Name ……………………………………… Date ……………

Tsunamis, Ocean Depth Estimationand Tsunami Prediction Exercise

GLENDALECOMMUNITYCOLLEGE

Dr. Poorna Pal

Objectives: This exercise seeks to familiarize you with …

the use of a simple formula to solve a problem; verifying an equation by conducting a simple

experiment; and

Materials Computer with internet access. Wave tank and stop watch. Pencil, paper and graph sheet and

calculator.

the predictability of tsunamis.

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 land-slides) 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 re-corded 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 earth-quake 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)

http://topex-www.jpl.nasa.gov/newsroom/press-releases/20050111.html

where g = 9.81 m/sec2 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 Administra-tion) 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).

Model arrival time (hours) of tsunami from Dec 26, 2004 Sumatra Earthquake

http://www.pmel.noaa.gov/tsunami/indo20041226/TT.pdf

Model maximum wave height (cm) of tsunami from Dec 26, 2004 Sumatra Earthquake

http://www.pmel.noaa.gov/tsunami/indo20041226/max.pdf

Indian Ocean Tsunami: Observed Arrival Times(http://www.pmel.noaa.gov/tsunami/indo20041226/global_obswavearr.jpg)

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 earth-quake (0529 hrs, IST). The arrival times are in IST (Indian Standard Time).

Visakhapatnam, India

0905 hr December 2004

0529 hr Visakhapatnam, India

0905 hr December 2004

0529 hr

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Chennai, India0529 hr

0905 hr December 2004

Chennai, India0529 hr

0905 hr December 2004

Tuticorin, India

0957 hr December 2004

0529 hr Tuticorin, India

0957 hr December 2004

0529 hr

Kochi, India

1110 hr December 2004

0529 hr Kochi, India

1110 hr December 2004

0529 hr

Marmagao, India

1225 hr December 2004

0529 hr Marmagao, India

1225 hr December 2004

0529 hr

Some other tidal gauge records Colombo, Sri Lanka

27 2826December 2004

Earth-quake0.59 hr,UTC

0300 hr, UTC

0

-100

100

Dis

turb

ance

(cm

) Colombo, Sri Lanka

27 2826December 2004

Earth-quake0.59 hr,UTC

0300 hr, UTC

0

-100

100

Dis

turb

ance

(cm

)

27 2826

0

-100

100D

istu

rban

ce (c

m)

Earth-quake0.59 hr,UTC

Point LaRue, Mauritius

0530 hr, UTC 27 2826December 2004

Earth-quake0.59 hr,UTC

Point LaRue, Mauritius

0530 hr, UTC 27 2826December 2004

27 2826

0

-100

100D

istu

rban

ce (c

m)

Earth-quake0.59 hr,UTC

Point LaRue, Mauritius

0530 hr, UTC 27 2826December 2004

Earth-quake0.59 hr,UTC

Point LaRue, Mauritius

0530 hr, UTC 27 2826December 2004

D e c 2 6 , 0 0 :5 9 h r U T C

Dis

turb

ance

(c

m)

2 92 8 3 1D e c e m b e r 2 0 0 4

3 02 7

D e c 2 7 , 0 8 :1 5 h r U T C W in te r H a rb o r , B C , C a n a d a2 0

0- 2 0

D e c 2 6 , 0 0 :5 9 h r U T C

Dis

turb

ance

(c

m)

2 92 8 3 1D e c e m b e r 2 0 0 4

3 02 7

D e c 2 7 , 0 8 :1 5 h r U T C W in te r H a rb o r , B C , C a n a d a2 0

0- 2 0

2 00

- 2 0

are given in Indian Standard Time (IST) here, the corresponding time for the Sumatra earth-quake 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)

Tsunami Velocity

Average velocity =

(e) 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.

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34

56

78

910

30°E 60°E 90°E 1 °E

30°N

0°

30°S

20

12

34

56

78

910

12

34

56

78

910

30°E 60°E 90°E 1 °E

30°N

0°

30°S

30°E 60°E 90°E 1 °E

30°N

0°

30°S

2020

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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

Distance

Time

Velocity

h = 2 cm Trial I Trial II Trial III Trial IV Trial V

Distance

Time

Velocity

h = 3 cm Trial I Trial II Trial III Trial IV Trial V

Distance

Time

Velocity

h = 4 cm Trial I Trial II Trial III Trial IV Trial V

Distance

Time

Velocity

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h = 5 cm Trial I Trial II Trial III Trial IV Trial V

Distance

Time

Velocity

(d) Use the data in the above Table to fill in the Table below. Here, O = observed (or

computed) and E = expected (or theoretical) velocity.

h = Average velocity Theoretical velocity = √(gh) % error = 100 × (O – E)/E

1 cm

2 cm

3 cm

4 cm

5 cm (e) Verify that graphing these results below, using equation (2), linearizes.

V2 /g (m

)

h = 0 1 cm 2 cm 3 cm 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:

Tim

e si

nce

the

eart

hqua

ke

occu

rred

(min

utes

)

Distance (km) from the epicenter

Tim

e si

nce

the

eart

hqua

ke

occu

rred

(min

utes

)

Distance (km) from the epicenter

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.

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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Kalutara Beach, Sri Lanka. Imagery collected Dec 26, 2004 (after tsunami) shows receding waters and beach damage from tsunami. http://www.digitalglobe.com/tsunami_gallery.html

TuaSbtpbstb1dm

oceanic trench several km wide, created over much the fault. Source: http://www.newscie

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Banda Aceh, Sumatra, South Overview. Imagery collected April 12, 2004 (before tsunami) http://www.digitalglobe.com/tsunami_gallery.html

Banda Aceh, Sumatra, South Overview. Imagery collected Jan 2, 2005 (after tsunami) http://www.digitalglobe.com/tsunami_gallery.html

Kalutara Beach, Sri Lanka. Imagery collected Jan 1, 2004 (before tsunami) shows the pristine tropical beach. http://www.digitalglobe.com/tsunami_gallery.html

his map of the ocean floor was captured sing high-resolution multi-beam sonar from UK Royal Navy survey ship, the HMS cott, and reveals a landscape transformed y the quake which occurred as the Indian ectonic plate pushed against the Burma late – its leading edge being driven further eneath it. Marine geologists aboard the hip identified features that bear testament o the earthquake that wrenched the ocean ed, including slabs of rock dragged up to 0 km along the seabed by the force of the isplaced water. The images also show ountainous ridges 1500 m tall and an

greater periods of time by activity along ntist.com/channel/earth/tsunami/dn6994

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.htmlhttp://news.bbc.co.uk/2/hi/in_depth/4126019.stmhttp://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 earth-quake. Aftershocks are distributed along much of the shallow plate interface and pri-marily extend northwards of the epicenter to the Andaman Islands.

This map of historical seismicity for the 1499-2004 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)

http://www.usgs.gov

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Cumulative number of earthquakes since the main magnitude 9.3 event of Dec 26, 2004 (00:58:49 UTC)

480Time (UTC) since Dec 26, 2004D

ec 2

6,

2004

Jan

01,

2005

Feb

20,

2005

960 1440hrs

0

100

200

300

400

500 Cumulative number of earthquakes since the main magnitude 9.3 event of Dec 26, 2004 (00:58:49 UTC)

480Time (UTC) since Dec 26, 2004D

ec 2

6,

2004

Jan

01,

2005

Feb

20,

2005

Dec

26,

20

04

Jan

01,

2005

Feb

20,

2005

960 1440hrs

0

100

200

300

400

500

0

100

200

300

400

500

Source: http://www.nio.org/jsp/tsunami.jsp

It is not only that the megathurst regions such as the Sunda arc have intermittent seismicity, seen in the above plot of 1499-2004 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

emphasizes, the worlds largest recorded earthquakes have all been megathrust events that occur where one tectonic plate subducts beneath another, e.g.,

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 UTC00:59 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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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.

Andaman Islands, India

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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