Earth and Space Science / Unit 4: Earthquakes and Volcanoes
4.4 Locating Epicenters
Notes
The difference between S-wave and P-wave arrival times increases with distance from the epicenter.
- Use a time-travel graph to turn the S-P time gap into distance.
- Simple model: if P waves travel 8 km/s and S waves 4.5 km/s, then distance $d$ satisfies $\displaystyle \frac{d}{4.5} - \frac{d}{8} = \text{gap}$.
- Example: gap of 70 s: $d(0.2222 - 0.125) = 70$, so $d \approx 720$ km.
- One station gives a circle of possible locations. Three stations whose circles intersect at one point locate the epicenter (triangulation).
Practice
Why are three seismograph stations needed to locate an epicenter?
Two circles intersect at two points; a third picks one.
As the S-P time gap increases, the distance to the earthquake:
The waves spread further apart in time with distance.
A station is 4,000 km away. The P wave travels at 8 km/s. How long does it take to arrive (assume constant speed)?
$4000 \div 8 = 500$ s.
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