Science 7–10 · Year 8

Locating an epicentre from S minus P times at three stations

Science understanding: Earth and space sciences (NSW Stage 4 focus areas Change and Data science 1)

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The idea

P waves outrun S waves, so the gap between their arrivals grows with distance; three distances drawn as circles cross at the epicentre.

What you need

three seismograms from one earthquake with P and S arrivals marked and station coordinates, from stations within about 150 km of the epicentre so the waves travel through the crust (the Geoscience Australia earthquakes activities); the IRIS lesson set uses stations around the world and reads distance from a travel-time curve instead
a map of the region at a known scale, a pair of compasses, a ruler
a calculator; the crustal wave speeds from the British Geological Survey: P 5 to 7 km/s, S 3 to 4 km/s

How to do it

On each seismogram read the P arrival and the S arrival and compute the S minus P interval in seconds.
Convert each interval to distance with d = dt / (1 / vS - 1 / vP) using vP = 6.0 km/s and vS = 3.5 km/s (inside the BGS crustal ranges), which is 8.4 km per second of interval. This holds only for crustal paths, stations within about 150 km; for distant stations use a travel-time curve.
Set the compasses to each distance at the map scale and draw a circle about each station.
Mark where the three circles cross; if they form a small triangle, mark its centre and use its size as the uncertainty.
Estimate the origin time by subtracting the P travel time (d / vP) from the first P arrival at the nearest station.

What you should see

With vP = 6.0 and vS = 3.5 km/s an S minus P interval of 5 s gives 42 km, 10 s gives 84 km and 15 s gives 126 km. The fixed crustal speeds hold only out to roughly 150 to 200 km: beyond that the first waves have travelled partly through the mantle, where the BGS gives P above 8 km/s and S 4.5 km/s, about 10.3 km per second of interval, so crustal speeds would draw a distant station's circle nearly a fifth too small and the circles would not meet. The three circles cross at or near one point; a small triangle is normal because real wave speeds vary along each path. The origin times worked out from the three stations should agree closely; any spread shows how far the assumed speeds are from the real ones. The learner knows it worked when the three circles meet in one small area and the origin times agree.

What changes

What you change: distance from the epicentre
What you measure: S minus P interval
What you keep the same: wave speeds assumed the same for all paths

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The station that shakes hardest is at the epicentre; distance comes from timing, not amplitude.
One seismogram can locate an earthquake; one gives only a distance, so a circle.
Waves travel at one speed; the P and S speed difference is what makes location possible.

Safety card

Low riskLearners carry it out

Hazards

compass point

Controls

handle the compasses by the hinge

Note

No hazardous chemical and no flame or heating apparatus: a generic classroom risk assessment (CSIS 1.7 or RiskAssess) covers trips, spills, warm lamps and sharp edges.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Science 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; codes read at curriculum.nsw.edu.au on 22 and 23 September 2026)SC4-CHG-01 SC4-DA1-01 SC4-WS-05 SC4-WS-06
Australian Curriculum v9AC9S8U03AC9S8I04AC9S8I05

Sources

The pages the author read to write this activity.

All Concept Studio activities