TSUNAMI SOURCE PARAMETERS OF SUBMARINE EARTHQUAKES AND
SLIDES
M. D. TRIFUNAC and M. I. TODOROVSKA
University of Southern California, Civil Engineering Department, KAP 216D, Los Angeles,
CA 90089-2531, USA
Abstract
The nature of the tsunami sources (displacement, duration, area and volume) is reviewed for
selected past earthquakes, slumps and slides, from the point of view of tsunami generation.
It is concluded that slides and slumps differ significantly form earthquakes in: (1) the
velocity of spreading, (2) the balance of the uplifted material, and (3) the vertical
displacements per unit horizontal area.
Keywords: Submarine slides, slumps, earthquakes, tsunami, near-field
1. Introduction
Tsunami are dispersive gravity water waves, propagating at long periods with phase
velocity cT = gh , where h is the ocean depth and g is the acceleration due to gravity
(Kajiura, 1963). The velocities of earthquake faulting are about 3 km/s, an order of
magnitude larger than cT. Therefore, most classical studies of tsunami generation by
earthquakes have neglected the details of wave propagation in the fluid during the source
time, and have assumed that the initial conditions for tsunami generation can be
approximated by specifying the initial disturbance of the ocean surface to be the same as the
vertical offset of the ocean floor (Todorovska and Trifunac, 2001). For most tsunamigenic
earthquakes, the average runup amplitudes (corrected for geometric spreading) correlate
well with the surface wave magnitude Ms (Pelayo and Wiens, 1992), but for some may be 1
to 2 orders of magnitude larger than the average trend. These have been named “tsunami
earthquakes”, and it has been suggested that they are caused by a long faulting process, so
that Ms underestimates the true value of the seismic moment (Kanamori, 1972). Very long
source times may result from multiplicity of the earthquake source, slow dislocation
velocities in the accretionary wedge (Pelayo and Wiens, 1992; Tanioka et al., 1997),
submarine landslides triggered by an earthquake, slumps (Hawaiian chain, Hading Bay and
Riangkroko, and Storegga), repeating submarine volcanic explosions (1883 Krakatau:
Yokoyama, 1987) and changes in the atmospheric pressure. Submarine slides and slumps
that cause tsunami may be triggered by earthquakes, volcanic eruptions, storm waves, or by
gravitational loading and instability (Hampton et al., 1996).
This paper reviews the source durations, displacement amplitudes, areas and volumes of
selected past earthquakes, slumps and slides that have or may have generated a tsunami. The
aim is to describe and quantify the differences between submarine slides and slumps on one
side and tsunamigenic earthquakes on the other, from the viewpoint of tsunami generation.
121
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Trifunac and Todorovska
2. The Nature of Tsunami Sources
2.1 VELOCITIES OF SPREADING
The seismological studies of tsunamigenic earthquakes (Kanamori, 1972; Comer, 1982)
capture the long periods of the wave motions, and allow the earthquake source to be
represented by a point. In contrast, the high frequency recordings of strong motion in the
near-field (0.1 to 25 Hz) can resolve fine time and space variations in the source time
function, and can be used in inverse studies to interpret the motions on the fault surface
(Trifunac, 1974). At high frequencies, a long lasting rupture of a large earthquake often
appears as a sequence of multiple events. The Nicaraguan tsunami earthquake of September
2, 1992, is an example of a multiple event (Ide et al., 1993).
The generation of tsunami by vertical displacement of the ocean floor depends on the
characteristic size (length L, and width W) of the displaced area and on the time, τ, it takes
to spread the motion over the entire source region. The ratio L/τ defines the average
spreading velocity, c (assuming unilateral faulting). During “ordinary” earthquakes
( 1 < c < 10 km/s), the slip propagates with velocities approaching the shear-wave velocity in
the medium, and reductions in the overall average value of c can result from multiplicity of
the source and delays associated with breaking of barriers. The “slow” earthquakes
( 0.1 < c < 1 km/s) may consist of one or several high velocity rupture events (thus
producing the usual train of high frequency waves), with the long delays between the
successive events accompanied by a slip that can contribute large amplitude low-frequency
excitation. Examples of such “slow” earthquakes are the June 6, 1960, Chile earthquake
which ruptured as a series of earthquakes for about an hour (Kanamori and Stewart, 1979),
and the February 21, 1978, Banda Sea earthquake (Silver and Jordan, 1983).
Figure 1 shows seismic moment (M0), magnitude (Richter, ML, surface wave, Ms, and
moment, Mw, magnitudes), and a moving source “volume”, all used as measures of the size
of the source versus different measures of the source duration. Here “volume” refers to $
for earthquakes, where is the average dislocation amplitude and A is the fault area, or to
(inferred) slide volume. The Grand Banks, 1929, and the Papua New Guinea, 1998, slides
are shown plotted versus two different measures of “size”: (1) magnitude of the
“earthquake” that triggered the slide or amplitudes of the seismograms recorded during the
sliding process, and (2) estimates of their volumes, respectively 185−550 km3 (Driscoll et
al., 2000; Hasegawa and Kanamori, 1987) and 4 km3 (Heinrich et. al., 2000). For these two
events, the “size” measured in terms of the volume of the displaced material is two to three
orders of magnitude “larger” than the size measured in terms of $(via M0 and M). The left
three shaded zones represent approximate boundaries between “silent” (0.01 < c < 0.1km/s),
“slow”, and “ordinary” earthquakes, assuming M ≈3.94 + 1.94L for c = 0.1, 1 and 10 km/s
(Trifunac, 1993). The solid lines are for unilateral faulting, while the top (left) ends of the
gray zones are for symmetric bilateral faulting. The velocities of underwater landslides and
gravity currents are one to two orders of magnitude smaller than the velocities associated
with earthquake dislocations. Based on a succession of broken underwater cables, Bjerrum
(1971) estimated the mean gravity current speeds to be 3−7 m/s. From data on broken
underwater cables in the Var river delta, Hamilton and Wigen (1987) computed gravity
current velocities along a 0.5° slope of 6 m/s. From the timing of breaks in underwater
cables during 1929 Grand Banks slide, Kuenen (1952) estimated the gravity current
Tsunami source parameters of submarine earthquakes and slides
123
velocities to be 5−30 m/s. The Grand Banks underwater slide had maximum velocities of
20−30 m/s, along slopes of 2°. The maximum velocity of the first Storegga slide was
estimated to be 35 m/s (Harbitz, 1992). Jiang and LeBlond (1992) simulated underwater
landslide velocities of 20−45 m/s on inclines 2−12°. The velocities of turbidity currents are
4−8 m/s (Shepard, 1963; Bowen et al, 1984; Reynolds, 1987).
τC - Beroza & Jordan (1990)
T-wave duration, Okal & Talandier (1986)
Pelayo & Wiens (1992)
26
/s
km
0 .1
ea r
th q
Slo
w
Hasegawa & Kanamori (1987)
1960 Chile
1960 Peru Kanamori & Stewart (1979)
4 km 3
1978 Banda Sea
10 0
s 1
c
- 3 0 = 10
m/
km
s
/s
10 1
Volume - km 3
7
c=
m/
c=
es
u ak
1992 Nicaragua
1994 Java
1896 Sanriku
1946 Aleutian
1929 Grand Banks Slide
185 km 3
10 2
MS
log M 0 - dyne cm
hq
km
550 km 3
8
28
Ea
rt
10
c=
MW
10 3
1k
10 4
/s
9
uak
s
es
30
itie
lo c
en
u rr
avi
ty c
10 -2
Papua New Guinea
Heinrich et al. (2000)
Gr
10 -3
22
0.1
t ve
t ea
Sile
n
5
1
10
100
1m
uak
rth
q
ML
24
c=
es
1979 Eltamin
10 -1
/s
1979 South of Panama
6
Turbidity currents
1-8 m/s
Shepard (1963)
Bowen et al. (1984)
Reynolds (1987)
1000
10000
Duration - s
Figure 1. Earthquake moment M0, magnitudes (ML, M, and Mw) and source volume, versus different measures of
source duration: (1) duration of T-waves (solid small circles); (2) characteristic source duration, τc (open small
circles); (3) duration of three tsunami and one tsunamigenic earthquakes (crosses); (4) approximate durations of
Sanriku, 1896, Aleutian, 1946, Nicaragua, 1992, and Java, 1994, events (solid large circles); (5) the overall duration
of two complex events: 1929 Grand Banks and 1960 Chile (horizontal bars). The shaded zones represent
approximate boundaries between silent, slow and ordinary earthquakes. The large solid and dashed circles show the
estimated duration of the Papua New Guinea slide. The grey zone at the bottom represents gravity currents, and the
grey cross-hatched zone turbidity currents.
124
Trifunac and Todorovska
In Figure 1, the velocities of underwater slides and of turbidity currents are compared with
those of “tsunami” earthquakes and “slow” earthquakes.
4
2
10 -1
Seward - 1964
10 0
10 -1
10 0
10 1
10 2
Area - km 2
10 3
10
10 4
0
Landslide area
10
20
Percent
10 2
10 1
N. California
P.N.G. - 1998
10 3
Munson Nygren
10 4
Hawaiian
slumps
10
G. Banks 1929
10
1
Hawaiian
Debris
avalanches
5
1
6
Magnitude
8
10000
5
1000
100
Water depth, h - m
1929 Grand Banks Slide
Hasegawa & Kanamori (1987)
10
100
Area - km 2
cT
cT
0.5
Silent
Slow
1000
10000
Tsunami, faulting and slide velocities - m/s
Ea
rth
qu
ak
ef
a
u
lt a
rea
Tanioka & Satake (1996)
Satake (1994)
1896 Sanriku
1992 Nicaragua
cT
100
50 c T
Johnson & Satake (1997)
1946 Unimak Island
20 c T
Heinrich et al. (2000)
10 c T
1/2
5 cT
1998 Papua
)
(gh
New Guinea
cT=
2 cT
How the vertical movements at the source displace the surface of the ocean will depend on
the ratio c/cT. For c/cT > 20 to 50, the water amplitudes above the source will approximately
be equal to the vertical amplitudes of the permanent displacements at the bottom. For c~cT,
wave focusing may occur above the spreading edge of the uplift. For c < cT , the amplitudes
of water waves above the source will be “small”, and at the instant the
source motion has ceased may cover much larger area than the area of the source. Figure 2
(left) illustrates five examples, three for c > cT and two for c < cT . The range of applicable
velocities c is plotted versus the depth of water above the source area.
Figure 2. (left) Comparison of long period tsunami velocities (diagonal lines) with velocity zones of "silent" and
"slow" earthquakes, versus depth of the water layer in meters. Also shown are the estimated velocity and depth
ranges for three tsunamigenic earthquakes (1946 Unimak Island: 1992 Nicaragua: and 1896 Sanriku) and two
submarine slides (1929 Grand Banks and 1998 Papua New Guinea). (right) Comparison of: (1) the distribution of
landslides by their area (bottom), (2) the areas of major debris avalanches and slumps of the Hawaiian Islands
(shown by short solid lines), (3) the areas of selected submarine slides, and (4) the source areas of earthquakes
versus their magnitude (top).
2.2 SOURCE AREA
For earthquake source areas larger than about 100 km2 (earthquake magnitudes greater than
6 to 6.5; see Fig. 2) the wave energy begins to be transmitted through the water with less
dispersion (Comer, 1982). Most submarine landslides (∼90 percent) are smaller than 100
km2 (Fig. 2), and so most undersea slope failures occur without being noticed. However,
submarine slides that are close to the coastline, and such that a “large” volume of material is
Tsunami source parameters of submarine earthquakes and slides
125
moving over a “small” area, can cause highly localized and devastating tsunami disasters
(e.g. Valdez and Seward, on 27 March 1964; Hampton et al., 1993). The largest known
slope failures have taken place off the coast of the Hawaiian Iislands (Figs 2 and 3). Some
were longer than 200 km, had volumes of 5 × 103 km3 (Figs 2 and 3), and may have
generated cataclysmic tsunami amplitudes, assuming that all the debris moved at once. In
1929, a magnitude 7.2 earthquake triggered a submarine landslide at Grand Banks. Part of
the failed material transformed into a turbidity current, which traveled more than 700 km,
breaking communication cables in its way (Trifunac et al., 2001b; 2002b).
10 4
Nuuanu, Hawaii
10 3
East Breaks (west)
Munson-Nygren
10 2
East Breaks (east)
P.New Guinea 1998
Alika-1 and Alika-2
Valdez 27 Mar. 1964
N California 8 Nov. 1980
Volume - km 3
Puerto Rico - Insular slope
Grand Banks 1929
10 1
10
Papua New Guinea 1998
Heinrich et al. (2000)
0
10 -1
10 -2
Seward 27 Mar. 1964
Grand Banks 1929
Hasegawa and Kanamori (1987)
Volume of
typical
slide
10 -4
4
Volume of ocean floor
uplifted by earthquakes
Hatori (1966)
uA = M 0 / µ
10 -3
5
6
7
8
Magnitude
Figure 3. Comparison of selected submarine slides by their volume (in km3), with
u A (= average dislocation
× fault area), and the volume of uplifted ocean floor by earthquakes, plotted versus earthquake magnitude.
2.3 SOURCE VOLUME
The largest known volume of a submarine mass movement is about 5 × 103 km3 and is
associated with the Nuuanu debris avalanche, northwest of the Hawaiian island Oahu. Its
estimated age is 1.4 to 2.6 million years. The Grand Banks slope failure of 1929 may have
displaced 5.5 × 102 km3. The smallest volume illustrated in Fig. 3 is that of the Seward
landslide of 1964, with only 5.4 × 10-4 km3 to 5.4 × 10-3 km3 (Hampton et al., 1993).
The “volume” of crustal displacement ( uA) associated with earthquakes, can be related to
the seismic moment M0 and crustal rigidity µ as uA = M 0 / µ , where u is the average
dislocation amplitude and A is the fault area. Because of different geometries of earthquake
sources and source depths, the “effective” volume of the displaced ocean floor is smaller. It
can be estimated from data on vertical movement in the source regions of well documented
tsunami events (Hatori, 1966), and from an estimate of the associated source areas. In Fig.
3, the range of observed values versus magnitude, for 6.5 < M < 8.5, is shown by a gray
band (parallel to uA , but smaller, by one to two orders of magnitude). This figure shows
that the largest submarine landslides are capable of displacing volume of sediments at ocean
floor two orders of magnitude larger than one displaced by large (M = 8.5) earthquakes. It
126
Trifunac and Todorovska
also shows that small landslides with volumes of 10-3 to 10-2 km3 can produce powerful,
though localized tsunami.
2.4 RELATIVE VERTICAL DISPLACEMENT
The spectral amplitudes of tsunami at long periods are determined by the volume of the
uplifted sea floor above the source region. The near-field tsunami amplitudes, however,
depend on the average amplitude of the uplift and on its variations in time and space in the
source area (Trifunac et al., 2001a,b; 2002a). Figure 4 (left) shows a comparison of
log10 ( u/A ) for eleven submarine mass movements ( u ) is the average vertical
displacement of the ocean floor) and for earthquakes that produced tsunami. It is seen that
u / A - km -1
100
10 -1
10 -2
10 -3
10 -4
10 -5
H
L
10 -6
es
Earthquak
10 -7
6
7
Magnitude
8
0
Scheidegger (1973)
average for subaerial
landslides
Edgers and
Karlsrud (1982):
upper bound
-1
log 10 (H/L)
101
Alika-1 0.1-0.3 MY
Alika-2 0.1 MY
Grand Banks 1929
102
Papua New Guinea 1998
Seward, Alaska, 1964
(all)
Munson-Nygren (segment)
Puerto Rico - Insular slope
(E) (W) East Breaks (mass floor)
N California 8 Nov. 1980
Sur submarine slide, 1500 yrs ago
Nuuanu, 1.4-2.6 MY
103
-2
-3
-6
Tristan de Cunha
Seward 25.0
4.8
quic
k cla
y sl
ide(
ssub
aer
ial
6.0 Alika - 2
2.0
1.5
Nuuanu
0.5
1.5
)
2.5
volcanos
3.5
non-volcanos
8.6 slope steepness (degrees)
2.0
-4
-2
0
log 10 Volume - km 3
2
8.6
4
Figure 4. (left) Comparison of u/A (average vertical displacement of the ocean floor / area of the uplifted region) for
selected submarine slides (points and vertical bars, plotted versus arbitrary magnitude coordinate), and earthquakes
(grey zone). (right, top) Runout model of submarine landslides. (right, bottom) H/L versus volume of failed mass,
for a compilation of known submarine landslides (after Hampton et al., 1996). Also shown are the upper bound
values from Edgers and Karlsrud (1982), the lower bounds for quick clay slides (subaerial), and the average trend
for subaerial landslides proposed by Scheidegger (1973).
most of the time this ratio is one to five orders of magnitude larger for submarine landslides
than for earthquakes. For most, particularly for the largest and older slides, it cannot be
assumed that all material slid during one event. It is possible that what is seen today is the
end result of repeated mass movements. On the other hand, both the Papua New Guinea and
Seward slides not only have the largest u/A (for this sample) but also represent single
events. An exception (in Fig. 4, left) is u/A for the Grand Banks, 1929, event.
2.5 RELATIVE SOURCE LENGTH
When the velocities of moving landslides become comparable to the long period tsunami
Tsunami source parameters of submarine earthquakes and slides
127
velocity gh , the parameter that governs the amplification of near-field water waves by
focusing is the ratio of slide length over water depth, L/h. Trifunac et al. (2001a,b) show L/h
for thirteen submarine slides and debris avalanches. For 9 of their 13 examples, this type of
amplification is possible.
2.6 RUNOUT
Figure 4 (right-top) shows a schematic cross-section of a submarine slide, which travelled
downslope, stopping at distance L and level H below its origin. Figure 4 (right-bottom)
summarizes known ratios of H/L versus the volume of failed mass (Hampton et al., 1996).
When known, the slope steepness in degrees is also indicated. Figure 4 further shows the
average value of H/L for subaerial landslides from Scheidegger (1973), and an upper bound
from Edgers and Karlsrud (1982). All the data fall above the trend for quick clay slides
(Locat and Demers, 1988). For the Hawaiian submarine slides, the runout data are close to
the trend for subaerial landslides (Hampton et al., 1996) and have H/L ratio larger than
those for the other submarine slides.
3. Conclusions
We presented a summary of the physical characteristics of tsunami sources. The main
differences between earthquake and tsunami sources are that (1) the earthquake rupture
usually spreads with larger velocities (2-3 km/s versus 0.001 to 0.1 km/s), and (2) the
balance of the total uplifted material for slides is usually small while for earthquakes it can
be considerable (0.01 of M0/µ). This affects the long period limit of the spectra of tsunami
amplitudes, proportional to the total uplifted volume of the ocean floor.
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