EARTHQUAKES
On 26 Dec 2004, an underwater 9.0-magnitude
earthquake off the coast of Aceh, Indonesia, sent
giant tidal waves into coastal areas in Indonesia,
Thailand, Malaysia, Sri Lanka, Bangladesh,
India, Myanmar, the Maldives and Somalia,
resulting in at least 159 000 people dead.
Questions: What does it mean when an
earthquake register 9.0 on the
Richter scale? How big is this
compared to a 8.0-magnitude
earthquake in Japan, on 26 Jan 2001
which killed at least 2 people?
 x 
The Richter scale is a measurement of earthquake magnitudes based on the formula R  lg 

 0.001 
where x is the intensity of the earthquake as registered on a seismograph.
Richter Value
Description
1
2
3
4
5
6
7
8
Cannot be felt except by instruments
Cannot be felt except by instruments
Cannot be felt except by instruments
Like vibrations from a passing train
Strong enough to wake sleepers
Very strong: walls crack, people injured
Ruinous: ground cracks, houses collapse
Very disastrous: few buildings survive, landslides
Section A: Investigation
1.
 x 
Make x the subject of the formula R  lg 
.
 0.001 
2.
Calculate the intensities x for both the 9.0-magnitude and the 8.0-magnitude earthquakes.
3.
How much greater in intensity is the 9.0-magnitude earthquake as compared to the 8.0magnitude earthquake?
4.
What is an easier way to compare the magnitudes of the two earthquakes without calculating
their intensities?
© Joseph Yeo
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Section B: Applications
5.
A 6.3-magnitude earthquake in Iran on 26 Dec 2003 killed 40 000 people. How much greater
in intensity is the 9.0-magnitude earthquake in Aceh as compared to that earthquake in Iran?
6.
The strongest earthquake ever recorded was 9.5 on 22 May 1960 in Chile. How much greater
in intensity is this earthquake as compared to the 9.0-magnitude earthquake in Aceh?
7.
The earthquake in Yunnan, China, on 26 Nov 2003 was 10 000 times weaker than the 9.0magnitude earthquake in Aceh. What is the magnitude of that earthquake in Yunnan?
8.
The earthquake in India on 26 Jan 2001 was 12.6 times weaker than the 9.0-magnitude
earthquake in Aceh. What is the magnitude of that earthquake in India?
9.
Why do you think we use the Richter scale, which is a logarithmic scale? Why can’t we just
use a normal scale based on the intensity x?
10.
The 6.3-magnitude earthquake in Iran on 26 Dec 2003 killed 40 000 people but the 8.0magnitude earthquake in Japan on 26 Sep 2003 only killed at most 10 people. What are some
of the reasons why the weaker earthquake was more devastating than the stronger one?
Section C: Conclusion
11.
Write down one main lesson that you have learnt in this worksheet.
Note: Did you notice that most of the earthquakes
mentioned in this worksheet occurred on the 26th
of the month? This mystery appeared in a Straits
Times article on 16 Jan 2005. But critics said that
there were major earthquakes occurring on other
days of the month as well! So there is nothing
special about the number 26.
© Joseph Yeo
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IMPORTANT NOTES FOR TEACHERS


May need to guide students to get the formula in Q1
Q4 and Q9 are the gist of this worksheet
ANSWERS
Section A: Investigation
1.
2.
 x 
Make x the subject of the formula R  lg 
.
 0.001 
x
 x 
R  lg 
 10 R  x  0.001  10 R
 
0
.
001
0
.
001


Calculate the intensities x for both the 9.0-magnitude and the 8.0-magnitude earthquakes.
Using the formula in Q1, x = 1 000 000 and 100 000 respectively.
3.
How much greater in intensity is the 9.0-magnitude earthquake as compared to the 8.0magnitude earthquake?
1 000 000  100 000 = 10 times
4.
What is an easier way to compare the magnitudes of the two earthquakes without calculating
their intensities?
Calculate the difference d in magnitudes, e.g. d = 9.0  8.0 = 1. So the Aceh earthquake is 10d
= 101 = 10 times stronger than the other one. Reason:
x 2 0.001  10 R2

 10 R2  R1  10 d .
R1
x1 0.001  10
Section B: Applications
5.
A 6.3-magnitude earthquake in Iran on 26 Dec 2003 killed 40 000 people. How much greater
in intensity is the 9.0-magnitude earthquake in Aceh as compared to that earthquake in Iran?
9.0  6.3 = 2.7. Therefore, the Aceh earthquake is 102.7 = 501 times stronger.
6.
The strongest earthquake ever recorded was 9.5 on 22 May 1960 in Chile. How much greater
in intensity is this earthquake as compared to the 9.0-magnitude earthquake in Aceh?
9.5  9.0 = 0.5. Therefore, the Aceh earthquake is 100.5 = 3.16 times stronger.
7.
The earthquake in Yunnan, China, on 26 Nov 2003 was 10 000 times weaker than the 9.0magnitude earthquake in Aceh. What is the magnitude of that earthquake in Yunnan?
10 000 = 104. Therefore, the magnitude of the Yunnan earthquake is 9.0  4 = 5.0.
© Joseph Yeo
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8.
The earthquake in India on 26 Jan 2001 was 12.6 times weaker than the 9.0-magnitude
earthquake in Aceh. What is the magnitude of that earthquake in India?
12.6 = 10R  R = lg 12.6 = 1.10. So the magnitude of the India earthquake is 9.0  1.10 = 7.9.
9.
Why do you think we use the Richter scale, which is a logarithmic scale? Why can’t we just
use a normal scale based on the intensity x?
If we use the intensity x, we will encounter very big and very small numbers, e.g. from 0.01
to 10 000 000. But we can’t simply scale down the very big numbers by dividing by 1000
because the very small numbers will become even smaller, e.g. 0.01  1000 = 0.000 01.
Therefore, we take logarithm to scale the numbers down, so that it goes from 1 to 10.
10.
The 6.3-magnitude earthquake in Iran on 26 Dec 2003 killed 40 000 people but the 8.0magnitude earthquake in Japan on 26 Sep 2003 only killed at most 10 people. What are some
of the reasons why the weaker earthquake was more devastating than the stronger one?

The Japan earthquake might have hit remote areas where there were less people.

The buildings in Japan were made of concrete but the buildings in Iran were built of wood.
Section C: Conclusion
11.
Write down one main lesson that you have learnt in this worksheet.

9.0-magnitude is not 3 times stronger than a 6.0-magnitude but 103 = 1000 times stronger

Why we use a logarithmic scale to measure earthquakes
© Joseph Yeo
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