Name ………………………………………
GLENDALE
COMMUNITY
COLLEGE
Tsunamis, Ocean Depth Estimation
and Tsunami Prediction Exercise
Objectives:
This exercise seeks to familiarize you with …
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Date ……………
the use of a simple formula to solve a problem;
verifying an equation by conducting a simple
experiment; and
the predictability of tsunamis.
Dr. Poorna Pal
Materials
„ Computer with internet access.
„ Wave tank and stop watch.
„ Pencil, paper and graph sheet and
calculator.
In the process, you will get to use geographic coordinates, particularly to find distances between
different locations on Earth, and learn about how tsunami velocities were first used to find the
average depth of the ocean, and about the region devastated by December 2004 Indian Ocean
tsunami.
Tsunamis and Ocean Depths:
Tsunamis are impulsively generated (i.e., by underwater earthquakes, volcanism and/or landslides) shallow water waves that, as evidenced by the December 2004 Indian Ocean Tsunami,
often prove to be very destructive. They tend to have wavelengths of 120-160 km and travel
with velocities of 650-700 km per hour. Although usually unnoticeable in the open ocean, where
they have heights < 3 m, their wavelengths and velocities decrease but heights increase greatly
as they break on entering the shallow coastal waters.
For instance, the map and graph on
the right show the observations recorded by the US-French satellites,
TOPEX/Poseidon and Jason-1, as they
passed over the Bay of Bengal two
hours after the magnitude 9.3 earthquake struck off the coast of Sumatra,
just about the time the leading edge of
the tsunami was hitting Sri Lanka and
India. The satellites saw the first two
wavefronts produced by the main
quake, spaced 500 to 800 km apart.
These waves reached a maximum
height of 50 cm in the open ocean,
only reaching their full devastating
height when entering the shallow
waters of the coast.
Now, the velocity V of shallow water
waves is given by
V = √(g.D)
(1)
2
http://topex-www.jpl.nasa.gov/newsroom/press-releases/20050111.html
where g = 9.81 m/sec is acceleration
due to gravity and D is the basin depth,
in meters.
Alexander Bache, a great-grandson Benjamin Franklin, was perhaps the first to use this
equation to formulate an ingenious strategy, in 1856, to estimate the then unfathomable depth
of the average ocean. Note that Equation (1) can be rewritten as
D =
V2/g
(2)
where D is the average depth of the intervening ocean if we estimate V = (distance/time) from
the observed data on tsunami travel times.
For instance, this chart below shows the NOAA (National Oceanic and Atmospheric Administration) estimates of travel time in hours for a tsunami to reach Hawaii from an earthquake at any
of the Pacific locations given here. Clearly, the farther the location, the longer the travel time.
But then, as the above equation shows, depth of the ocean (D) also matters, i.e., the deeper the
ocean the faster the velocity and lesser the travel time.
Activity 1: Suppose we assume a tsunami velocity V = 200 m/sec. What would be
the average ocean depth, then, based on the equation D = V2/g?
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The Indian Ocean Tsunami Data:
Observational data on the December 2004 Indian Ocean tsunami amply corroborate the NOAA
model estimates for Pacific Ocean shown above. The following three maps show the worldwide
arrival times for this tsunami (top figure) and the model estimates of arrival times (bottom left)
and maximum wave heights (bottom right).
Indian Ocean Tsunami: Observed Arrival Times
(http://www.pmel.noaa.gov/tsunami/indo20041226/global_obswavearr.jpg)
Model arrival time (hours) of tsunami from Dec
26, 2004 Sumatra Earthquake
Model maximum wave height (cm) of tsunami
from Dec 26, 2004 Sumatra Earthquake
http://www.pmel.noaa.gov/tsunami/indo20041226/TT.pdf
http://www.pmel.noaa.gov/tsunami/indo20041226/max.pdf
The panel below shows some of the tidal charts that recorded the arrival times of disturbances
from the December 26, 2004 Sumatra earthquake. The arrival time data for tidal gauges in India
Survey of India Tidal Gauge Data (http://www.nio.org/jsp/tsunami.jsp)
These tidal
gauges recorded
the arrival time of
disturbances from
the Dec 26, 2004
Sumatra earthquake (0529 hrs,
IST). The arrival
times are in IST
(Indian Standard
Time).
0529 hr
Visakhapatnam, India
0905 hr December 2004
3
Chennai, India
0529 hr
0957 hr December 2004
0905 hr December 2004
0529 hr
1110 hr
Tuticorin, India
0529 hr
0529 hr
Kochi, India
Marmagao, India
1225 hr December 2004
December 2004
100
0
Disturbance (cm)
Disturbance (cm)
Some other tidal gauge records
Colombo, Sri Lanka
Earthquake
0.59 hr,
UTC
-100
26 0300 hr, UTC
27
28
100
0
Earthquake
0.59 hr,
UTC
-100
26
26
Disturbance
(cm)
December 2004
20
0
- 20
D e c 2 6 , 0 0 :5 9 h r U T C
27
0530 hr, UTC 27
December 2004
28
28
W in t e r H a r b o r , B C ,
Canada
D e c 2 7 , 0 8 :1 5 h r U T C
27
Point
LaRue,
Mauritius
Point
LaRue,
Mauritius
29
28
30
31
D ecem ber 2004
are given in Indian Standard Time (IST) here, the corresponding time for the Sumatra earthquake being 05:29 hr IST on December 26, 2004. The tidal gauge records for Colombo, Sri
Lanka, Point LaRue, Mauritius, and Winter Harbor, British Columbia, Canada, are also shown
here, with arrival time data in UTC.
Activity 2: We can use these observational data to ascertain if our earlier
assumption of ~200 m/sec for tsunami velocity is indeed reasonable.
To do so,
(a)
Find the latitudes and longitudes of the cities/locations for which the tidal charts are shown
above, using the URL: http://worldatlas.com/aatlas/imageg.htm and enter these data in
Table below.
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(b)
Use the URL http://www.export911.com/convert/distaCaIc.htm to find the distances of
these cities/locations from the epicenter (3.30ºS: 95.78ºE) of December 26, 2004 Sumatra
earthquake and enter these results in Table below.
(c)
Read the time difference between the tsunami generating event (the December 26, 2004
Sumatra earthquake) and tsunami arrival times from tidal charts and enter the results in
Table below.
(d)
Use the tabulated results to compute tsunami velocities and enter the results in the last
column in Table below.
Location
Latitude Longitude
Distance from
Epicenter (km)
Tsunami Travel
Time (hrs)
Average velocity
(e)
Tsunami
Velocity
=
Do any of these observations yield exceptionally high or low velocity estimates? What can
be the possible explanation?
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(f)
Use this average velocity to estimate the average depth of Indian Ocean.
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(g)
Use this average velocity to estimate the tsunami arrival time at (i) Mombasa, Kenya and
(ii) Phuket, Thailand.
Mombasa, Kenya
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Phuket, Thailand
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(h)
Plot the Indian Ocean locations from amongst these in the map below.
30°N
1
0°
30°S
10
30°E
9
8
7
6
4
5
60°E
3
2
90°E
6
120°E
Experimental Verification:
Using equation (1) to estimate the average ocean depth from tsunami velocities, and the match
between the average tsunami velocities obtained in Activity 2 and the value of 200 m/sec2 that
was assumed in Activity 1 suggests that our identification of tsunamis as shallow water waves
can be experimentally verified.
Activity 3: Verify experimentally that the tsunamis are indeed shallow water waves.
(a)
Fill the water tank to 1 cm (= h). Now lift its one end by about 5 cm and drop it,
starting the stop watch at the instant it is dropped. Stop the watch as soon as the
waves created on dropping the tank complete one runs (try two runs if the time taken
by one run is too short to be recorded accurately). Record your observations in the
Table below.
(b)
Repeat (a) four more times. You thus have a total of five trials for 1 cm water level.
(c)
Repeat (a) and (b) with water levels (h) of 2 cm, 3 cm, 4 cm and 5 cm.
h = 1 cm
Trial I
Trial II
Trial III
Trial IV
Trial V
Trial I
Trial II
Trial III
Trial IV
Trial V
Trial I
Trial II
Trial III
Trial IV
Trial V
Trial I
Trial II
Trial III
Trial IV
Trial V
Distance
Time
Velocity
h = 2 cm
Distance
Time
Velocity
h = 3 cm
Distance
Time
Velocity
h = 4 cm
Distance
Time
Velocity
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h = 5 cm
Trial I
Trial II
Trial III
Trial IV
Trial V
Distance
Time
Velocity
(d)
h=
Use the data in the above Table to fill in the Table below. Here, O = observed (or
computed) and E = expected (or theoretical) velocity.
Average velocity
Theoretical velocity = √(gh)
% error = 100 × (O – E)/E
1 cm
2 cm
3 cm
4 cm
5 cm
Verify that graphing these results below, using equation (2), linearizes.
V2/g (m)
(e)
h=
0
1 cm
2 cm
3 cm
8
4 cm
5 cm
6 cm
(f)
Why is the above graph linear? Can we extrapolate it to the observed Indian Ocean
tsunami velocity data? Discuss.
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(g)
Discuss the possible sources or error.
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Tsunami Predictability:
Time since the earthquake
occurred (minutes)
The fact that tsunami velocity in
the open ocean is ~200 m/sec
means that the time of a tsunami
arrival can be easily predicted.
This is because the earthquake
body waves travel 20-30 times
faster, the average velocity of
seismic P (primary) waves through
the crust being ~6 km/sec and that
of the S (shear) waves ~4 km/sec.
Thus, as shown in the graph
alongside, information about an
earthquake is available in a matter
of minutes, no matter where in the
ocean the temblor occurred.
Distance (km) from the epicenter
However, neither do all earthquakes, however strong, produce devastating tsunamis nor do all
such tsunamis result from earthquake activity. True, the December 2004 Indian Ocean tsunami
was one of history’s most devastating natural disasters, as the satellite pictures reproduced
below amply testify, and was produced by the magnitude 9.3 earthquake, perhaps the most
powerful one in recorded history. Some details about this earthquake too are shown below.
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Banda Aceh, Sumatra,
South Overview. Imagery
collected Jan 2, 2005
(after tsunami)
Banda Aceh, Sumatra,
South Overview. Imagery
collected April 12, 2004
(before tsunami)
http://www.digitalglobe.com/tsunami_gallery.html
http://www.digitalglobe.com/tsunami_gallery.html
Kalutara Beach, Sri Lanka.
Imagery collected Dec 26,
2004 (after tsunami) shows
receding waters and beach
damage from tsunami.
Kalutara Beach, Sri Lanka.
Imagery collected Jan 1,
2004 (before tsunami)
shows the pristine tropical
beach.
http://www.digitalglobe.com/tsunami_gallery.html
http://www.digitalglobe.com/tsunami_gallery.html
This map of the ocean floor was captured
using high-resolution multi-beam sonar from
a UK Royal Navy survey ship, the HMS
Scott, and reveals a landscape transformed
by the quake which occurred as the Indian
tectonic plate pushed against the Burma
plate – its leading edge being driven further
beneath it. Marine geologists aboard the
ship identified features that bear testament
to the earthquake that wrenched the ocean
bed, including slabs of rock dragged up to
10 km along the seabed by the force of the
displaced water. The images also show
mountainous ridges 1500 m tall and an
oceanic trench several km wide, created over much greater periods of time by activity along
the fault.
Source: http://www.newscientist.com/channel/earth/tsunami/dn6994
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http://www.usgs.gov
Try these links to learn more about the
tsunamis in general and about the Dec
2004 Indian Ocean tsunami in particular:
http://observe.arc.nasa.gov/nasa/exhibits/tsunami/tsun_bay.html
http://news.bbc.co.uk/2/hi/in_depth/4126019.stm
http://iri.columbia.edu/~lareef/tsunami/
According to the USGS, the Dec 26, 2004
earthquake that produced the tsunami was a
megathrust earthquake that occurred on the
interface of the India and Burma plates and
was cause by the release of stresses that
develop as the India plate subducts beneath
the overriding Burma plate. The India plate
begins its decent into the mantle at the
Sunda trench which lies to the west of the
earthquake's epicenter. The trench is the
surface expression of the India-Burma plate
interface.
Preliminary locations of larger aftershocks
following the megathrust earthquake show
that approximately 1000 km of the plate
boundary slipped as a result of the earthquake. Aftershocks are distributed along
much of the shallow plate interface and primarily extend northwards of the epicenter to
the Andaman Islands.
This map of historical seismicity for the 14992004 AD period of shows 2181 events. The
star marks the position of the main shock of
Dec 26, 2004 earthquake. The vertical cross
section along line AB is shown below.
(Source: http://tsun.sscc.ru/tsulab/20041226.htm)
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Cumulative number of earthquakes
since the main magnitude 9.3
event of Dec 26, 2004
(00:58:49 UTC)
500
400
300
200
100
480
960
Time (UTC) since Dec 26, 2004
Feb 20,
2005
Jan 01,
2005
Dec 26,
2004
0
1440
hrs
It is not only that the megathurst regions
such as the Sunda arc have intermittent
seismicity, seen in the above plot of 14992004 data for instance, but also that the
events such as that of Dec 26, 2004, seldom
occur in isolation. Thus, as is graphed
along-side, the two month period since this
event had already witnessed 400-plus
aftershocks, several of them of magnitudes
7-8. But the much feared recurrence of the
Dec 26, 2004 tsunami did not materialize.
Nonetheless, as the USGS report on the
Dec 26, 2004 events in Indian Ocean region
Source: http://www.nio.org/jsp/tsunami.jsp
emphasizes, the worlds largest recorded earthquakes have all been megathrust events
that occur where one tectonic plate subducts beneath another, e.g.,
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the magnitude 9.5 Chile earthquake (1960),
the magnitude 9.2 Prince William Sound, Alaska earthquake (1964),
the magnitude 9.1 Andreanof, Alaska earthquake (1957), and
the magnitude 9.0 Kamchatka earthquake (1952).
As with the 2004 Indian Ocean region event, megathrust earthquakes often generate
large tsunamis that can cause damage over a much wider area than is directly affected
by ground shaking near the earthquake's rupture.
As for the Indian Ocean region, though, the last major tsunami of comparable severity is
associated with the 1883 catastrophic volcanism at Krakatoa. A series of three explosions
on the morning of August 27, 1883 (about 05:28 local time) destroyed Krakatoa's peak and led
to a tsunami that propagated across the Indian Ocean. An hour later, at 06:36 hours, the 500 m
peak at Danan exploded and collapsed while the third and final blast tore the remaining part of
Krakatau Island (Rakata Island) apart. The total energy released by the explosion amounted to
the equivalent of 200 megaton atomic bombs (8.4 x 107 joules). The fatality count was at least
36,000, particularly in Java and Sumatra, as wave heights reached 15 to 42 m.
00:59 UTC
Tide-gauge record from the Sibolga port, Sumatra, shows that the rise of tsunami there, close to
the epicenter, was almost instantaneous
(Source: http://tsun.sscc.ru/tsulab/20041226.htm)
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Andaman Islands, India
How is it, then, that some
tsunamis prove calamitous
while the others do not? To
understand this, we need
to understand why waves
break in the first place.
After all, as some
members of the otherwise
avowedly primitive tribals
of the Andaman and
Nicobar Islands and some
Sri Lankan fishermen
already knew, open ocean
away from where the
waves break is perhaps
the safest place to be in
when a tsunami strikes the
shore.
Why is that so? This is because waves break on reaching the shore. Wave velocity (V), also
defined as wave celerity = L/T where L denotes wavelength and T the wave period, varies
directly with wavelength (L) but long waves die out in the shallow coastal waters. In the open
ocean, V = √(gL/2π) ≈ 1.25 √L. Thus, in the open ocean, tsunamis with L ≈ 200 km and T ≈ 20
minutes have velocities (or celerities) of ~170 m/sec compared to the velocities (or celerities) of
~30 m/sec for the typical wind-generated waves (L ≈ 600 m and T ≈ 20 sec). In the shallow
coastal ocean of depth D, on the other hand, V = √(gD) so that a tsunami traveling at the rate of
~200 m/sec in the open ocean must suddenly slow down to ~30 m/sec in a ~100 m deep basin
and ~10 m/sec if the basin depth is ~10 m. This clearly makes the wave closer to the shore
slower than the one immediately behind, so forcing them to topple over one another.
The problem with wave interference, however, is that one can never tell whether it will be
constructive or destructive. The former produces tall waves by amplifying the effects of the
individual wave components, and therefore causes coastal destruction. The latter subdues the
heights of the component waves, on the other hand, and therefore causes no harm whatever.
Question: Would a boat crossing the path of a tsunami traveling in the open
ocean capsize? Explain your answer.
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