The mathematics in earthquakes

Holidays are good in many ways. They give us the headspace we need to refresh and reflect. They also give us the time to explore opportunities such as the one I attended last night.

The University of Melbourne holds free seminars for the public on various themes and there was one last night on earthquakes.

It was very well attended, there was a lot of information presented and a lot to think about afterwards. Of particular interest to teachers of mathematics were the following aspects of the presentation…and of great relevance to students, I would imagine, given the current world interest and situation regarding earthquakes.

(1) Importance of collecting data to provide evidence for any predictions or conclusions about behaviours noticed.

(2) Connection to data analysis and what data can, and cannot, tell us. Records have been kept since the start of the 20th century. This data has shown a continuous pattern in the number and severity (on the Richter scale) of earthquakes over time for those not classified as ‘giant’ (over 9 on the Richter scale). There have also been 3 clusters of events where earthquakes have been over 9 in strength, the last set being those the earth has experienced in the last 10 years. However, 3 clusters over the timespan for which we have data is not sufficient to be able to predict the occurrence of the next cluster. It just isn’t enough given the age of the earth.

(3) Despite Simon Winchester’s ‘prediction’ in a recent Newsweek article that these recent events are triggers that indicate an even bigger event is yet to come, and that it will come to the American West Coast, the data just isn’t good enough to point to this. There is some evidence that earthquakes occur along the same fault line (the ‘load’ increases along the line generally, but not always, in the same direction so that a 10km stretch along the fault line will be followed by some other distance along the fault line etc) but it doesn’t do so in a continuous manner (sometimes missing 6 km along the fault line) and sometimes it goes back in the direction in which it came. And the time between events along the fault line has yet to show a known pattern. So it isn’t a simple ‘unzipping’ along the fault line at known intervals of time that could be predicted well ahead of events.

(4) The mathematics of the Richter scale itself. As we know, the scale is logarithmic using base 10. So an earthquake of size 7 is 10 times more powerful than one of size 6 and 100 times as powerful as one of size 5. Students in Y7 & 8 & 9 or even younger could do some wonderful mathematics with this and look at powers of 10 at the same time. Students who know about the decimal system could then consider problems such as: “How much stronger than an earthquake of 8.9 is one of 9.2?” Answer: 30 times as strong. How come? Some really good thinking here that would re-inforce the concept of place value and powers of 10.

(5) For students looking at the graphs of sine and cosine functions, consideration of the tsunami wave and its wavelength and its amplitude would add value to their mathematical understanding. In particular, we were told in this presentation how many tsunamis formed through earthquakes out in the open oceans caused little damage due to the force being converted into waves with long wavelength (period) and low amplitude (height of the waves). However, if the earthquake occurs near a coast, the same force has less space to disperse so the wavelength is much shorter and the amplitude much higher. This is explained in more detail here.

(6) The mathematics of building response under stress from an earthquake. Some buildings shake at a response rate of 10Hz (10 cycles per second). Perhaps some exploration of rates using actual data on frequency responses of buildings could be done in classes.

(7) One of the presenters talked about the actual structure of the ground in which structures are situated. Most of these are granular structures. These act unpredictably. Apparently, only 40% of the grains in such a structure carry the load of any weight placed on them (like a building). There are ‘force chains’ in the granular structure formed between the grains that carry the weight and when these chains are disrupted or broken (like in an earthquake), the building can become unstable in the ground in which it is situated. Students could estimate the number of grains of sand in a jar then work out 40% of this to see just what this amount looks like. A valuable visualisation within a real context.

Not a ‘nice’ context for much of this mathematics.

But one, it seems, to be coming even more necessary to study in order to understand and predict future events. We cannot stop earthquakes, but increasing our knowledge of their behaviours and their consequences on aspects of human life, can only assist our understanding and thus better control their impact.


About Linda

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