PA,"Ll_," r .rs YIvIFA

ASSESSMENT OF TSUNAMI HAZARD

PRESENTED BY POSSIBLE SEISMIC EVENTS

SAI-82-383-WA

lA TLANTA ANN ARBOR *BOSTON * CHICAGO 0 CLEVELAND * DENVER * HUNTSVILLE * LA JOLLA A LITTLE ROCK 9 LOS ANGELES a SAN FRANCISCO o SANTA BARBARA o TUCSON 9 WASHINGTON

TABLE OF CONTENTS

Section 1

Secion2 Section 2

Section 3

Section 4

Page

INTRODUCTION ........................... 1-1

1.1 Tsunamis ...... 1-1 1.2 The Pacific Threat ................ 1-2 1.3 The South American.Threat ......... 1-4 1.4 Purpose of the Study .............. 1-4 1.5 Structure of the Report ........... 1-7

TSUINAMI MODELS2-SNM OES.......................... 2-1

2.1 Equations of Motion ............... 2-1 2.2 Earlier Studies ................... 2-3 2.3 SEAWAVE . ...... ...... ..... ....... 2-4

2.3.1 Numerical Solution Scheme .. 2-4 2.3.2 Boundary Conditions ........ 2-5 2.3.3 Bottom Displacements ....... 2-6 2.3.4 Bottom Topography o......... 2-8

2.4 Procedure ....... o...... o. ........ 2-12

CHOICE OF EARTHQUAKE SITES AND SOURCE MOTIONS ............. .......... . 3-1

......3.1 Site Selection ... 3-1..... 3.2 Focal Mechanisms .................. 3-8 3.3 Earthquake Energy ........ 3-10 3.4 Source Motions ............... e.3-17

MODEL RESULTS ............ 41...41

4.1 Method of Analysis ........ ...... 4-1 4.2 Source Zone A .......... ..... ...o.. 4-2

4.2.1 Cases A-1-1, A-2-1, A-3-1 .. 4-4 4.2.2 Cases A-4-1, A-4-1, A-4-1 .. 4-10 4.2.3 Summary of Source Zone A .. ° 4-11

4.3 Source Zone B ... ............. .... 4-16 4.3.1 Cases B-1-l, B-2-1, B-3-1 .. 4-16 4.3.2 Cases B-1-1, B-2-1, B-3-1 .. 4-22 4.3.3 Summary of Source Zone B ... 4-22

i

TABLE OF CONTENTS

Page

4.4 Source Zones C and D .............. 4-27 4.4.1 Cases C-I-1, C-1-4, C-I-5 .. 4-27 4.4.2 Cases D-1-1, D-1-4, D-1-5 .. 4-34 4.4.3 Summary for Sources C and D. 4-34

4.5 Source Zone E ...................... 4-34 4.6 Intercomparisons .................. 4-41

Section 5 CONCLUSIONS ...... ..................... . 5-1

5.1 Tentative Conclusions ............. 5-1 5.2 Caveats ...... ................... 5-2 5.3 Implications ...................... 5-3

REFERENCES ...................... R­

Section 1

INTRODUCTION

1.1. TSUNAMIS

Tsuuamis are very long ocean surface gravity

waves generated by sudden displacemebts of large volumes of

water. While tsunamis have been generated by landslides

(both submarine and coastal) and volcanoes, the predominant

source of tsunamis is the rapid displacement of the sea

floor due to shallow focus submarine earthquakes. The

displacement of a volume of sea water (usually a vertical

displacement) moves the sea surface in the vicinity of the

displacement away from the quasi-equilibrium state known as

mean sea level (MSL). The action of gravity and buoyancy in

trying to return the surface to its equilibrium state

produces wave energy which propagates away from the dis­

turbance into the surrounding ocean. Tsunami waves propa­

gate very rapidly and can cross a basin the size of the

Pacific Ocean in less than a day.

In the open ocean, tsunamis are relatively

insignificant. They are low enough (amplitudes of no

more than 1-2 m) to be masked by normal sea and swell. But

if in their passage across a basin they have retained a

significant amount of energy and if they enter the coastal

zone of the basin margins in a region with suitable topog­

raphy, they can rise to great height as they encounter

shoreline areas. And these are the areas, of course, in

which they can do the most damage in terms of loss of human

life and property.

1-1

1.2

Fortunately, destructive tsunamis are not very

frequent. Every year several earthquakes produce waves

which leave measurable tracks on tide gauges, but only

rarely are major waves recorded. Since 1946, in the

Pacific Ocean, only five tsunamis have produced widespread

destruction far from their source. Localized tsunamis, in

which severe wave activity only occurs near the source, are

more common. But the threat of basin-wide events is always

present when large submarine earthquakes occur.

THE PACIFIC THREAT

Most tsunamis seem to be generated by shallow,

thrust type earthquakes, such as are associated with

the subduction of one tectonic plate under another.

Since many subduction zones are located on the margins

of the Pacific basin, most of the tsunamis recorded to

date have occurred in the Pacific Ocean. Figure 1.1

depicts the locations of epicenters of tsunamigenic earth­

quakes in the Pacific. We can see that epicenters tend to

cluster in several geographic regions: South America,

Alaska and the Aleutian Islands, Kamchatka and the Kurile

Islands, Japan, and the Southwest Pacific. The Southwest

Pacific source area rarely produces tsunamis which cause

serious effects throughout the entire Pacific region. But

tsunamis generated in the other areas do potentially pose a

Pacific-wide threat.

1-2

IV

000

if

Figure 1.1: Epicenters of tsumamigenic earthquakes in the Pacific Ocean during the period1900-1969. (Courtesy EDIS/NOAA.)

1-3

1.3 THE SOUTH AMERICAN THREAT

The west coast of South America is the site of

the subduction of the oceanic Nazca Plate under the conti­

nental South American Plate. The result is a band of

strong seismicity running the length of the continent and

roughly paralleling the axis of the Peru-Chile Trench. As

Figure 1.1 shows, tsunamigenic earthquakes have occurred all

along this zone. One of the largest tsunamigenic earth­

quakes of at least the last two centuries, the earthquakes

of 22 May 1960, produced motion of the sea floor along a

stretch of Chilean coast nearly 1000 km long and caused a

tsunami which killed approximately 1000 people throughout

the Pacific. Fortunately, such events have not occurred

often. But the continued seismicity of the region and its

history of frequent large* earthquakes of the type which

have produced tsunamis mean that this region continues to be

a possible source of destructive tsunamis.

1.4 PURPOSE OF THE STUDY

If we accept the two basic assumptions of this

study - (1) that tsunamis pose a threat to life and property

*Throughout this document the terms large, major, and great will be used to describe earthquakes. This is a loose application of the terminology of Isacks et al. (1968) and Kanamori (1977). A large earthquake has a Richter magni­tude (see section 3) greater than 7.0, while a major or great earthquake has a magnitude of at least 7.8-8.0. Note that a difference of one whole magnitude unit denotes a ten-fold change in earthquake energy.

1-4

throughout the Pacific, and (2) that the South American

coast is a likely source of tsunamis - then the purpose of

this study is quite easily stated: we plan to examine the

western coasts of Chile and Peru to determine what areas are

most likely to be the sites of large tsunami-producing

earthquakes, what types of tsunamis these earthquakes would

produce, and to what extent these tsunamis would pose a

threat to the rest of the Pacific region. The scientific

tools to carry out this plan are available. Somewhat

similar studies have been performed in recent years (see

Section 2), but this is the first time that this type

of threat analysis has begun to take into account the

historical seismicity patterns of potential source areas.

Having stated in general terms what this study

will attempt to accomplish, we will now lay out explicitly

what it will and will not do. This report will describe the

results obtained by using numerical models to provide

information about the characteristics of the tsunami wave

field (in terms of energy, elevation, directivity) as it

propagates away from the source area of an hypothetical

earthquake with specific characteristics (seismic moment,

rupture length, rupture width, displacement pattern, etc.)

which occurs in a certain location. This study will not

attempt to predict actual earthquakes and resulting

tsunamis. The uncertainties involved in putting together

reasonable bottom motions are so great that detailed agree­

ment between historic or future earthquakes and the possible

events outlined in this study could only be classed as a

coincidence. To the extent that the source motion scenarios

developed for this study are, in fact, representative of

those which could occur in a given area, the tsunamis

1-5

simulated in the study will bear a reasonable resemblance to

actual tsunamis which could be generated. Thus we will be

able to reach conclusions about the nature of the potential

tsunami threat posed by a given type of seismic event

without attempting to predict specific details.

The study will be carried out in phases. This

initial phase of the study focuses on the seaward portion of

the immediate vicinity of the earthquake zones. None of the

areas described in this phase (i.e., the areas within which

wave propagation is simulated) extend westward much beyond

15o-200 of longitude from the epicenter. The nature of the

modeling technique used is such that the generating area must be examined with fairly fine horizontal resolution

(1/30 (20') latitude and longitude, in this case), while

the propagation of the fully developed tsunamis across

the open Pacific can be modeled with coarser resolution.

Hence, this first phase constitutes the fine resolution,

near-source phase of the overall problem. Later phases

will draw on this work to follow the waves across the basin

to shorelines far from the source.

At this point we should also note that this

study does not address the situation of tsunamis striking

the coast near the source zone. This aspect of the tsunami

problem is quite important; indeed, it is near-source

effects which usually cause more tsunami damage than long

range effects. For example, the Colombian earthquake of

12 December 1979 caused severe tsunami damage in Ecuador and

Colombia but minimal waves at distant locations (Pararas -Carayannis, 1980; Herd et al., 1981). However, the near­

source tsunami problem requires a somewhat different

1-6

1.5

technique for modeling than is used for the open ocean

propagation problem. The two techniques are not compatible

enough to model both problems simultaneously.

STRUCTURE OF THE REPORT

This report is presented in four parts. The

first part (Section 2) describes common approaches to

modeling tsunami generation and propagation and provides

a detailed look at the wave model used here. The second

part (Section 3) describes the seismological evidence used

to develop hypothetical source motions to provide the impulse for tsunamis. The third part (Section 4) describes

the results of the various cases modeled in this study. The

last part (Section 5) draws conclusions on the basis of

these results and describes how the results can be used

in subsequent phases of the study and also how they can be interpreted for purposes of disaster preparedness and

planning.

1-7

2.1

Section 2

TSUNAMI MODELS

EQUATIONS OF MOTION

Since tsunamis are long wavelength ocean waves

it is possible to model their generation and propagation by

using equations of motion for long waves propagating in a

thin layer of water on a rotating sphere. The equations can

be simplified if we make the assumption that the processes

involved are linear. Ursell (1953) showed that, for long

waves in shallow water, the decision of whether or not to

use the linear form could be based on the value of a param­

eter, commonly referred to as U, defined by

h2 k 3U (2.1)

Here rL is the free surface elevation relative to MSL,

Xis the crest-to-crest wavelength of the waves, and h

is the water depth below MSL. If U<<l, linear equations

apply; if U>>I, non-linear equations apply. If U = 0 (1),

equations of the Boussinesq or Korto;weg-de Vries type, which

balance amplitude- and frequency-dispersion effects, are

required. The value of U for tsunamis in the open ocean is

on the order of 0.01 (Brandsma et al., 1975, 1976;

Garcia, 1976).

The linearized equations of motion and continuity

in spherical coordinates can be expressed as

atu - fv + gR-lan = 0 (2.2)

atv + fu + g(R sin e )-lan - 0 (2.3)

2-1

Bt(h+n) + (h4n) + (e sn e-1 86(U sin ) 0. (2.4)

The variables in the equations are defined as:

- displacement of free surface from MSL.

u - horizontal velocity component in * direction,

v - horizontal velocity component in e direction,

e - co-latitude North Pole),

(i.e., measured from 00 at the

- longitude measured eastward from 00 at

Greenwich,

t - time,

g - acceleration due to gravity,

h - depth of water below MSL,

R - radius of the earth, and

f - coriolis parameter (f = 2 Q cos e, where Q ­angular velocity of the earth).

The notation Bx denotes partial differentiation with respect

to the subscripted variable.

2-2

2.2

Note the lack of a vertical velocity component,

w, implying neglect of vertical accelerations. Note also

the presence in (2.4) of a ath term. This is the term

through which bottom displacements due to seismic motion

generate sea surface deformations.

EARLIER STUDIES

The use of linearized equations to study the

generation of tsunamis and their propagation out of the

source area is not a new idea. Garcia (1976) used a model

similar to that expressed in (2.2)-(2.4) to study the

variation in radiation patterns of tsunamis generated

by one specific type of bottom motion as the source location

was moved to different spots along the Peru-Chile Trench.

Brandsma et al. (1977) reported on a similar study, using

(2.2)-(2.4), to assess the potential threat to the west

coast of the United States due to, again, a single type

of bottom motion as the source location was moved to dif­

ferent locations around the Pacific margins. In both. of

these studies the source motion used was patterned, at

least in part, after the hypothesized pattern of the 1960

Chilean earthquakes, although the exact nature of Garcia's

source motion is not clear. The source motion used by

Brandsma et al. constitutes an earthquake several times more

energetic than the Chilean event. Both of these studies

represent "worst case" studies of the type used in making

engineering decisions for zoning, power plant construction,

harbor design, etc. They were also concerned primarily with

the threat to the west coast of the United States.

2-3

The purpose of this tsunami hazard assessment

study, which in total will include the present near-source

study and companion studies of far-field hazards, is to

supplement the worst case approach with an examination of

the threat posed by more probable events. This is in

keeping with AID's mission of disaster assistance. This

series of studies is not designed to help engineers develop

standards for construction of seawalls, piers, etc. In­

stead, the goal is to help civil authorities to assess the

types of hazards likely to occur and .tb aid in their plan­

ning for mitigation of effects prior to the event and for

emergency action during and after.

2.3 SEAWAVE

The model used in this study is a slightly

modified version of the SEAWAVE code developed by Tetra

Tech, Inc. for tsunami modeling (Brandsma et al., 1975,

1976). This model was used successfully to simulate the

tsunami resulting from the 28 March 1964 Gulf of Alaska

earthquake and to evaluate the threat to California coastal nuclear power plants from locally generated tsunamis.

2.3.1 Numerical Solution Scheme

The code uses a finite-difference algorithm to

approximate solutions of (2.2)-(2.4), subject to suitable

boundary conditions. The numerical scheme is explicit,

time- and space-centered, and time- and space-staggered.

The details of the scheme are not described in this report.

The interested reader may consult Brandsma et al. (1975) for

details.

2-4

2.3.2 Boundary Conditions

The version of SEAWAVE used for this study requires two types of boundary conditions: shoreline

conditions and open-sea conditions.

Since in this phase of the study we are not concerned with Drsdicting coastal* runup and inundation zones, we cp9 require that waves striking the coasts be

fully reflected. This can be expressed, in terms of the

velocity component normal to the shore, as

un = 0 at land boundaries (2.5)

Setting the normal component of velocity to zero at the

coastal boundary implies that no wave energy crosses the

shore onto dry land.

At open-ocean boundaries (that is, when the

region defined by the model grid ends not on dry land

but in water) we require that wave energy approaching the

boundary from within the model area pass through the bound­

ary without reflection. This is referred to as a radiation­

type condition. One way that it can be expressed is

t'n = -c[R-1 cos 6) e + (R sin e )-l(sin 6 )an]. (2.6)

Here c is the wave phase speed, approximated by

c = [g(h+n)]i/ 2, and 6 is the angle of incidence between the

direction of wave propagation and the opeh boundary.

2-5

<1

We should note that the numerical method used

to implement (2.6) is based on simplifying assumptions which lead to approximate solution,. These solutions are

not completely free of reflections back into the grid, as

will be seen in contour plots of surface wave fields. More complicated forms have been suggested (Wurtele et al., 1971;

Bennett, 1976; Hebenstreit et al., 1980), but the form used

in SEAWAVE is sufficiently accurate for the purposes of

this study.

2.3.3 Bottom Displacements

The heart of this application of SEAWAVE is the speciiication of the submarine bottom motion which displaces

a volume of water and sets the surface waves in motion. The

ground motion in the source area can be specified in a number of ways, depending on the uscr's assumption about the tsunami generation process. If we assume that the water

column reacts nearly instantaneously to bottom motion, then the displacements (either as an analytical function of

(0,e) or as arbitrary values specified at each grid point in the source area) are simply added to the bottom depth so

that the resulting depth is

d(O,e) = h(O,8) - e(O,e), (2.7)

where e(@,8) is the ground motion taken so that uplift

implies d<h and downthrust implies d>h. If this approach is used, then the initial sea surface (usially taken to be

at rest at MSL) is adjusted so that

2-6

n e(,e).* (2.8)

A second approach depicts the sea floor motion

as occurring over a finite time period (longer than a

single time step of the model) and allows the sea surface,

initially undisturbed, to adjust to the movement.

If the "instantaneous response" approach to

generation is taken, then the model requires specification

of the final displacement due to fault motion in the source

area. This can take the form of a table of displacements at

grid points within the source area or an analytical function

for displacement as a function of horizontal distance from

the main fault line. This latter form allows a good deal of

flexibility in the positioning of the source since all

displacements are located in relative coordinates. The

information requir-!ments for this generation approach are

limited to the orientation of the fault and the uplift

pattern.**

* We seem to be saying that depth below MSL is positive, while elevation above MSL is also positive. This apparent confusion of coordinates does not affect the model equa­tions, which can be looked on as predicting the time vari­ation of the height of the sea surface above the bottom, i.e., h + n.

**A subroutine, WARP, in the current version of SEAWAVE

specifies the bottom displacement as a roughly elliptical area with elevations along its major axis given by a Gaus­sian and elevations along its minor axis given by x exp(- x ), where x is the normal distance from the major axis. The pattern can be a dipole (ice., an area of up­lift and a mirror image area of down thrust) or a positive/negative monopole.

2-7

If the "time evolution" approach to generation

is taken, then the information requirements increase.

In addition to the orientation of the faulting and the

pattern of displacement, the model must also be supplied

with information concerning the location of the epicenter,

the velocity of fault propagation away from the epicenter-,

and the time over which uplift occurs. The program, as it

exists at present, does not contain a time varying bottom

displacement algorithm; one would have to be developed.

This would allow for such refinemerts as variable rates of

uplift, if these were deemed desirable. This type of

refinement has not been used in this phase of the study.

Most previous large-scale tsunami simulation

studies have employed the instantaneous response approach

with remarkable success. The time evolution approach has

largely been restricted to studies of near-field (i.e.,

within the immediate vicinity of the source) behavior,

without any attempt to simulate specific historical events

or specific geographical locations. Some seismological

evidence, (Kanamori, 1975) however, does seem to indicate

that long period (>100 sec) motions can impart large amounts

of energy to the water column. (This is longer than the

time step used in this study.) We employ the instantaneous

response technique in all but one case examined in this

report.

2.3.4 Bottom Topography

Sea floor topography plays an important role in determining how the energy contained in the tsunami spreads

out into the open ocean. Thus the model must employ values

2-8

of h(€,e) to obtain reasonable simulations. Because of

computational considerations, the bottom depth data must be

provided on a regularly spaced grid; that is, the spacing in

degrees latitude and longitude between adjacent points must

be uniform (which does not imply uniform physical distances

between points). In addition, the spacing should be as

small as possible in order to ensure that the model can

resolve adequately waves throughout the tsunami wavelength

and period range. We have chosen a resolution. of 20' in

both latitude and longitude for the. model grid. Spacing

this fine will allow resolution of wavelengths as short as

roughly 60 km, or, to put it another way, a wave 200 km long

will cover 6-.7 grid intervals per wavelength.

Bottom data with 20' resolution for the southeast

Pacific Ocean was not readily available in digital form at

the time of this study. Instead, we obtained fine reso­

lution bathymetry charts from the Naval Oceanographic

Office* and hand-digitized data at the needed intervals.

An example of the NAVOCEANO charts is presented in Fig­

ure 2.1. The overall region modeled ranges in latitude

from 0oS to 400S and in longitude from 70oW to 900W.

Note that these are reckoned in the normal fashion as

north/south of the equator and east/west of Greenwich,

rather than the scheme used to obtain eand 0 for SEAWAVE.

This model area is shown in Figure 2.2. The continental

outline as represented by the 0 m position in the digitized

*Charts SP-3A and SP-6A/SA-3A were obtained from the World Bathymetry Unit, NAVOCEANO, NSTL Station, Bay St. Louis, MS 39522.

2-9

\I

\. " .. . . . ..•.

". ..

too

Figure 2.1: Example of bottom topography chart used to

obtain depth field in this study.

2-10

. .. .

I

...­± j j.-. --

.-- -- ---. . .-i-4.. .

"-I---­ *--- .-- t

I

-.

!

--.

I

4"

I

-- -. 4'-j

-

-.-­

- "-'I-!-­f' -'-­t--.__

. .. .. ---I_

*---.------t-.----­4 --­ i---

-11-

-­

-~i-­

-- ---

r rtg

f

e

S

...o -I--,

- .

-­- - --­ 1- '. - - - -

1,SES~-

111"1NNM-­-.

1 , .- i

to - - -­

so*

"M~AIM~ PforcliCN

Figure 2.2: Overall simulation grid used in this phase of the study. Approximate axis of the Peru-Chile trench is shown by the solid line. Individual source motion cases use subsets of this grid. The two major offshore ridge systems are shown in rough outline also.

bathymetry set is denoted by the cross hatched line. The

seaward line denotes the grid point of deepest depth along

each parallel of latitude. This is a rough indicator of the

axis of the Peru-Chile Trench, although it does not always

represent the absolute axis of the trench. This would

only happen at those places where the deepest portion

of the trench fell at a grid point. The actual axis is

usually within +20 km of the line.* The line of deepest

model depth could fall on the landward or seaward slope of

the trench, or, in regions where the t.rench is very narrow

(<30 km wide),, may not actually be in the- trench. We feel

that this lack of resolution in the depth field around the

trench does not greatly effect the results of the study and

thus have not altered the grid or the topography to include

all the deepest portions.

2.4 PROCEDURE

The procedure followed in this study is as

follows. Sources for possible tsunamigenic earthquakes

were chosen on the basis of seismological evidence; reason­

able bottom displacement patterns were developed for each

source zone; the bottom displacements were used as initial

conditions (or, in the time varying case, as bottom boundary

conditions) for SEAWAVE; the resulting wave field in each

case was allowed to propagate outward from the source until

it had propagated out of the model area; and finally the

wave patterns (both the whole field and time histories at

specific points inside the model area) were analyzed for

trends in energy directivity. Time variations in wave

2-12

height along the outer (open ocean) boundaries of the model

area were saved and will be used as input conditions in

later phases of the threat assessment study.

The basis for the choice of sites and motions

is described in Section 3. The method of analysis and the

results are described in Section 4.

2-13

3.1

Section 3

CHOICE OF EARTHQUAKE SITES AND SOURCE MOTIONS

In order to specify the bottom displacement needed

to drive SEAWAVE we must supply the location of the source

area, type of focal mechanism, and energy level in the

earthquake. Section 3.1 describes the choice of sites

in terms of seismic gap information. Section 3.2 shows

how historical data on the seismicity of the region is

used tu specify focal mechanisms. Section 3.3 describes

the use of historical data and seismic theory to estimate

the energy released by various size earthquakes. In

Section 3.4 all of this information is consolidated to

provide the various source scenarios which will be used in

this study.

SITE SELECTION

The Pacific coast of South America has a long

history of strong shallow seismic activity caused in large

part by the subduction of the oceanic Nazca Plate beneath

the continental South America Plate (Stauder, 1973, 1975).

A number of these earthquakes have generated tsunamis.

Silgado (1978) described data from 21 tsunamigenic earth­

quakes which occurred in the region between 1749 and

1968. One of these events, the earthquake of 22 May 1960,

is among the largest seismic events ever recorded.

The Peru-Chile Trench, which is the result of

the subduction process, forms the seaward limit for a band

3-1

of intense activity all along the coast. Analysis of histor­

ical seismicity patterns of the region indicate several

areas with strong potential as sites of large earthquakes.

Since this zone coincides with the zone of tsunami-producing

earthquakes, we will use these locations as the sites of the

hypothetical sources used to drive the SEAWAVE model.

McCann et. al. (1978) examined the plate bound­

aries of the world for evidence of the existence of seismic

gaps, which they define as "any region along an active plate

boundary that has not experienced a large thrust or strike­

slip earthquake for more than 30 years." As two plates

collide, strain tends to increase along the interface zone.

If strain release does not occur over a long period of time,

by either seismic or aseismic mechanisms, this may indicate

the accumulation of tension to the point that a large

earthquake will occur-to release the stress. The lack of.

large seismic events may thus be evidence of long-term

stress buildup.

In their survey of the South America-Nazca plate

boundary McCann et al. indicated several areas between 00

and 450S as likely gaps (see Figure 3.1). The first gap,

spanning the coast from 0o-90S, has been quiet for so long

(roughly 400 years) that large earthquakes are highly

unlikely ualess the return period for earthquakes is

extremely long.

The region spanning roughly 16o-240S is postu­

lated to be an extremely likely candidate for a large

earthquake. The last large earthquakes in this zone

3-2

'V

' / I

A GREAT EARTHQUAKESMAX RUPTURE LENGTH

"'a ABOUT 150KM

NO KNOWN GREATCANEGIE RIDGE E..ARTHQUAKES.INFREQUEI:...:

5. ILARGE SHOCKS PM

0.o C '7A ; , *00

46er0

I IDI

50")

• r65085' 80 750 70'

Figure 3.1: Potential seismic gaps along the western coast of South America (from McCann et. al., 1978).

3-3

occurred in 1868 (northern end) and 1877 (southern end).

Both events produced destructive tsunamis (Pararas-

Carayannis and Calebaugh, 1977). McCann et al. assign this

zone "highest seismic potential."

Two smaller gaps exist farther south. Both

are assigned moderate seismic potential levels because of

recent activity. The first, with a recurrence period of

roughly 40 years, is the zone from 25o-26oS; the second, with

a somewhat longer period of 85 years, is the zone south

of Valparaiso, Chile along 34o-35oS.

McCann et al. feel that a long existing gap south

of Callao, Peru (120S) was filled by a great earthquake

(magnitude of 8.1) in 1974. B. Brady (Bureau of Mines) and

W. Spence (U.S. Geological Survey) have amassed a body of

evidence which indicates that this event was not, in fact,

gap-filling, but instead was one in a long series of precur­

sors to a future major earthquake (Brady and Spence, various

unpublished memoranda and personal communications). Brady

has developed a theory of earthquake mechanisms which

leads him to ascribe an extremely strong seismic potential

to two adjacent zones. The larger zone follows the Peru-

Chile Trench from 120S to roughly 280S. A gap-filling

event in this areW-would have an extremely high energy level

(Kanamori magnitude,* Mw = 9.8). The smaller zone runs

northward from 12oS-8oS. A gap-filling event in this region

*See Section 3.1.3 for a discussion of the implications of this magnitude scale.

3-4

would be a lesser magnitude (Mw = 8.8) great earthquake.

Brady and Spence indicate that if the great earthquake in

the southern zone occurred it would be followed several

months later by an event in the northern zone.

Since the difference of opinion over the existence

of gaps from 8oS-15oS is unresolved, we will assume that

they do indeed exist. Thus we will model possible tsunami­

genic bottom motions in five source zones along the South

American coast. These are listed in Table 3-1.

Figure 3.2 depicts the various source regions

used in this study.

3-5

TABLE 3-1

Potential Tsunami Generation Sites

Location Latitude Range Seismic Potential Source

Southern Peru- 160 S-240 S High McCann, et al.

Northern Chile (1978)

Capiapol Chile 250-260S Model.ate o

Valparaiso, Chile 34o-35oS Moderate

Lima, Peru 12o-28oS High Brady and Spence

and

80- 120 L.igh o

3.2 FOCAL MECHANISMS

While no one type of focal mechanism can be

applied to all possible earthquakes in the gaps outlined in

the last section, we can draw some conclusions about the

likely nature of these events based on known historical

data.

Tsunamigenic earthquakes almost always display

shallow focus thrust-type faulting. Examination of the

tsunami catalogs (lida et al., 1967; Pararas-Carayannis

and Calebaugh, 1977) show that most tsunamis are produced by

earthquakes with focal depths no greater than 50 km.

Vertical sections of seismicity in this region (Stauder,

1973, 1975) show that most submarine earthquakes are indeed

shallow.

- Kelleher et al. (1974) presented an hypothesis

connecting the width of the interface between the over­

thrusting and underthrusting slabs of lithosphere involved

in subduction and the maximum size of ruptures. As

Figure 3.3 shows, the width of the interface depends in part

on the angle of dip between the two slabs. Thus a wide

interface implies shallow dipping plates. This hypothesized

surface projection of the interface along South America

appears in Figure 3.4. These estimates lend creedence, to

the assumption of shallow dip angle faulting along the

coast. The dip angle seems to vary between 100 and 300

(Stauder, 1973, 1975; Barazangi and Isacks, 1976).

3-8

-VI

t'...f et'

Figure 3.3: Interface area between overthrust and underthrust slabs of lithosphere at a subduction zone. (a) Perspective view. (b) Side view showing relationships among width of interface, zone of shallow earthquakes, and angle of dip. (Kelleher et. al., 1974.)

C SON

00

SOUTH AIMERICA

200

OCEAN A

* 300

- . . 40

100 KM

I *, 50"

90'W 80" 60

Figure 3.4: Estimated width of interface along western South America. (Kelleher et. al., 1974.) 3-9

3.3

McCann et al. (1978) stated that most focal

mechanisms in the region show faulting of the thrust

type. That is, the net motion results in the overthrust

plate rising vertically relative to the underthrust plate.

The usual direction of the descending slab is roughly

ENE.

For ease of calculation we will assume that the earthquake focal depths will be 20 km. The source

zones will be rectangular and oriented so that the rupture

extends parallel to the trench axis. The width of the

zones will correspond roughly to the interface widths

of Kelleher et al. (1974) and the lengths will be consistent

with those of similar events in the vicinity of the source.

Dip angles, when used, will vary from 100 to 300.

EARTHQUAKE ENERGY

The common means of conveying a sense of the

energy released by an earthquake is the assignment of

a magnitude. This is normally based on the spectral

amplitude of the 20 second period surface waves which

radiate from the source. This magnitude, referred to

as Ms,* is a sufficient descriptor to small and inter­

mediate earthquakes, where Ms < 7.0. However, for large

earthquakes (Ms > 7.0) the use of Ms can lead to con­

fusion, because in these events a good deal of the energy

is released at periods longer than 20s. The result can be a saturation of the Ms scale - Ms approaches a limit even

though seismic moment (Mo, based on the spectral amplitude at very long periods) increases. An upper bound on Ms

*Ms is the magnitude scale usually referred to as the Richter or Gutenberg-Richter magnitude, although the empirical constants used to obtain Ms have been refined from their original study.

3-10

implies a maximum "size" for earthquakes which is not

reflected in a similar limitation on Mo (see Figure 3.5).

Since tsunamigenic earthquakes usually have Ms values greater than 7.0 this confusion in the use of Ms is a

matter of some concern.

Kanamori (1977) argued that Mo is a much better

indicator of seismic energy in major earthquakes than Ms because it is based on the amplitude of the spectrum at

periods much longer than 20s. He proposed a new magnitude, Mw, defined as

Mw = (log Mo - 16.1)/1.5 . (3.1)

This scale is not susceptible to saturation and for small

earthquakes Mw Ms. Table 3.2 lists a number cf tsunamigenic events for which Ms, Mo, and Mw have been

calculated. Note that the largest Mw value is assigned to the Chilean earthquake of 22 May 1960. This event had a seismic moment of over 1030 dyne-cm. Chinnery and North

(1975), in their correlation of Mo versus frequency of occurrence for great earthquakes, indicated that events of this size should have a return period of 15-20 years. Their

empirical relationship implied that events with return

period of 50-100 years would have moments in the range 2-8 X 1031 dyne-cm. This provides an upper limit to the Mo values of the hypothetical earthquakes.

3-L1.

I-.. S..

I '. ."

Figure 3.5: Estimates of Mo as a function of Ms .

The solid line is a visual curve fit.

(Chinnery and North, 1975.)

3-12

Date Latitude

18 Apr 06 38N

17 Aug 06 33S

11 Nov 22 28.5S

3 Feb 23 54N

1 Sep 23 35.3N

7 Mar 29 5LN

3 Jun 32 19.5N

2 Mar 33 39.3N

10 Nov 38 55.5W

24 Aug 42 153

7 Dec 44 33.8N

20 Dec 46 32.5N

22 Aug 49 53.8N

4'Mar 52 42.5N

4 Nov 52 52.8N

9 Mar 57 10 Jul 58 58.6N

6 Nov 58 44.5N

4 May 59 52.5N

22May 60

13 Oct 63 44.8N

28 Mar 64 61.1N

4 Feb 65

17 Oct 66 10.7S

16 May 68

11 Aug 69 43.6N

3 Oct 74 12.3S

TABLE 3-2

Tsumani-Prodining Great Erutquakes for which Mo is Reported (Kanamori, 1977)

Longitude Location Me

123W San Francisco 8.25

72W Chile 8.4

70W Chile 8.3

161E Kamchatka 8.3

139.5E Kanto 8.2

170W Fox Island 8.1

104.3W Mexico 8.1

144.5E Sanriku 8.5

158W Alaska 8.3

76W Peru 8.1

136E Tonankai 8.0

134.5E Nankaido 8.2

133.3W Alaska 8.1

143E Tokachi-Oki 8.3

159.5E Kamchatka 8.25

Aleutians 8.25 137.1W Alaska 7.9

148.5E Kurile Islands 8.7

159.5E Kamchatka 8.25

Chile 8.3

149.5E Kurile Islands 8.1

147.6W Alaska 8.4

Aleutians 7.75

78.6W Peru 7.5

Tokachi-Oid 7.9

147.8E Kurile Islands 7.8

77.8W Peru 7.6

3-13

MW (1027 dyne-=l)

10 7.9 29 8.2

69 8.5

37 8.3

8.5 7.9

6.7 7.8

15 8.1

43 8.4

28 8.2

27 .8.2

15 8.1

15 8.1

15 8.1

17 8.1

350 9.0

585 9.1

29 8.2

40 8.3

26 8.2

2000 9.5

67 8.5

820 9.2

125 8.7

20 8.1

28 8.2

22 8.2

15 8.1

The use of Mw to specify the magnitude of hypo­

thetical events is especially attractive because of the

relationship of Ho to other important parameters. Abe

(1975) showed that, by making several approximations about

large circum-Pacific earthquakes, an approximate relation­

ship can be established between Mo and the area, S, of the

fault:

Mo = 1.23 X 1022 S3 /2 dyne-cm, (3.2)

where S is expressed in km2 . Essentially three assumptions

are required to arrive at this relationship:

(a) stress drop in large earthquakes is total

(i.e., all the accumulated stress is relieved

in a single event),

(b) stress drop is relatively constant in these

earthquakes, and

(c) the ratio of fault length (L) to fault

width (w) is roughly constant at 2:1.

Kanamori (1977) pointed out that the evidence for

or against complete stress drop in major earthquakes is

inconclusive; Purcaru and Berckhemer (1978) argued strongly

that stress drop varies significantly from event to event;

and, as Figure 3.6 illustrates, the L vs. w relationship is

by no means exact. Despite these difficulties, however,

(3.2) is probably accurate enough to allow for reasonable

modeling. The degree to which Mo and S are related can be

seen in Figure 3.7.

3-14 ,~

100

SOs

£ @.50 Paii

• Peeffis5 .4. • Jepeis benes

, Nerth Ameris

I, I 1, , V ,I I I I 1 11 5 I0 L O?km) .I0 SW I000

Figure 3.6: Fault length L vs. fault width w for large earthquakes (Abel 1975).

'" 1 ... .. 10 6" 1 I a'"all I" a of

300

02 /" //o0A.ulla 8.0

/Tokacmd/6

E Nonokoido,,b

,o2 ' / ....,'-/oa - ./ Ivli,'on " C Ner / //_..

"=10kul // o

/oWakas. Day •0 PocificS o / / Japanese Islnds "6.5 1025 / orkfltld/ . North America

/£Truckee.. -

1024 Fernand -

0 102 Japa1 Isl s 10

Fault Area (kin2 )

Figure 3.7: Relationship among fault area, seismic moment, and stress drop for large earth­quakes. (Abe, 1975).

3-15

A second important parameter in the specification

of seismic energy is the vertical displacement of the sea

floor. This implies a knowledge of both the amplitude and

the horizontal pattern of the displacement. Abe (1975)

showed that the mean slip displacement over the fault

could be obtained from

D Mo/( S) (3.3)

where ) is the rigidity of the earth's crust (roughly

5x10 1 1 dyne/cm2 ). If we substitute (3.2) into (3.3) and

adjust coefficients so that S is expressed in km2 and D in

cm we find

D - 2.46 S1/ 2 . (3.4)

This equation implies that the mean displacement.

of the fault depends only on the area displaced. While this

may not be a satisfying assumption, it will serve to provide

a starting value for displacements. Further descriptions of

the displacement values used are provided in Seciton 3.4.

We now have the tools available to specify the

energy (and thus the displacement) of our model earth­

quakes. We can obtain reasonable estimates of the source

areas and, by accepting all of the assumptions which go into

(3.2), calculate D directly from (3.4). Or we can specify

both the area and reasonable values of Mo and use (3.3).

Kanamori's Mw will allow us to ensure that the Mo values are

realistic.

3-16

3.4 SOURCE MOTIONS

As we indicated in an earlier section, the purpose

of this study is not to predict what earthquakes will

appear in the vari.ous selected source areas. Instead, we

have used available seismic source theory and information

about seismicity patterns to postulate generalized features

of possible events. The source motions chosen for this

study may not be accurate reflections, of what earthquakes

would really do to the sea floor, but they should have

characteristics representative of the earthquakes likely to

occur in the various zones.

The first parameters to be specified were the

length and width of the fault zone. The upper limit to the

length of the fault was taken to be the entire length of the

seismic gap. Thus Site A, located from 8o-12oS, would

have a maximum length of roughly 450 km. Historically,

however, rupture zones in this area are no longer than

150 km (see Figure 3.1). Site A, then, was broken into

three subzones, each 150 km long. A fourth source area,

equal to the full length of the gap, was also modelled.

Fault widths were estimated from the theory of

Kelleher et al. (1974) depicted in Figure 3.4. In most

cases the interface width corresponded roughly to the

distance along a normal between the trench axis and the

shore. Motions on dry land do not effect the computations

in SEAWAVE. The average interface width for Site A is

roughly 150-160 km.

3-17

When estimates of w and L are substituted into

(3.2) and (3.4), estimates of seismic moment and average

For the source withvertical displacement can be obtained. Mo-4.2x10 2 8

the resulting values arew=l50km, L=150 km,

This value of seismic moment resultsdyne-cm and D=3.7 m.

in a magnitude of Mw=8.3.

Values of L, w, MO, -, and Mw calculated in this

way for the various sources are listed in Table 3-3 and

in this study.Figures 3.8a-b show the source zones used

Sites A and B have been subdivided into three smaller zones

in keeping with historical evidence (although for each site

one gap-long source motion is also considered.) Source

zones C and D are both relatively small, and so all tests

were based on the assumption that the entire gap was in­

the other hand, is extremelyvolved. Source zone E, on

large. This zone was not subdivided for two reasons.

Events in zones B and C already cover events in most of the

portion of the large rupture zone from 160-280Ssouthern

thus did not need to be repeated. The orientation ofand the zone, from 12°-16OS, isthe northern portion of

similar to that of all of the A- series runs and run B-1.

Results from these earlier tests showed that most of the

wave energy radiated toward the southwest, away from areas

of concern. Thus, to avoid needless duplication, events in

this zone were treated as single gap-long motion.

The first bottom displacement scenario applied

to the source areas consisted of a uniform simultaneous

uplift of the entire region with displacement D. This case

is.in many ways the most difficult one used in this study.

A uniform displacement is basically a step function imposed

3-18

Table 3.3 PARAMETERS OF TEST CASES

Test Code L(km)

A-1 150

A-2 150

A-3 150

A-4 450

B-i 300

B-2 300

B-3 300

B-4 900

C-1 120

D-i 150

E-1 2000

w(km)

150

150

150

150

100

100

100

100

125

125

150

S2 (km2 )

2.25x10 4

2.25x10 4

2.25x10 4

6.75x10 4

3.0x104

3.0x104

3.0x104

9.0x104

1.5x10 4

1.88x104

3.00x105

3-19

Mo(lO2 7dyne-cm) Mw D(m)

41.5 8.3 3.7

41.5 8.3 3.7

41.5 8.3 3.7

215.7 8.8 6.4

63.9 8.5 4.3

63.9 8.5 4.3

63.9 8.5 4.3

332.1 8.9 7.4

22.6 8.2 3.0

31.6 8.3 3.4

2021.0 9.5 13.5

--. ..

fT -

.

-qo'S 'ips

91 1e rr-vI

--- I- I.--..I I .. -I-----.........

- _

'II

_ - _ -

V1 11 I Teof I I I I t11 0T TI*

I.- N-

1 v

- _.

. ..

1 So

-1 rv so

n ,

.... ..... --Site .. , LI..8- A / i L L i A .-. L . L L L ,,,Lw

. .

"MAWR'( PROkCTifld . .. gL

Figure 3.8a: Locations of source zones and subzones for Sites A-D.

wo yj* - lop so go'r-f

I I r I r r v 1"- rM

- °)-" - =--. " - - -Is.

I-IV

.. . .. I.. .A t L.ja7

7se

C,. ..

Figure 3.8b: Source zone for Site E.

on the sea surface. Its effect is to impart wave energy

across a wide band of frequencies; other, more realistic,

less uniform displacement patterns tend to have a much

narrower frequency band width, which will excite fewer wave

periods, and, presumably, produce less broadly energetic

tsunamis.

Two additional tests with uniform uplift were

identical to the firstcarried out at Site C. These were

case, except that the specified displ.acements were 2D and

5U. The only differences noted among the three runs were in

the wave amplitudes (see Section 4 for further details) and

similar tests for other zones were not carried out.

The second. ground displacement pattern applied

zones called for a roughly triangular uplift.to the source

The highest elevation was parallel to the axis of the

onrupture, with elevations dropping off linearly either

side of the axis. The slope of the triangle was chosen so

that the mean elevation was approximately D. Side and plan

views of this pattern are shown in Figure (3.9).

A third source motion applied was based on the

pattern used in subroutine WARP in SEAWAVE. The plan view

of the pattern (see Figure 3.10) shows a series of imbedded

ellipses with major axis parallel to the fault and minor

axis normal to it. The maximum elevation was chosen so that

the approximate potential energy imported ot the water was

case.comparable to that imported in the uniform uplift

An additional set of two or three source motions

for this phase of the study.had originally been planned

3-22

PLA

Figure 3.9: Triangular displacement pattern.

°lI

°U

Figure 3.10: Elliptical displacement pattern (posi­tive side only) generated by WARP

(Brand~ma et. al., 1978).

3-24

AU

These would have been derived from the fault displacement

model of Savage and Hastie (1966) and would have taken into

account not only width, length, and mean displacement but

also focal depth and dip angle of the earthquake. Unfortun­

ately, the algorithm was not operational in time for the

completion of this report. Once the algorithm is working

satisfactorally it would not be difficult to supplement

future phases with additional runs based on this model.

3-25

Section 4

MODEL RESULTS

4.1 METHOD OF ANALYS IS

One of the major problems in presenting results

from a set of tests such as this is the mass of data gen­

erated by any single test. We have simplified theitask to

some extent by concentrating on two forms of presentation:

contours of the surface wave field at specific times after

the earthquake and time series and power spectra of wave

elevation at specific points in the modeling region. By

combining the information from these presentations we

were able to draw some tentative conclusions about the

directionality of tsunamis generated in the different source

zones.

SEAWAVE allows the user to print out the surface elevation field at any time step(s) desired during the

simulation. We chose to print at 15 time step (15 min) intervals. However, because contouring of the fields had to be done by hand, results were actually plotted only at one

or two times. Entire .iave fields were not contoured, only the leading crest and, possibly, the secondary crest if it

was sufficiently coherent. Intermediate troughs were not contoured in order to keep the plots from getting too

confusing.

Values of wave elevation at each of several spec­

ified locations were stored at every time step. Simulations

for sources A-D lasted 300 time steps (5 model hours), while

4-1

4.2

those for source E lasted 350 time steps. The resulting

time series were operated on by a fast Fourier transform

(FFT) algorithm to determine the amount of wave energy

contained in frequency bands ranging from the very low

(= 5 x 10-5 cycles/sec or a period of 300 min) to the very

high (= 8 x 10- 3 cps or a period of 2 min). These power

spectra impart two important pieces of information.

Comarisons of the energy level in various bands indicate

which wave periods are most strongly excited by the source

motion; comparisons of overall energy. levels between sta­

tions indicate which stations receive the most energy as the

waves radiate away from the source.

A third form of output, not presented here, was

also obtained. We stored, on magnetic tape, time series of

wave elevation at every time step for points all around the

perimeter of each model zone. These will be used as forcing

boundary conditions to drive the basin-wide propagation

models used in the next phase of this study.

SOURCE ZONE A

Source zone A was divided into three subzones.

Figure 4.1 shows the zone and the locations of the five

points at which time series were recorded. Six simulations

were run for this zone. The first four,* A-i-1, A-2-1,

A-3-1, and A-4-1, consisted of uniform uplift with areas and

Each run is assigned a three character code. The first

letter refers to the source zone, the second to the subzone if any (default of 1 for the small zones), and the third to the displacement pattern (1 = uniform, 4 - triangle, 5 - ellipse). Only case E violates these guidelines.

4-2

--

.jW --- v-- t Ia.. 40... ....I .. . . . ....... . ...... ..... . . .. ... ....W! I'I

'-I-- .. . ..-- 7-- - - - ­... .­ -t.f.7.7.7.

---

C4) 7- -'-AL.J- 1. .... .. ... A91aI-A4 -- . ......

up... M.1 .. ... ... ILA LL

Figure 4.1 Source Zone A with Recording Stations

elevations as indicated in Table 3.3. Case A-4-2 used

subroutine WARP to specify the source motion, depicted in

Figure 3.10, over the whole area. Case A-4-3 was based on

the triangular uplift over the entire zone. Since runs

based on the subzones resulted in greatly reduced wave

activity, variations .inbottom displacements in these cases

were not performed.

4.2.1 Cases A-1-1, A-2-1, A-3-1

These three cases consisted of relatively small,

localized events. All three faults were oriented in the same direction relative to the coastline. The average

estimated potential energy imparted to the water from the

three events was 2.13 x 1022 ergs.* Surface elevation

contours at 60 min showed basically the same patterns (Figure 4.2a-c), with the central wave crest moving toward the southwest. All three wave fields showed some distrup­

tion due to the presence of the.Carnegie Ridge at about 50S. Case A-3-1 showed disruption to the south in the

vicinity of the Nazca Ridge.

Time series at point 6 are similar, although by no

means identical (Figure 4.3). Amplitudes at this station,

which is in the path of some of the highest waves in this

set of cases, range from 40-60 cm.

Power spectra for the five stations for base A-2-1

are shown in Figures 4.4a-e. They are arranged in order,

Estimated potential energy is calculated by numerical

integration of 1/2 g 2dS over S, the area of uplift.

4-4

_ _

•.I . . .....1 ....- ... . -­. ..... I - .-.......

'----l-----I-----i.---... + •­-- 4 .,... ----F: I'

... J&1, 1. r so so-s

Figure 4.2a Surface wave contours for Case A-i-1 at 60 min after the ground motion. Contour interval is 10 cm.

,,,. .' "i l'M" 7".. ~ ~ ' " ] -I i S"~- ­" P'" W, . r .. . 0 I Ws ^G IT.-,,-'- ,-,-,.-.- ­- "--.-" -'- , . ­- gem

7 - .. . . -" ' - ­-I. .. .. ! .. . . "

1V .

CAIE'.LAIlP AJL LA--LAd

Figure 4.2c. Same as 4.2a except for Case A-3-1

Time (Him 2

1.5

-0.5

TIME (Mimi

0.5

e.g,

TIME tHiN)6.55

0.0 ,,t I *.

LLT; 4,71.4 kOLN 16.£?

Figure 4.3 Time series of wave elevation at station 6 for cases A-l-1(a),A-.2-l(b), and A-3-l(c). Wave elevation is in meters.

4-8

~~c 5

IOPE

Figure 4.4 Power spectra, at the f ive monitorig stations

based on time series from Case A-2-1.

4-9

0'Y

%led S

........

.... _~~ -

....

-j

,g~g . . . ..,u.

_ ... ..-- ---- -__-__*1_ .....

t- -I.. . .. .

- -12....

" ; 1 . .

----­--...--

I'.

, -s

t.. .. +. IT i4.. , ''- . <

-l

"

!

-

- I

77-,2 ..

b

....... . .-­

- fr i as..

a 4 2. . i

e 4.2b. Sam. as 4.2b except for Case A-2-1

from north to south along the arc formed by the stations.

Stations 6 and 10 showed generally higher energy levels than the other three, presumably the result of wave directional­

ity toward the southwest. This pattern is typical for these three cases. Energy levels for case A-3-1 are slightly

higher than for the other two.

Before we continue, we need to say a word about these spectra. Since tsunamis are .ssentially transient

phenomena, time series are necessarily. of limited duration.

Therefore, in a record five hours long, a wave recorder

would only see five 60 min period waves. This low resolu­

tion of some data leads to "spiky" spectra at frequencies lower than about 10- 3 cps. Thus comparison of individual

peaks between spectra can be quite misleading. For this

reason we have chosen to plot spectral densities averaged

over five bands and positioned at the midpoint of the

averaging window. This serves to smooth the spectra without

eliminating too much information

Also, tsunamis are frequency-dispersive waves.

That is, the wave train tends to scrt itself out by fre­

quency, with the low frequency waves traveling faster.

Since the low frequency waves .are also very long wavelength,

they are more likely to reach large amplitudes in shallow

water. Thus we tendeJ to give more weight to high energies 3at frequencies below 10- cps than to high energies above

this frequency.

4.2.2 Cases A-4-1, A-4-2, A-4-3

These three cases were all gap-filling events. The energy levels ranged from 5.8 to 29.1 x 1022 ergs.

4-10

Case A-4-2, the elliptical uplift pattern, imparted the

lowest energy, even though it had a maximum displacement of

lOm. The triangular uplift produced the greatest energy.

The 60 min contours for the three cases (Fig­

ures 4.5a-c) show patterns similar to the smaller earth­

quakes, but amplitudes are much higher (note that the

contour interval is now 25 cm instead of 10 cm). And the

longer fault length leads to a much broader central crest. The elliptical pattern falls off toward the edges of the

source zone, and thus radia ion at low angles from the

ruptu're axis is less energetic than in the other two cases,

in which displacements are high all along the fault axis. Peak amplitudes at station 6 ranged between 2-3m.

Spectra for stations 3, 6, and 10 were markedly

higher than those for 7 and 15 in case A-4-1 (Figure 4.6).

This indicates higher-concentrations of energy along a

broad span of directions ranging from W to SSW. Similar

patterns were apparent in the other two cases, although

case A-4-2, with much lower energy levels, tended to be more

focused toward the southwest (station 6).

4.2.3 Summary of Source Zone A

Events in this zone, because of its orientation,

tend to radiate most of their energy to the west and south­west. The smaller events produced low amplitude waves whic"

might not have much effect rit great distances. The gap­

filling events produced sizeable waves focused mostly to the west and southwest. Their effect on distant regions is

4-11

"I- -" ".

-... j.......

- -- --- i.

,------m.....

- -- .... .....

-,.......*-,....-

.-­ -- Z. - -

Ii--*----1

II --' - - .... '- ........*** a

Si --­

....-- 1..., 7

1IEIiCAWI PROKC IPN

Figure 4.5a Surface wave elevation contours for case A-4-1 at 60 min after ground motion. Contour interval is 25 cm.

--

pa qta S r . mm.I.Itil - ..... ,. l.oe--I- -v-*

±...111121- jz - ir-. ---" ... i.. as -- "~ *.. ---- . ---- r ......I ..-....-.....--.- * ..-.. .. ---- --­

-.- _"_: '

... ...I.... - I ..-- ..I-. ..--

Figue a 4.b4.5, Saeexeptfor ase -4­.I-.. L--11 ? g o

Figur.. aeoCA4

1 "U..

.. .. -.-I I- ........

' -- ,. ...l-ot.. r.

....... ....

Irs.

7.x---

--

-­ ..-.

'-.---- -'

'@So

!I

-- - -

....... -I - -.---

-------..

.

.I...~

-- --------.

/....

A--.

4-4

I -N

..................I- --rr .-

HLECAICR I',OJF C N

Figure 4.5c Same as 4.5a except for Case A-4-3

OA,

" S.

.2

£x

,

U' :A [

Figure 4.6 Spectra for the five recording stations for case A-4-1

4-15

4.3

difficult to assess. The events with large displacements

all along the rupture zone did produce side lobes which

could have significant effects to the northwest of the

source.

SOURCE ZONE B

Source zone B is a large gap straddling the bend

in the continent. Again, because of its length, we divided

it into subzones. The zones and the recording stations are

shown in Figure 4.7.

4.3.1 Cases B-1-1, B-2-1, B-3-1

Because of the change in fault orientation from

case B-1-1 to case B-3-1 the surface wave fields were

noticeably different. The 90 min field for case B-1-1

(Figure 4.8a) showed waves heading mostly southwesterly

with little spreading to the sides. The wave field for

B-2-1 (Figure 4.8b)was oriented more to the west, but it

spread over a much wider arc with a generally lower ampli­

tude. The wave field for B-3-1 (Figure 4.8c) appeared to

head due west with a fair amount of spreading. All three.

cases produced roughly equal energy (average = 4.8 x 1022

ergs), so orientation was the dominant difference. Maximum

amplitudes (at station 10 in case B-1-1 and station 4 at the

others) were somewhat less than a meter.

Spectra for case B-1-1 (Figure 4.9) revealed

higher energy levels at stations 4 and 10, while for case

B-2-1 levels were relatively uniform at all stations except

5 (which was generally lower). Case B-3-1 spectra showed

that same general uniformity, although a slight increase

toward stations 4 and 10 could be.observed.

4-16

,en e, .M I

S I 1S

t o" tlr i l

,* p

N Oe. '.rI

, l ip S

-IV

. -I,...--,-*-------- . .. 4',, --­

_ _

0.. . - -.--

--

-

-ii--

-~ -

--­ ...±..-

__.",,,..

---. __--7

- -

A

1' rA- I;~lI

713q .- *... --L.&J ...L .L. * 6.. LII a A. L. 1i.L I. L .6. -

ItI'UA'I'' reo -ciu

1. .1I.i. .JI. I 111

Figure 4.7 Source zone B with recording stations.

'" ", i' $, -llflis srvi"olr, I -'1 v- " " * 1 " ,,.r," " " '-" I 1'__I_"- - -""

--T . . . . --[ ­.. . ..* . -. J - ..... . .1 . --- r--- -­

"7 lo

IIRCIpR PROJECTION

Figure 4.8a Surface wave elevation contours for case B-i-i at 90 min after ground motion. Contour interval is 20 cm.

_...

-[--

-Ire

_-!.. .....-- -..- I....... ....... -....tji-i ....

I I18

_ ,I

e r--t-I-r--

. -

-. Tv

_ |

sue

w .,- 1 , 'U-t­

"d.J J''"L....A.z

Figure 4,8b Same as 4.8a except for case B-2-1

- 9 1 *1 To of is Il ' 'l s r r vl o l jlv1 -w-ie - l r r vr- 7 9P -. .

AS

a j", ' itI " N IwX I

! i ",, ; i ,~

Faer

,l 30. Is...

so a-

Figure 4.8c Same as 4.8a except for case B-3-1

00 06*

10 1

IO

ws l

40 So 40 30 1o0o

Figure 4.9 Spectra for the five recording stations for case B-1-1

4-21

4.3.2 Cases B-4-1 and B-4-2

These two cases were gap-filling events.

Case B-4-1 used uniform uplift, while case B-4-2 used the

triangular uplift pattern. The elliptical source was not

used because of difficulties presented by the bend in the

fault.

The two cases produced the highest waves seen

thus far. Peak amplitudes at station 4 were of the order 4-5m. The 90 min fields (Figures 4.10a-b) showed extremely

high, broad peaks. The general wave direction was south­

westerly, although the triangle uplift produced strong wave

activity along a northwesterly path also.

Energies in case B-4-1 (Figure 4.11) were higher

at station 4 than at other stations, although levels at

station 10 were only slightly lower. Similar trends were apparent in case B-4-2 (Figure 4.12). But these latter

spectra also displayed a sharp roll-off in energy at fre­

quencies higher than 10- 3 cps. This seems to indicate

that although relatively more long period energy may

be concentrated toward the southwest, still significant long

period energy is headed toward the northwest.

4.3.3 Summary of Source Zone B

The directionality of the tsunamis from this gap is strongly dependent on which portion of the gap

experiences a large earthquake. The southern end of the

gap seems to pose a more widespread threat to northern

4-22

-- --- - - -

weS ''i'e -'ja rt'i i-. :--: -i:: - _ _ . _ _ . l _ " _._ ....-i r rT v[- -r T-1 I ISl* I r .rr1ug19 11* * r 1V r c-I-l-----lI __fllKT_

-A--- -i- zc---z=~zzz CIMP

%asRR RM

Figure 4.lOa Surface wave elevation contours for case B-4-1 at 90 min after ground motion. Contour interval is 50 cm.

" " -5-I. , - , .. _ _ , ..IS .. ..---,-J-.-I-.... - i -­t'-l-- I-.,.-I-.,-,-.--I at!

. .IA - -A- I LA ,i,._A. CL . L I L LA i ALLLI.

Figure 4.10b Sam~e as 4.10a except for case B-4-2.

0'

AmO

£

!I,

al-a

E

?CV1,o D mi Figure 4.11 Spectra for the five recording stations for

case B-4-1

4-25

VI-

X io

£ .

Q

lu

,az; ,¢ j

Lj9

' , I a

6o S0 to U.

Figure 4.12 Same as 4.11 except for case B-4-2.

4-26

4.4

population centers. Gap-filling events would probably

contain sufficient energy to pose a basin-wide hazard.

SOURCE ZONES C AND D

Source zones C and D are quite small and lo­

calized. The zones and the recording stations are shown in

Figures 4.13 and 4.14.

4.4.1 Cases C-i-1, C-I-4 and C-I-5

Cases C-i-1, C-1-4, and C-i-5 employed uniform,

triangular, and exponential uplift patterns, respectively.

The 90 min contour fields for these cases are shown in Figures 4.15a-c. These waves were not strongly directional,

probably because the source zone is small enough to pro­

duce a wave pattern approximating the uniform spreading

associated with a point.source. A little more energy seemed

to head toward the northwest than toward other directions.

Amplitudes were generally less than a meter. The spectra

for case C-1-4 (Figure 4.16) show that somewhat more wave

energy passed through stations 13, 9, and 5 than through the

two southern stations.

We noted in Section 3 that three cases with

uniform uplift were run in this zone. In case C-1-2, uplift

was twice that of case C-1-1; in case C-1-3 the uplift was

five times that of C-1-1. The results were identifical in

all cases, except for the amplitues, which maintained

roughly the same ratios as the uplift values. This was not

surprising, since we employed a linear wave model with

4-27

.64%l S' 70 lip9T--. N-IL ..111 svj. .. . r re ,I...III . ' I1' t'' TII. v:"ese V' '' V. .. .. . I- . . i -t---!--t ;- --­

--- ..... ,,.....---4.-r<--- -<

'x­

... J- ,.X-.A -. -- t

MA ImlA lu s g

-K:! -

Figure 4.13 Source zone C with recording stationls

---

qloS .it P,* -. .0e !A 11

w -0I rv -1- 1i to te l of o il-sell i s it IT Ir it u 1"t r r of is as Iyr1 i -I 'r'' -r aif SONS

7- .... ... ... -.@ . [.. ..... ­- - .- 4- -.. ­-..1--II- :44 I--,-........J I

U-1

... V­.. ZO

Figure 4.14 Source zone D with recording stations

- - -

ri I.. . I .1.1fr rr 1v,1" IT MT1 ,I I l.. ! ,Ip- ir'"I

0 - Lj- -- l-i" 'A: I I'.,. I M1, "

',7 T .....-- .r.i F]

"&I XI"; W lot: so HERCRII'R PFOATcr11w

Figure 4.15a Surface wave elevation contours for case C-1-1 at 90 min after ground motion. Contour interval is 10 cm.

- - -- - ,-- -- '- - ...--t-­" '_ - -77--I 1L •' Thi " - 11L(- --~rY--­

: ,,•

v-i " +. 00,

e,-- ._ I0'I, ....

Figure....5 a-e as except r - ,.... case

"~ ~ ~---X -%1---.. Fiur 4.5oaea .5 xetfrcs -­

-S3W.. .. .. ..... .. .. .. .. .. .. .. .. ?I I S . ..F*I i I . .. . .. .. ...F F? .. .. TI .. .. .. 0Se .... . .. .. .. ?. r . .. .. . ..

.. I

elll

7'-7 JANJ

S. # me no HERcPtR rROJECTlIN

I* 10i

Figure 4.15c Same as 4.15a except for case C-1-5

AI 69

x is

t.2

40 o 1#0 3o 2.o It$

Figure 4.16 Spectra for the five.recording stations for

case C-1-4

4-33

instantaneous uplift. Had we used nonlinear equations, or

had we used time dependent displacements, the results would

have been somewhat different. The essentially identical

results, however, imply that one could simulate any magni­

tude earthquake with uriform uplift merely by scaling a

single case appropriately.

4.4.2 Cases D-1-1, D-1-4, and D-1-5

Cases D-1-1, D-1-4, and D-1-5 also employed

uniform, triangular, and exponential displacement patterns.

The wave elevation contours (Figures 4.17a-c) show rela­

tively uniform radiation with only a small tendency to focus

toward the northwest. Spectra for case D-1-4 (Figure 4.18)

are typical of these events. Energy levels at stations 5, 7

and 11 were generally higher than for the other two sta­

tions. Station 7 seemed to see the most energy over all.

This reinforces the notion of a tendency of focus energy

toward the northwest.

4.4.3 Summary for Sources C and D

These two small source zones tend to produce low amplitude tsunamis which pose a far-field hazard to a

large sector of the Pacific. Had the source zones been

larger (as in the 100 km long 1960 Chilean earthquake, which

was located south of source D), these zones would likely

have produced more imposing tsunamis. Since the historical

rupture length in this section of the coast has been at

least twice as long as these postulated gaps, these scenar­

ios may underestimate the hazard.

4-34

OuID 09 sl T1JAJOIUI Jfoluoo -uorlow punojz2 aaljv' uTw 09 4v I-i-a esvo J0Jlol nOu uo UivAele eAvm 9oejnS 'GLlp ean2TA

.5 tho r&IJ.1JVS

All ­ -4

.5. ........

At

'Sip.S vr . .

Yi -r.. v- i-s I-I

jt I

s 1 1 1 r r I . .- .i up

'-- - - jZ9 f f..':"]ffLiLjj... ]. tri -_"_ ___

- - --­ i-t_-___---i--'~-h--

IX

- , --

--

I f'

"A ....i..-I LL-.L ... A A.. A.. A& noW

Figure 4.17b Same as 4.17a except for case D-1-4

5 ..r.-:-M

IT 11 1.: r II '' IvT lvs gi

sib. ! . ...

- ......

...

.

i.

,...

. . .__. .....

. --. IV / :/ l !Ole

WI Fiur 4......ae.a10"

. ................... Z 4 ...

. ..... ......

a. exep

..... r for .caeD­

,€so ,h

Figure 4.17c Same as 4.17a except for case D-1-5

* J!

IMPI

a.. q^

fA

P,.,o ' Ii,. JLU

Figure 4.28 Spectra for the five recording stations for case D-1-4

4-388

4.5 SOURCE ZONE E

This source zone was by far the largest of the

group examined. It was approximately 2000 km long, or about

twice as long as the Chilean earthquake of 1960. For

reasons outlined earlier, we did not atempt to break this

zone into subzones, but rather concentrated on source

motions filling the entire region.

Because this rupture zone ts so long, it would

have been totally unrealistic to specify simultaneous

uplift. Instead we allowed the fault to propagate from the

northern to the southern end of the zone at a speed of 4

km/sec. Thus it took roughly seconds 575 sec to complete

the uplift (8 model time steps). Figure 4.19 shows the source zone broken into 8 subzones of roughly equal extent.

At the beginning of each of the first 8 time steps the appropriate bottom section was displaced, causing a cor­

responding surface displacement. This is as close to a

continuous uplift process as one can get with a discrete

model.

Two cases were run. E-1-2 corresponded to an overall uniform uplift pattern; E-1-3 corresponded to the

triangular pattern. A case E-1-1, which would correspond to

uniform simultaneous uplift, was rejected. The numbering

scheme differs from that described earlier in the assignment of the last digit.

The results from these two cases were quite

spectacular. Each case had a maximum displacement of 13.5m.

4-39

IVW q0 SI ' -.1.

.. .. . 81 A. "k- 2.J -AA A2A 21.1 A -.

0

Figure 4.19 Source zone E with recording stations. The subzoneC C" are numbered in the time sequence in which they undergo uplift.

The uniform uplift case (Figure 4.20a) showed a maximum

height of over 15m persisting 90 mir after the uplift. The

triagnular pattern (Figure 4.20b) produced an 11m wave over

the same time interval. The central crests and indeed most of the extreme energy in both cases propagated toward the

southwest.

The spectra for case E-1-2 (Fig 4.21) showed

consistently higher energies at the southerly stations. On

the other hand, the spectra for case.E-1-3 (Fig 4.22) did

not show a definite pattern, except for generally low

energies at the northern most station (8). The lack of a definite northerly, propagation of energy was somewhat

surprising, since a large portion of the uplift took place

south of the bend in the Trench at 200S. Apparently the

interaction of wave fields converging along different paths

(i.e., from the northeast for waves generated north of the

bend and- from the east for waves generated south of the

bend) caused enough interference to suppress significant

northerly energy components. The concave nature of the

leading edge of the crest and the intense peak are almost

certainly the result of constructive and destructive inter­

ferences.

Despite strong evidence for propagation into the North Pacific, the presence of this much wave energy would

have to be considered a basin-wide hazard.

INTERCOMPARISONS

Because the source motions vary so widely from zone to zone, intercomparisons between zones are difficult.

4-41

4.6

V1-...-.-....

---I-

"IS

Figure 4.20a

-,-IT-,, 1' TO, "9' 'I" 1, "'" Sr~1 0 " ------ - -I -­- I--I-­

- :--i- L..L--4 ,._. .... - -...... -i---.­..._,_. I . ­

--.- I----mI

OAfi ,. 111ip r

Surface wave elevations for case E-1-2 at 90" miin

-after thle start of ground motion. The contour. interval is one meter. Contours around the central peak have been left out to reduce crowding.

4-7

40 - r - -- i s - r T- v - lr- I I I r

I I 1/"*" "I'l l i "f I 1 e IT Ir I. l e'- r e"v-r o-i eI -q " r -rv

irim

-­ t ­ 1-

Figure

AL. A

a

- .

aec

____._,

... 1..

Figure 4.20b Same as 4.20a except for case E-1-3

1: ' W--­

S72 0 12

I i

6.

40*

4-4

4O 0 so 40 )o2.0I

Figure 4.21 Spectra for the five recording stations for case E-1-2

4-44

g gg

'.\.

E\

Figure 4.22 Spectra for the five recording stations for case E-1-3

4-45

We are more interested in assessing the threat posed by

events in each zone than in deciding whether one zone has

greater or lesser potential for hazardous tsunamis than any

other. It seems clear that all of the source zones examined

could be generating regions for significant tsunamis. The

few tentative conclusions to be drawn from this initial

phase of the overall project are indicated in the next

section.

4-46

5.1

Section 5

CONCLUSIONS

TENTATIVE CONCLUSIONS

We have pointed out that the research presented

in this report is only the first phase of a larger study for

evaluating the Pacific wide tsunami hazard posed by earth­

quakes in areas of strong seismic potential. Conclusions

based on this phase must be tentative and subject to a

number of caveats. We will discuss these in turn, with

emphasis on the caveats.

0 Earthquakes occuring south of 200S are more

likely to produce tsunamis which will radiate

significant portions of their energy toward

the central and northwostern Pacific. Earth­

quakes occurring betweeu 50 S and 200S are more

likely to produce tsu,.amis which will radiate

energy toward the southwestern Pacific.

* All other things being equal, a large area of

uplift will introduce more wave energy than a

small area.

* Small-area events will probably pose a strong­

threat in near-source regions, while large­

area events will posed a basin-wide threat.

5-1

None of these conclusions are particularly start­

ling. Informed intuition and a familiarity with historical

tsunamis would lead one to much the same results. What is

important, though, is the demonstration that, under the

right set of circumstances earthquakes in all of the source

zones studied could generate tsumamis which pose a threat to

populated areas throughout the Pacific. We will examine the

implications of this for the rest of the study after we

establish the limitations of this phase.

5.2 CAVEATS

Any modeling effort entails a number of restrict­

ions which may or may not be explicitly stated. The

primary of these is that the results of a model are only as

good as the modeler's understanding of the process under

examination. The plain truth is that little is known about

why certain earthquakes cause tsunamis while others, quite

similar, don't. In many ways the tsunami generation

process, which from a fluid dynamics standpoint is quite

easily modeled, is not well understood. Nor, for that

matter, are earthquake mechanisms well understood. The

result is that a study of this type is forced to deal on a

very simplistic-level with the seismological phase of the

problem. The state-of-the-art does not allow us to postu­

late with much certainty the type of earthqt ke a potential

source zone will likely experience. Thus simulations can

only be idealized versions of realistic situations.

A second limitation stems from the problem of

modeling continuous phenomena with discrete models. It is

quite difficult to set up a model like SEAWAVE to simulate

hypothetical source motions accurately in every detail. For

5-2

5.3

example, it is probably impossible to exactly duplicate a

rectangular source area on a uniformly spaced spherical

coordinate grid if the fault axis is oriented any way but

along a parallel or a meridian. The dimensions of the zone

will vary somewhat from that desired despite the best

efforts of the modeler. This discrepancy between the

postulated situation and the situation implemented in the

model must be accomodated.

The final limitation concerns the failure of one

portion of the study. We had hoped to employ a fault

displacement model to allow us to take factors such as dip

angle into account in developing bottom motion patterns. Lack of this software forced us to use quite simplified

notions of earthquake displacements, Thus all motions are

due to normal thrust faults with no downwarp and only

strictly simple geometrical height variations in the source area. This makes the results obtained thus far less realis­

tic than originally envisioned.

IMPLICATIONS

What do the tentative conclusions and the several

limitations mean in terms of the rest of the Tsunami Hazard Assessment Project? Essentialiy two things:

1) Since all of the source zones produced

tsunamis, all of. them should be used to model

the far-field threat. Even the low amplitude

waves caused by the small events could prove

5-3

dangerous in shallow coastal zones in the far

field. The large source zones should receive

somewhat more attention, however.

2) Efforts will continue to implement a fault

displacement model. This will enable us to

apply more sophisticated notions of the

characteristics of possible events and help

close somewhat the gap between the model and

reality. This development will be an immedi­

ate priority in the following phases.

5-4

References

Barazangi, M. and B. Isacks, 1976, Spatial distribution of earthquakes and subduction of the Nazca Plate beneath South America, Geology, 4, 686-692.

Bennett, A. F., 1976, Open boundary conditions for disper­sive waves, J. Atmos. Sci., 33, 176-182.

Brandsma, M., D. Divoky, and L. S. Hwang, 1975, SEAWAVE--A revised model for tsunami applications, Tetra Tech Inc., Pasadena, CA.

, 1 and , 1976, User's guide to SEAWAVE: A model of tsunami generation and propagation, Tetna Tech Inc., Pasadena, CA.

,__ ,_and _ _ , 1978, Circumpacific variations of computed tsunami feat;ures, Proceedings, Symposium on tsunamis, IUGG tsunami Committee, Ensenada, Mexico, 1977, 132-151, Manuscript Rept. Series #48, Dep. Fisheries and Evn., Ottawa, Canada.

Chinnery, M. A. and R. G. North, 1975, The frequency of very large earthquakes, Science, 190, 1197-1198.

Garcia, A. W., 1976, Effect of source orientation and loca­tion in the Peru-Chile Trench on tsunami amplitude along the Pacific coast of the continental United States, flS Army Corps of Eng., Waterways Experiment Sta., Vicksburg, MS, Rept H-76-2, NTIS: AD-A032991.

Hebenstreit, G. T., E. N. Bernard, and A. C. Vastano, 1980, Application of improved numerical techniques to the tsunami response of island systems, J. Phys. Oceanogr., 10, 1134­1140.

Herd, D. G., T. L. Youd, H. Meyer, J. L. Arango C., W. J. Person, and C. Mendoza, 1980, The great Tumaco, Columbia earthquake of 12 December 1979, Science, 211, 441-445.

lida, K., D. C. Cox, and G. Pararas-Carayannis, 1967, Pre­liminary catalog of tsunamis occurring in the Pacific Ocean, Hawaii Inst. of Geopnys. Rept. HIG-67-10, Univ. of Hawaii, Honolulu.

Isaks, B., J. Oliver, and L. R. Sykes, 1968, Seismology and the new global tectonics, J. Geophys. Res., 73, 5855­5899.

R-1

References (Continued)

Kanamori, H., 1972, Mechanism of tsunami earthquakes, Phys. of the Earth and Planetary Interiors, 6, 346-359.

, 1977, The energy release in great earthquakes, J. Geophys. Res., 82, 281-2987.

Kelleher, J., J. Savina, H. Rowlett, and W. McCann, 1974, Why and where great thrust earthquakes occur along island arcs., J. Geophys. Res., 79, 4889-4899.

McCann, W. R., S. Nischenko, L. Sykes, and J. Krause, 1978, Seismic gaps and plate tectanics: seismic potential for major plate boundaries, in Proceedihgs of Conference VI, Methodology for identifying seismic gaps and soon-to-break gaps, U. S. Geol. Survey Open-File Rept. 78-943, 491-584.

Pararas-Carayannis, G. and J. Calebaugh, 1977, Catalog of tsunamis in Hawaii, Report SE-4, World Data Center A for Solid Earth Geophysics, EDIS/NOAA, Boulder, CO.

Y 1980, Earthquake and tsunami of 12 December 1979 in Columbia, Tsunami Newsletter, 12(1), ITIC, Honolulu, 1-9.

Purcaru, G. and Berckhemer, 1978, A magnitude scale for very large earthquakes, Tectanophysics, 49, 189-198.

Savage, J. C. and L. M. Hastie, 1966, Surface deformation associated with dip-slip faulting, J. Geophys. Res., 71, 4897-4904.

Silgado, E., 1978, Recurrence of tsunamis in the western coast of South America, Marine Geology, 1, 347-354.

Stauder, W., 7.973, Mechanism and spatial distribution of Chilean earthquakes with relation to the subduction of the oceanic plate, J. Geophys. Res., 78, 5033-5061.

,_1975, Subduction of the Nazca Plate under Peru as evidenced by focal mechanism and by seismicity, J. Geophys. Res., 80, 1053-1064.

Ursell, F., 1953, The long-wave paradox in the theory of gravity waves, Proc., Cambridge Phil. Soc., 49, 685-694.

Wurtele, M. C., J. Paegle, and A. Sielecki, 1971, The use of open boundary conditions with the storm surge equations, Mon'thly Weather Rev., 99, 537-544.

R-2