1. How frequent are earthquakes?
Nuffield Free-Standing Mathematics Activity
How frequent are earthquakes?
Epicentres of earthquakes, 1963 – 1998, Image courtesy: NASA

2. How frequent are earthquakes?
It isn’t straightforward to answer this question as there are thousands of very minor earthquakes occurring every day.
But there are far fewer high magnitude earthquakes.
We can look at data on earthquakes to see if there is some relationship between the magnitude of earthquakes and how frequently they occur. We can then use functions and graphs to model any relationships.

3. How frequent are earthquakes? Average Annual Frequency
Description
Magnitude
Average Annual Frequency
Great Earthquakes
8 and higher 1
Major Earthquakes
7 – 7.9 18
Strong Earthquakes
6 – 6.9
120
Moderate Earthquakes
5 – 5.9
800
Light Earthquakes
4 – 4.9
6 200 (estimated)
Minor Earthquakes
3 – 3.9
(estimated)
Very Minor Earthquakes
2 – 2.9
approx per day
1 – 1.9
approx per day
Data Source: US National Earthquake Information Center

4. How frequent are earthquakes? Average Annual Frequency
Description
Magnitude
Average Annual Frequency
Great Earthquakes
8 and higher 1
Major Earthquakes
7 – 7.9 18
Strong Earthquakes
6 – 6.9
120
Moderate Earthquakes
5 – 5.9
800
Light Earthquakes
4 – 4.9
6 200 (estimated)
Minor Earthquakes
3 – 3.9
(estimated)
Very Minor Earthquakes
2 – 2.9
approx per day
1 – 1.9
approx per day
How can we convert magnitudes from a range to a single value for a data point?

5. How frequent are earthquakes?
Average annual frequency (N) of earthquakes
of magnitude at least M M N 8 1 7 19 6
139 5
939 4
7 100 3
56 000 2
Can you suggest some functions that you could use to model the data?

6. How frequent are earthquakes?
Average annual frequency (N) of earthquakes
of magnitude at least M M N 8 1 7 19 6
139 5
939 4
7 100 3
56 000 2
What techniques could you use to change a curved graph into a straight line graph?

7. How frequent are earthquakes?
The relationship Log10N = a - bM, between the magnitude (M) of earthquakes and the average annual number (N) of earthquakes of magnitude at least M, is a particular case of the
Gutenberg-Richter Law.

8. How frequent are earthquakes?
Reflect on your work
How did plotting the log graph help you to model the relationship between magnitude and frequency?
If plotting a log graph from a set of data points gives a straight line, does that mean the data can be modelled by an exponential function?
Could you have used ln N instead of Log10N to help you find a relationship between M and N? Would it have affected the final model?

9. How frequent are earthquakes?
The US Geological Survey Earthquake Archive search facility
allows one to extract bespoke data sets, using which one could model the data for particular geographical regions.