Discussion
At a station the S wave arrives 8 seconds after the P wave. Taking P and S velocities as 8 km/s and 4 km/s, the distance to the focus is
Answer: C
Correct answer: 64 km
The two waves cover the same distance at different speeds, so the difference in travel time is
\[ \Delta t = \frac{d}{V_s} - \frac{d}{V_p} = d\left(\frac{1}{4} - \frac{1}{8}\right) = \frac{d}{8} \]\[ d = 8 \times 8 = 64 \text{ km} \]This is the basis of single-station distance estimation: the S minus P interval in seconds, multiplied by a constant that depends on the velocity model, gives the distance. It fixes the distance but not the direction, which is why three stations are needed for a location.
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