Mathematics 7–10 · Year 10
Logarithmic scales: what one unit of earthquake magnitude means
Number and algebra
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The idea
On a logarithmic scale each step multiplies rather than adds, so one unit of earthquake magnitude is ten times the shaking amplitude and about 32 times the energy, and two magnitudes from a real catalogue can be compared as a ratio.
What you need
- Geoscience Australia recent earthquakes list (earthquakes.ga.gov.au) for two real Australian events with their magnitudes
- Calculator with powers of ten
How to do it
- Read from the USGS explanation that each whole unit of magnitude is a tenfold increase in seismogram amplitude and about 32 times the energy release.
- Choose two recent Australian earthquakes from the Geoscience Australia list and record their magnitudes, dates and locations.
- Compute the amplitude ratio 10^(M2 − M1) and the energy ratio 10^(1.5 (M2 − M1)) for the pair.
- Plot magnitude against amplitude on ordinary axes and then on a logarithmic axis; describe why the second is a straight line.
- Extension: compute how many magnitude-4 earthquakes release the energy of one magnitude-6.
What you should see
As a worked check, a difference of 2.9 magnitude units (a magnitude 5.8 against a magnitude 8.7) is an amplitude ratio of 10^2.9 = 794 and an energy ratio of 10^4.35 = 22 400. One magnitude 6 releases the energy of 10^3 = 1000 magnitude 4 events. On the logarithmic axis the points lie on a straight line of gradient 1 per magnitude unit for amplitude and 1.5 for energy. The learner knows it worked when the ratios for their chosen pair are computed from the catalogue magnitudes and the amplitude ratio equals ten raised to the magnitude difference.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A magnitude 6 is twice as strong as a magnitude 3.
- Equal steps on a logarithmic axis are equal amounts.
- Magnitude measures the damage caused.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 5 Logarithms (Path); the content group on establishing and applying the laws of logarithms ends with a point on examining logarithmic scales and explaining their use in various contexts, so a logarithmic scale is syllabus content in its own right and not merely the setting in which the laws are applied; earthquake magnitude is named on the page only in the cross-curriculum links, which send the Richter scale to Stage 5 Science and Stage 6 Earth and Environmental Science; the glossary term in that content point loads after the page, so a read that catches the line early renders it as 'Examine Loading and explain their use in various contexts'; page read 2026-09-23MA5-LOG-P-01
- Australian Curriculum v9AC9M10M02AC9M10A03
Sources
The pages the author read to write this activity.