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How frequent are earthquakes?

Explore the relationship between earthquake magnitude and occurrence frequency using data and mathematical modeling techniques. Reflect on the use of logarithmic graphs and the Gutenberg-Richter Law. Use the US Geological Survey Earthquake Archive search facility to extract customized data sets for specific geographical regions.

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How frequent are earthquakes?

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  1. 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? Data Source: US National Earthquake Information Center

  4. How frequent are earthquakes? 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 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 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. http://en.wikipedia.org/wiki/Gutenberg%E2%80%93Richter_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 Ninstead of Log10Nto help you find a relationship between Mand N? Would it have affected the final model?

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

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