

the process of acquiring tools to provide this capability for selected categories

of disasters, including tsunamis [see URL http://www.pdc.org].

Potentially, the best approach to forecasting the impact of a particular tsunami event on a specific coastal site is to perform real-time tsunami

model simulations that include real-time data assimilation. With such a

capability, forecasts of tsunami impact would be computed immediately following a potentially tsunamigenic earthquake. As a community, we should

work toward this difficult “Holy Grail” of tsunami forecasting. However,

insufficient real-time earthquake data and a lack of confidence in tsunami

generation and inundation modeling presently render the implementation of

such an operational capability imprudent.

Fortunately, however, existing numerical models are good enough to provide useful guidance, if exercised with care by an experienced tsunami modeler. Event- and site-specific inundation estimates can be computed far in

advance of the earthquake, thoroughly tested and scrutinized for reasonableness and sensitivity to errors, and then stored as a database. When an

event occurs, the appropriate pre-computed results can be recalled, modified

by data assimilation schemes that utilize a user-friendly interface to incorporate real-time tsunami measurements, and made available to aid hazard

assessment and evacuation decision-making.

Such a database of pre-computed results cannot contain all possible

tsunami events, simply because there is too much variability in the mechanism of tsunamigenic earthquakes. The database must contain a finite
2 Titov et al.

number of events chosen from an infinite number of possible scenarios. A

study of tsunami wave sensitivity to parameters of their earthquake sources

can provide guidance for selecting events for the database. In particular, the

sensitivity study can identify earthquake parameters that are not critical in

determining the heights, periods and directionality of the resulting tsunamis.

Tsunami generation is commonly modeled by assuming that the initial

sea surface displacement is formed by the permanent vertical displacement of

the ocean bottom induced by an earthquake. The shape of the earthquake’s

vertical displacement can be inferred by applying a so-called “double-couple”

source model and computing the elastic deformation of the earth’s crust (e.g.,

Okada, 1985). This approach assumes that an earthquake can be modeled

as the rupture of a single rectangular fault plane that is characterized by

parameters describing the location, orientation, and rupture direction of the

plane. These parameters are the length of the rupture plane L, the width

of the plane W, the depth of the source h, dip angle δ, slip angle λ, strike

angle θ, and the average slip amount u0. The moment magnitude of this

model source is determined by the formula

M0 = μu0LW, (1)

where μ is the rigidity of the earth crust with a value ranging from 1 to 6

× 1010 N/m2, depending on the local geological structure (in this study, we

use a value of 4.5 × 1010 N/m2). The moment magnitude of the earthquake

source, as well as its depth, dip angle, slip angle, and strike angle, are obtained from the moment tensor analysis of seismic waves. Then Equation

(1), together with ancillary data such as aftershock patterns, can then be

used to estimate the L, W, and u0 of the earthquake.

The double-couple source is a very simplified model of an earthquake.

But estimates of the five parameters of the double-couple model are available

fast enough after the earthquake to be relevant for tsunami mitigation. More

sophisticated models include multiple sub-faults with parameters that vary

along the multi-fault structure. This fine structure of a fault can be obtained

only after months of data analysis, provided that enough high-quality data

(including tsunami data) exist for a particular event. More general, nondouble couple models of earthquakes are also emerging (Julian et al., 1998).

One approach for constructing a database of pre-computed inundation

estimates is to vary each parameter of an earthquake source model, including

the location, and then compute inundation values for each scenario. Even

with the elimination of certain mechanisms and very sparse incrementation

of the parameters, such a database can be enormous. In spite of these

difficulties, this approach is being tested by Japanese scientists for a new

tsunami warning system in Japan (Tatehata, 1997).

We have taken a different approach based on a two-step methodology.

First, linearity of the generation/propagation dynamics is exploited to develop an offshore forecast database of “basis” scenarios that can quickly be

arithmetically combined to relate earthquake parameters to the height, period, and direction of a tsunami wave off the coast. Second, these results are

used as input to non-linear transfer functions that have been developed to relate the offshore wave characteristics to inundation (and/or current speeds)
Offshore forecasting of Hawaiian tsunamis 3

at specific sites in harbors or at sites along the open coast. The advantage

of the transfer function approach is its flexibility and compactness.

In principle, an infinite number of tsunami propagation scenarios can

be constructed by linear combinations of a finite number of pre-computed

“basis” scenarios. The linearity of this first stage also greatly simplifies

data assimilation schemes for determining a tsunami source from deep-ocean

gage recordings. A sensitivity study is an essential part of this concept,

since it determines which earthquake parameters are the most important for

tsunami generation. This is done by quantifying the influence of variations of

earthquake parameters on the characteristics of the resulting tsunami waves.

In this study, the focus is on the sensitivity of deep-water tsunamis

near Hawaii to the parameters of underwater earthquakes in the AlaskaAleutian Subduction Zone (AASZ). This region is a major source of destructive tsunamis that strike Hawaii. The inundation patterns of these tsunamis

in Hawaii will be determined by work proposed for FY 1999. The FY 1998

work reported here can be thought of as providing the necessary open boundary conditions for the planned FY 1999 tsunami inundation modeling of the

Hawaiian region.

2. Methodology of This Study

Tsunami sensitivity was analyzed by studying numerical simulation results of

different earthquake scenarios. The numerical analysis is focused on the first

wave of each tsunami. Analytical studies of cross-ocean tsunami propagation

(Section 3) indicates that bathymetric features affect the first wave only

weakly. The following wave train, on the other hand, is complicated because

it includes reflected and refracted waves. Thus, the leading wave carries the

most information about a tsunami source. At many Hawaiian sites, the first

waves of historic tsunamis are frequently the highest and therefore the most

destructive.

The offshore sensitivity analysis exploits the assumed linearity of the

tsunami propagation process, which implies that multiplication by a constant

or addition of another solution will produce a valid tsunami propagation scenario. This linear assumption works very well for tsunami propagation in

the open ocean. Nonlinear effects only become important as the tsunami

approaches a coastline, at the depth less than 100–200 m, or during propagation over a very long continental shelf. Nonlinearity becomes dominant

during tsunami inundation.

Analytical methods are first used to investigate wave-trapping and reflection processes in the earthquake source regions and during the wave propagation across the Pacific. Resulting theoretical estimates serve as a valuable

guide in the design of the numerical experiments and help to constrain the

range of parameters in the subsequent simulations.
4 Titov et al.

3. Analytical Studies of Cross-Ocean Tsunami

Propagation

A set of analytic and one-dimensional models were developed to help interpret the results of the MOST model and to verify the use of the Sandwell/

Smith bathymetry in this model. These models were also used to investigate wave-trapping and reflection processes in the earthquake source regions.

These simplified models show that geometric spreading is the main process

affecting the amplitudes of the first waves of a tsunami to propagate from

the AASZ to the deep ocean off Hawaii. Geometric spreading is augmented

by the wave refraction that occurs as the tsunami waves propagate over progressive deeper water, from just south of the Aleutian Trench to the vicinity

of Hawaii. Although the bottom topography in the North Pacific includes

large seamount fields and numerous escarpments, estimates of wave scattering indicate that this fine-scale topography does not attenuate the first

tsunami waves substantially. This is because these topographic features do

not extend over a major fraction of the water column and their spatial scales

are very short compared with a tsunami wavelength. The exception is the

Emperor Seamount Chain/Hawaiian Ridge, which is seen in the MOST simulations. These features produce significant wave channeling. The deep-water

scattering by very fine bathymetric features does not substantially attenuate

the first tsunami waves. Hence, the spatial resolution and accuracy of the

Sandwell/Smith bathymetry is fully adequate for use in the development of

the tsunami database.

3.1 Analytic Theory

The analytic theory uses idealized tsunami waves incident on idealized bottom topography to better understand and scale tsunami wave reflection and

scattering. The derivation of a formula for the reflected wave generated over

lineal bathymetric features shows that its amplitude depends on the bottom

slope, water depth, incident angle, and the horizontal scale of the features

relative to the wavelength λ. For normal incidence on a submarine ridge with

Gaussian cross-section, the maximum scattered energy is proportional to 2,

the square of the height of ridge relative to the surrounding water depth.

The maximum occurs approximately when kσ = √2, where k = 2π/λ is the

wavenumber off the ridge and σ is the half-width scale of the ridge. At longer

tsunami wavelengths (lower frequencies) the amount of scattering decreases

significantly with increasing wavelength. The application of this ridge theory

is made later in this section for ridge-like features associated with the Mendocino Escarpment, the highest short-scale feature encountered by tsunamis

propagating from the AASZ to Hawaii.

For circularly symmetric seamounts, the energy flux of the scattered

wave is also proportional to 2. This type of scattering is weak in the

open North Pacific between the AASZ and Hawaii since the seamounts here

do not extend far up into the water column and they are very small compared with tsunami wavelengths. What scattering occurs is very sensitive

(∼ ω5) to wave frequency ω, i.e., scattering effects are much stronger for
Offshore forecasting of Hawaiian tsunamis 5

high-frequency waves. Since the seamounts in the North Pacific generally

occur in irregular patterns, the amount of energy scattered from a tsunami

propagating through a field of seamounts (e.g., the Alaska Seamounts) can

be found by assuming that the scattering from one seamount is independent of the scattering from the others. This scattering, like that of the lineal

ridges, is included in the MOST model simulation, since the Sandwell/Smith

bathymetry in the model resolves these short-scale features.

3.2 One-Dimensional Monochromatic Model

The one-dimensional (1-D) numerical model solves the linear, inviscid

shallow-water wave equations at a given wave frequency and alongshore

wavenumber. The results are the surface elevation and water velocities as

functions of the offshore (southward) distance from the AASZ. The numerical method adjusts the spatial increment so that the solutions are accurate

within a preset limit δ. In the results described below, the equations are

solved using double precision calculations, with δ set to 10−9. For idealized

bathymetry, the model is found to compute solutions that match analytic

solutions to this accuracy.

Two types of coastal boundary conditions are used: a sloping beach to

allow coastal reflection in the Alaska Peninsula region and an open-boundary

condition to allow northward-propagating waves in the Aleutian Arc region

to pass freely into the Bering Sea. The beach-condition provides information

about coastal reflection and nearshore amplification, as well as bathymetric

trapping near the earthquake source. The open-boundary condition allows

a study of offshore wave reflection in the shelf/slope/trench region; it is

also used to study wave scattering and refraction in the open North Pacific

between the AASZ and Hawaii.

3.3 Model Testing Using Gulf of Alaska Tides

Since the tides are also shallow water waves and there are extensive tidal

observations in the northern Gulf of Alaska that have been made by PMEL,

it is appropriate to test the 1-D model against these observations. The

observations were taken at 36 bottom pressure stations in a region (51◦–

55◦N, 154◦–159◦W) that extends from the lower continental slope, across

the Aleutian Trench and onto the abyssal region. The 1-D model was solved

along the 315◦T transect for largest diurnal (K1) and semidiurnal (M2) tidal

constituents. It was tuned to the amplitude and phases of these tides at a

single station, with the complex alongshore wavelength adjusted to match

the alongshore distributions of these constituents. The Coriolis effect is

included in the model because it strongly affects tides in the open ocean.

The results show close agreement between along-transect tidal distributions between the model and the observations. For an average over the 36

stations, the model values differed from the observations by only 0.1% and

0.3% in amplitude and 0.2◦ and 0.06◦ in phase for K1 and M2, respectively.

The largest deviations occurred at the stations farthest from the transect

(M2: 3.2%, 4.2◦), due to an assumption of pure wave propagation in the
6 Titov et al.

alongshore direction. There is also close agreement of the tuned 1-D model

tides with the latest global tidal models.

3.4 AASZ Source Region

The results of the 1-D tsunami simulations in the AASZ Source Region show

that near-source wave trapping is significant only for waves propagating

nearly alongshore. Because the AASZ fault zones are roughly parallel to

this direction, the tsunami waves are primarily directed perpendicular to it

(and toward Hawaii). Hence, this type of trapping does not substantially

affect the first tsunami waves. There will be trapping and scattering of some

waves, which will complicate the pattern of the later wavetrain and extend

its duration in time. The Aleutian Trench has little effect on tsunami waves

propagating directly across it, but does enhance wave trapping for the wave

components propagating nearly parallel to the Trench.

For tsunamis generated on the continental slope, the northwardpropagating component will be reflected only slightly (reflected wave amplitude ∼2–3% for a normally incident wave with a period of 20 minutes)

on the upper slope/outer shelf region. Reflections of tsunami waves in the

Aleutian Arc region are therefore due primarily to island reflections and resonance, rather than reflection at the shallow-to-deep-water transition between

the Arc and the Bering Basin.

3.5 Deep North Pacific Between the AASZ and Hawaii

The amplitudes of tsunami waves propagating from the AASZ and the vicinity of Hawaii decrease primarily in response to cylindrical spreading from a

source of limited spatial extent. This decrease amounts to ∼76%, with an

additional 4% decrease due to refractive (Snell’s Law) spreading. East-West

escarpments and seamounts scatter only a small fraction of the energy of

southward-propagating tsunami waves.

Computations based on the dispersion relation for gravity waves shows

that differences in propagation times is negligible for wave periods greater

than 10 minutes. This is for propagation in deep water from the Aleutian

Trench to the Hawaii Rise. Longer period waves are expected for major

tsunamigenic earthquakes in the AASZ. This result supports the assumption

in the MOST model that non-dispersive wave theory applies to the major

AASZ tsunami events.

The application of the ridge theory to ridge-like features associated with

the Mendocino Escarpment (at 157◦W) shows that the highest of these features has a maximum scattering energy of 2 × 10−4 relative to the incident

energy. Hence, very little energy is scattered from the incident wave by these

ridge features. The southward increase in water depth across the whole escarpment occurs over too large a distance at 157◦W to scatter significant

tsunami energy. However, near the U.S. West Coast, this distance becomes

much shorter and the relative depth contrast across the Mendocino Escarpment becomes much larger. Hence, the Escarpment can be expected to

interact significantly with tsunamis incident on the West Coast.
Offshore forecasting of Hawaiian tsunamis 7

4. Numerical Study of Tsunami Sensitivity to

Source Parameters

How sensitive are far-field tsunami model time series to changes in the source

parameters? In the limit, the generation region will look more and more like

a point source, so that the time series should become less and less sensitive

to details of the source as the distance increases. This issue is central to the

whole notion of a pre-computed forecasting database, since source parameters available only a short time after an earthquake occurs are preliminary

in nature and may be somewhat inaccurate. To explore this question, an

analysis was performed that exploited the availability of deep ocean tsunami

time series collected in the far-field.

The MOST generation and propagation model has been tested against

the deep-ocean data from bottom pressure recorders (BPRs) collected after

the June 10, 1996 Andreanov Island tsunami; excellent agreement with observations was obtained (Titov and Gonz ́alez, 1997). Since the Andreanov

tsunami was generated in the AASZ, our area of interest here, and since this

event is considered to be a typical subduction zone tsunamigenic earthquake

(Tanioka and Gonz ́alez, 1998), it was chosen as a “reference point” for this

study. In particular, we wish to explore the sensitivity of the model simulations to changes in the earthquake parameters—i.e., how much could we

change these parameters before the model-data comparison was unsatisfactory?

To reduce the number of parameters to a manageable level, certain reasonable assumptions were made about the fault plane models. First, the

upper edge of each fault plane was set to the shallow depth of 5 km, since

large subduction earthquakes with shallow faulting are believed to be the

most effective in generating tsunamis. Second, we set the strike to align

with the Aleutian Trench, since this appears to be true of most large underthrust earthquakes in the AASZ. As a third, important constraint, all

model sources were required to have a fixed seismic moment M0 equal to the

estimated moment of the Andreanov earthquake of 7.3 × 1020 N m.

With these constraints, the sensitivity analysis is restricted to variations

of the position of the earthquake epicenter along the AASZ and the four

fault plane parameters length, width, dip angle, and slip angle that are varied about the reference length = 140 km, width = 70 km, dip = 20◦, and

slip = 108◦ used by Titov and Gonz ́alez (1997). (Similar values of these

parameters were estimated by Tanioka and Gonz ́alez (1998) through comparison of the computed tsunami with near-source coastal tide gage data.)

With these parameters set, the mean slip, u0, is determined by means of the

moment magnitude relationship, equation (1).

This study was conducted in two parts. First, model simulations were

performed in which the Andreanov fault plane model of Titov and Gonz ́alez

(1997) was placed in different locations along the AASZ; this tested the sensitivity of the results to epicentral position. Second, model simulations were

done for fault plane models located at the Andreanov earthquake epicenter,

but with variations in the length, width, dip angle, and slip angle.
8 Titov et al.

A BC

D

E

F

G

1

2

3

4

5

6

7

50oN

60oN

40oN

30oN

20oN

190oE 200oE 210oE 220oE 230oE 240oE

Figure 1: The locations of the earthquake sources and wave gages for the sensitivity study computations

shown with the bathymetry of the computational area.
Offshore forecasting of Hawaiian tsunamis 9

Table 1: Model source parameters for the study of tsunami sensitivity to earthquake location. The seismic moment magnitude is

the same as that of the 1996 Andreanov earthquake for each case.

Sources Long. Lat. Length Width Strike Dip Rake Depth Slip

A 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 108◦ 5 km 2 m

B 51.2◦N 185.0◦E 140 km 70 km 253◦ 20◦ 108◦ 5 km 2 m

C 51.2◦N 187.0◦E 140 km 70 km 253◦ 20◦ 108◦ 5 km 2 m

D 52.0◦N 190.0◦E 140 km 70 km 253◦ 20◦ 108◦ 5 km 2 m

E 53.3◦N 195.0◦E 140 km 70 km 245◦ 20◦ 108◦ 5 km 2 m

F 54.1◦N 200.0◦E 140 km 70 km 238◦ 20◦ 108◦ 5 km 2 m

G 56.5◦N 208.0◦E 140 km 70 km 230◦ 20◦ 108◦ 5 km 2 m

Computed tsunami time series were saved at the locations shown in Figure 1, and our analysis concentrated on Gage 1 near Hawaii, Gage 2 between

Hawaii and the AASZ, and Gage 3 off the West Coast. Both locations are in

deep water where the wave dynamics are linear; Gage 1 is at 4747 m depth

and Gage 2 is at 5910 m. Other important locations shown in Figure 1

are positions of the bottom pressure recorders (BPR) where the time series

of the Andreanov tsunami were recorded and compared with the MOST

simulations. Gage 3 is located on Axial Seamount, at a depth of 1550 m.

4.1 Sensitivity to Earthquake Location

The position of the earthquake epicenter is one of the most important parameters in determining the characteristics of the resulting tsunamis. A

series of numerical experiments were performed to quantify the effect of the

earthquake positioning on the tsunami characteristics near Hawaii and off

the West Coast. Seven different earthquake locations were modeled. The

strike direction for each source is adjusted to align the sources along the

Aleutian Trench. Positions of the sources are shown on Figure 1, and the

fault plane parameters are summarized in Table 1.

Figure 2 shows results of numerical simulations for the sources listed in

Table 1. For the purpose of comparison, the time scale of all computed

tsunamis, except for the Andreanov record, has been moved to the same

arrival time. Time series at Gages 2 and 3 show that the first wave amplitude

varies significantly with source location. At Gage 2, the amplitude of the first

wave decreases gradually when the source location is moved eastward. For

instance, the tsunami generated by the western-most source A has 2.7 times

higher amplitude than the wave from the eastern-most source G. At Gage 3,

the effect is inverted and amplified: the largest wave generated by the source

G has 5.5 times higher amplitude than the smallest wave generated at source

A.

One obvious reason for the decrease of amplitudes is cylindrical spreading, which causes tsunami wave amplitudes to decrease with distance from

the source. Another reason is the directionality of the tsunami wave pattern.

The shape of a tsunami source and the bathymetric profile near subduction

zones make tsunami energy very directional, with most of the wave energy
10 Titov et al.

-0.06

-0.04

-0.02

0.00

0.02

0.04

amplitude, m

2 3 4 5

time, hrs

Gage 2

-0.04

-0.02

0.00

0.02

amplitude, m

4 5 6

time, hrs

Gage 1

 Andreanov source (A)

 source at 185°E (B)

 187°E (C)

 190°E (D)

 195°E (E)

 200°E (F)

 208°E (G)

0.04

0.02

0.00

-0.02

-0.04

amplitude, m

4 5 6 7

time, hrs

Gage 3

Figure 2: Tsunami time series at gages 1, 2, and 3 computed for different source locations. The time scale

of all computed tsunamis, except for the Andreanov record, has been moved to the same arrival time.
Offshore forecasting of Hawaiian tsunamis 11

Table 2: Model source parameters for the study of tsunami sensitivity to fault dimensions. The locations of the epicenters are the

same as that of the 1996 Andreanov earthquake.

Sources Long. Lat. Length Width Strike Dip Rake Depth Slip

H 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 108◦ 5 km 2 m

I 51.2◦N 182.7◦E 140 km 105 km 260◦ 20◦ 108◦ 5 km 1.3 m

G 51.2◦N 182.7◦E 200 km 70 km 260◦ 20◦ 108◦ 5 km 1.4 m

K 51.2◦N 182.7◦E 105 km 70 km 260◦ 20◦ 108◦ 5 km 2.7 m

L 51.2◦N 182.7◦E 140 km 35 km 260◦ 20◦ 108◦ 5 km 4 m

M 51.2◦N 182.7◦E 70 km 70 km 260◦ 20◦ 108◦ 5 km 4 m

propagating at right angles to the earthquake fault. This effect is demonstrated in Figure 3, where contours of maximum computed amplitudes are

presented for two sources A and G. The amplitude of the off-shore propagating tsunami is larger in the direction perpendicular to the trench (and

the tsunamigenic fault). The farther away the site is from this main beam,

the smaller the amplitudes of the waves are, even if the site is fairly close to

the source.

Amplitudes of the first waves at Gage 1, the nearest to Hawaii, are very

similar for almost all the sources. The only exception is source G, which

generated half the tsunami amplitude at Gage 3 as compared with the other

sources. The bathymetry of the area around source G is quite different from

the other source locations. There are a series of seamounts in the Gulf of

Alaska that can affect the propagation from that source. Also, some of the

tsunami energy generated by source G appeared to be trapped by the shallow

bathymetry off the West Coast.

The period and the shape of the leading tsunami waves for different

sources are quite similar at all the gages. In contrast, the wave train following

the first wave is quite unique for each source. This wave train is formed by

interference patterns of tsunami waves that have taken different propagation

paths to the gage. Reflections from bathymetric features that determine the

appearance of the wave train appear to have little influence on the leading

wave, confirming the analytical results described in Section 3.

4.2 Sensitivity to Fault Dimensions

The dimensions of a fault plane can only be estimated with reasonable accuracy when indirect data, such as a three-dimensional aftershock distribution, is available and analyzed. It takes months, or even years, after the

earthquake to obtain such information. The problem of rapidly estimating

rupture-size is still unresolved. Presently, the only means of quickly estimating fault size for a real-time tsunami assessment are several empirical

formulas that roughly evaluate the size and extent of rupture as a function

of earthquake magnitude.

To determine the tsunami sensitivity to the dimensions of the fault plane,

six different sets of dimensions were used. The slip amount of each has been

adjusted to preserve the magnitude of the earthquake. Parameters of the
12 Titov et al. (a) (b) Figure 3: Contours of maximum computed tsunami amplitudes for source A (a) and source G (b). Contour intervals are 2 cm.
Offshore forecasting of Hawaiian tsunamis 13

Table 3: Model source parameters for the study of tsunami sensitivity to dip and rake. The locations of the epicenters are the same

as that of the 1996 Andreanov earthquake.

Sources Long. Lat. Length Width Strike Dip Rake Depth Slip

N 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 108◦ 5 km 2 m

O 51.2◦N 182.7◦E 140 km 70 km 260◦ 15◦ 108◦ 5 km 2 m

P 51.2◦N 182.7◦E 140 km 70 km 260◦ 10◦ 108◦ 5 km 2 m

Q 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 90◦ 5 km 2 m

R 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 100◦ 5 km 2 m

S 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 120◦ 5 km 2 m

T 51.2◦N 182.7◦E 140 km 70 km 260◦ 20◦ 135◦ 5 km 2 m

model sources are summarized in Table 2. As seen in Figure 4, the leading

waves at Gage 1 (near Hawaii) and Gage 2 (between Hawaii and Alaska)

show very little sensitivity to the dimensions of the rupture plane. The

difference in amplitudes of the leading waves is within 25% of the maximum,

although the corresponding vertical displacements of the ocean bottom (and

areas of the fault planes) differ by a factor of three. The variation between

different solutions is larger at Gages 3 and 4, located near the continental

coast. However, the leading waves from the different sources (Table 2) are

within 50% of the maximum at these gages.

4.3 Sensitivity to Rake and Dip Angles

Several numerical experiments were conducted to study the influence (Table

3) of small variations in dip and rake angles on the tsunami waves, using the

Andreanov source location. Figure 5 shows that lowering the dip angle from

20◦ to 10◦ (the typical range for subduction earthquakes in AASZ) leads to

a 30% decrease in the amplitudes of leading tsunami waves. However, the

period and the shape of the first wave stays very much the same for all dip

angles.

Variations in the rake angle do not affect the tsunami waves significantly

(Figure 6). Five different rake angles are computed ranging from pure dipslip mechanism (rake = 90◦) to a 50% strike-slip component in the fault

motion (rake = 135◦). The smallest amplitude (rake = 135◦) is only 20%

less than the largest (for rake = 90◦).

5. Application to Tsunami Database

Construction

The main purpose of the sensitivity study of the previous section was to provide guidance for the construction of a database consisting of pre-computed

tsunami scenarios. The results demonstrate that, for a fixed location and

magnitude, there is very weak dependence of the offshore tsunami characteristics on a reasonable range of other AASZ earthquake parameters. In all

computed scenarios, the first wave amplitude does not differ from the observed Andreanov tsunami amplitude by more than 25%. The half-periods
14 Titov et al.

-0.02

-0.01

0.00

0.01

0.02

amplitude,

m

1 2 3 4

Gage 4

 Andreanov(140x70,2m)

 140x105, 1.3m

 200x70,1.4m

 105x70,2.7m

 140x35, 4m

 70x70, 4m

-0.02

-0.01

0.00

0.01

0.02

amplitude,

m

4 5 6 7

Gage 3

-0.08

-0.04

0.00

0.04

0.08

amplitude,

m

4 5 6 7

Gage 1

-0.08

-0.04

0.00

0.04

0.08

amplitude,

m

2 3 4 5

time, hrs

Gage 2

Figure 4: Tsunami time series at Gages 1, 2, 3, and 4 computed for different source dimensions. The slip

amount of each source is adjusted to preserve the magnitude of the earthquake (Mo = 7.3 × 1020 N m).
Offshore forecasting of Hawaiian tsunamis 15

-0.06

-0.04

-0.02

0.00

0.02

0.04

amplitude, m

0 1 2 3 4 5 6 7

time, hr

 Andreanov source(dip=20°)

 DIP=10°

 DIP=15°

Gage 2

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

amplitude, m

0 1 2 3 4 5 6 7

time, hr

Figure 5: Tsunami time series at Gages 1 and 2 computed for different dip angles of the tsunami source.

are also within 5% of that of the Andreanov tsunami, and the shapes of the

first waves are similar for all the sources. Hence, the leading tsunami waves

generated by AASZ earthquakes are characterized in the far field mainly by

the earthquake magnitude and location.

5.1 Method of Database Construction

A typical subduction mechanism for an Mw = 7.5 earthquake was chosen as the “unit source” for the model database. The parameters of the

unit source are length = 100 km, width = 50 km, dip = 15◦, rake = 90◦,

depth = 5 km, slip = 1 m. The strike of each source is adjusted to align

the source along the local orientation of the subduction zone. The fault dimensions of 100 × 50 km2 were chosen because they coincide with the size

of observed AASZ asperities, which have been estimated to be the areas of

actual vertical ground deformation associated with AASZ earthquakes (see

review by Johnson, 1998). These unit sources are placed at locations along

the AASZ 100 km apart from each other, forming a continuous line of faults

along the Aleutian Trench (B-sources on Figure 7). A second line of similar

sources (line A on Figure 7) is placed immediately north of the B-sources.

To form a continuous fault plane, the epicenters of the A-sources are placed
16 Titov et al.

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

amplitude,

m

0 1 2 3 4 5 6 7

time, hr

Gage 1

-0.06

-0.04

-0.02

0.00

0.02

0.04

amplitude,

m

0 1 2 3 4 5 6 7

time, hr

 Andreanov source (slip=108°)

Slip=90°

 Slip=100°

 Slip=120°

 Slip=135°

Gage 2

Figure 6: Tsunami time series at gages 1 and 2 computed for different rake angles of the tsunami source.

at a depth of 17.5 km (the depth of the north edge of B-faults). Tsunami

propagation has been modeled for each unit source and the results of each

simulation have been stored in the database. Computations were performed

on a 4-minute bathymetric grid using a time step of 15 seconds. To reduce

the database size and access time, the solutions are stored with a coarser

sampling of 1◦ in space and 1 minute in time.

5.2 User Interface and Real-Time Data Assimilation

It is expected that real-time reports of tsunami wave heights will soon be

available operationally in the open North Pacific during tsunami events (Milburn et al., 1996). These direct tsunami observations can be combined

with the forecast database to improve the accuracy of the tsunami forecast methodology. A flexible user interface has been developed that employs

World Wide Web technology (http://corona.pmel.noaa.gov/∼tsunami/

model/) and is designed with real-time data assimilation in mind. The

interface exploits the linearity inherent in the tsunami forecast database.

It greatly simplifies and speeds the addition of unit sources that are mul-
Offshore forecasting of Hawaiian tsunamis 17

Figure 7: The locations of the unit tsunami sources along AASZ (stars) and preselected gage sites (open

circles). Model results of tsunami propagation from these sources form the model database.

tiplied by factors to form larger fault planes characterizing a major earthquake. The multiplier for each unit solution can be different, thus simulating

non-uniform slip distribution within the larger earthquake fault plane. The

computed tsunami waveforms (Figure 8) are then quickly available for geographical coordinates corresponding to the locations of existing or planned

real-time observations (as well as other locations near Hawaii and around

the Pacific Rim). When the user (forecaster or emergency manager) obtains

a satisfactory correspondence between computed and observed tsunami time

series, a map of maximum computed amplitudes in the North Pacific can be

examined to guide the forecast (Figure 9).

6. Future Plans

Prediction of tsunami inundation is the next logical step in the development

of tsunami forecasting tools. Development of these inundation prediction

tool is planned for FY 1999–2000 as a continuation of the current project.

Site-specific sensitivity studies of inundation as a function of offshore tsunami

characteristics will be performed, and an inundation database will be developed. The final goal is to integrate the results of this offshore tsunami sensi-
18 Titov et al.

Figure 8: The waveform output of the tsunami model database. The waveforms are computed for the same

tsunami source as in Figure 9, at the locations shown in Figure 7.
Offshore forecasting of Hawaiian tsunamis 19

Figure 9: An example of the database output shows maximum computed wave heights produced by a

tsunami in the computational area. The source of the tsunami is a combination of three unit sources (stars).

tivity study and the offshore forecast database with the inundation database

and a real-time data assimilation scheme to produce a systematic methodology for tsunami forecasting guidance that is both source- and site-specific.

This work could also be extended to include pre-computed scenarios for

sources along the entire Pacific Rim. For instance, the Kuril-Kamchatka and

Japan Subduction Zones are very active and produce very strong tsunamigenerating earthquakes almost every year. The Cascadia Subduction Zone

is also active and capable of a mega-thrust event that would generate a

large tsunami (e.g., Atwater, 1987). To add these potential sources to the

database, a sensitivity study should be performed for each of the areas using

the same methodology as for the AASZ sources. Then pre-computed scenarios could be used to forecast offshore tsunamis not only for the Hawaiian

Islands but for all Pacific Rim coastlines included in the computations.

7. Acknowledgments

Funding for this work was provided by the Assistant Deputy Under Secretary of

Defense for Space Integration, Contract NM8600019. Maui High Performance Com-
20 Titov et al.

puter Center provided computer time and support for parallelization of the tsunami

propagation model.

8. References

Atwater, B.F. (1987): Evidence for great Holocene earthquakes along the outer

coast of Washington State. Science, 236, 942–944.

Johnson, J. (1998): Heterogeneous coupling along the Alaska-Aleutians as inferred

from tsunami, seismic, and geodetic inversions. Advances in Geophysics, 39 (R.

Dmowska, ed.), Academic Press.

Julian, B.R., A.D. Miller, and G.R. Foulger (1998): Non-double-couple earthquakes.

Rev. Geophys., 36(4), 525–568.

Milburn, H.B., A.I. Nakamura, and F.I. Gonz ́alez (1996): Real-time tsunami reporting from the deep ocean. Proceedings of the Oceans 96 MTS/IEEE Conference,

23–26 September 1996, Fort Lauderdale, FL, 390–394.

Okada, Y., 1985, Surface deformation due to shear and tensile faults in a half-space.

Bull. Seismol. Soc. Am., 75, 1135–1154.

Tanioka, Y., and F.I. Gonz ́alez (1997): The Aleutian earthquake of June 10, 1996

(Mw 7.9) ruptured parts of both the Andreanov and Delarof segments. Geophys.

Res. Lett., 25(12), 2245–2248.

Tatehata, H. (1997): The new tsunami warning system of the Japan Meteorological

Agency. In Perspectives on Tsunami Hazard Reduction, G. Hebenstreit (ed.),

Kluwer, 175–188.

Titov, V.V., and F.I. Gonz ́alez (1997): Implementation and testing of the Method of

Splitting Tsunami (MOST) numerical model. NOAA Tech. Memo ERL PMEL112 (PB98-122773), PMEL, Seattle, WA, 11 pp.
Offshore forecasting of Hawaiian tsunamis 21

Appendix A: Notes on parallelization of the

MOST propagation model

W. Smith and V.V. Titov

The propagation part of the MOST numerical model has been adapted for

computations on a parallel supercomputer. The MOST code has been modified using Message Passing Interface (MPI) to perform parallel computations

on distributed-memory machines. An IBM SP2 system at the Maui High

Performance Computer Center (MHPCC) was used to perform the computations using the MOST parallel code.

A Master-Worker parallelization scheme has been adopted for the MOST

parallel code. It appeared to be the least disruptive of the original code. The

master passes a column to a worker node, then another column to another

worker and so on until all the workers have a column to process (Figure A1).

Then the master gathers the columns back up. This is repeated until no

more columns exists. The process is repeated with the rows. The master

doesn’t do any of the computation, only the workers do.

CPU 2

CPU 3

CPU 4

CPU 1

Master

Figure A1: Master-Worker parallelization scheme applied for the MOST propagation code.
22 Titov et al.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

1 2 3 4 5 6 7 8 9 10

Nodes

Speed

Up

(T/ Tref )

Figure A2: Speed-up of the MOST parallel code computed with different numbers of computer nodes.

In a test simulation, the non-parallelized code ran Tref = 1 hour 28 minutes for 1000 time steps, which models 2 hours 45 minutes of tsunami propagation time. The parallelized code has been tested for different numbers of

processors. Figure A2 shows the increase in speed obtained on the IBM SP2

parallel computer. The 5-node parallelized code ran in 50 minutes. It was

a bit less than a 2X speed-up. It is expected that on larger data sets, the

speed-up will be much greater. The master-worker parallelization is only the

first attempt to adapt the MOST code for the parallel ccomputation. There

are other methods of parallelization that can produce a much faster version

of the code, such as non-blocking sends and receives, domain decomposition,

and many others.

Future plans include further optimization of the MOST parallel code using domain decomposition method to obtain fast working propagation and

inundation models. Application of nested grids during the inundation computation can produce a very efficient parallel algorithm, where all the subgrids are computed simultaneously on different nodes. The data assimilation

algorithm is another task where the full potential of the parallel computing

can be exploited. It requires computing many independent tsunami scenarios at the same time in order to obtain an approximation of the tsunami

source. These types of algorithms are usually very well suited for parallel

computations.