Mathematics 11–12 · Years 11–12
Earthquake magnitude: the 1989 Newcastle earthquake on a logarithmic scale
Further graph transformations and modelling: Modelling with functions (Mathematics Advanced, Year 12); Exponential and logarithmic functions: Logarithmic functions (Mathematics Advanced, Year 11)
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The idea
A one-unit step in earthquake magnitude multiplies the recorded wave amplitude by 10 and the energy released by about 32, which a logarithmic scale compresses into equal steps.
What you need
- Geoscience Australia's account of the 28 December 1989 Newcastle earthquake (ML 5.6, MW 5.4, epicentre about 15 km south-west of the Newcastle CBD)
- The USGS statement of the amplitude and energy change per magnitude unit
How to do it
- Write the amplitude as A = A0 x 10^M and the energy as E = E0 x 10^(1.5 M) and explain why each is a logarithmic scale.
- Compute the amplitude and energy ratios between an ML 5.6 event and a magnitude 4.6 event, then a magnitude 6.6 event.
- Compute the energy ratio for a difference of 0.3 in magnitude.
- Plot energy against magnitude on linear axes and with a logarithmic energy axis and describe the two graphs.
What you should see
Magnitude 5.6 against 4.6: 10 times the amplitude and 10^1.5 = 31.6 times the energy (the USGS gives about 32). Magnitude 6.6 against 5.6: the same factors again. A difference of 0.3 gives an energy ratio of 10^0.45 = 2.82. On a logarithmic energy axis the graph is a straight line of gradient 1.5. The learner knows it worked when the energy ratio for two whole units equals (10^1.5)^2 = 1000.
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 earthquake is twice a magnitude 3; it releases about 31 600 times the energy.
- Magnitude measures damage; damage depends on depth, distance and buildings, which is why a moderate event near Newcastle did so much harm.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals and no 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 Advanced 11–12 Syllabus (2024), Year 12 focus area Further graph transformations and modelling; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-12-02
- Mathematics Advanced 11–12 Syllabus (2024), Year 11 focus area Exponential and logarithmic functions; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-11-07MAV-11-08
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-advanced-11-12-2024/content/year-12/fa3b2bda67
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-advanced-11-12-2024/content/year-11/fa576d8dce
- www.ga.gov.au/news/30-years-on-commemorating-the-1989-newcastle-earthquake
- www.usgs.gov/programs/earthquake-hazards/earthquake-magnitude-energy-release-and-shaking-intensity