Epicentral Distance from the S–P Interval

This is the oldest trick in observational seismology and it still works. Because the P wave travels faster, it arrives first, and the gap before the S wave arrives grows steadily with distance. Rearranged, the gap IS the distance: $d = \Delta t / (1/V_s - 1/V_p)$. Nothing else is required — no second station, no synchronised clock, not even a knowledge of when the earthquake happened. A single trace and a ruler will do it.

The reason no clock is needed is worth stating plainly, because it is the elegant part. Both waves left the source at the same instant, so the unknown origin time cancels out of the subtraction. What survives is a difference of travel times, which depends only on distance and the two velocities. This is the same idea that makes GPS work in reverse: there, differences in arrival time from known positions give your location; here, a difference in arrival time at a known position gives the source's distance.

With the standard crustal pair $V_p = 8$ km/s and $V_s = 4$ km/s, the slowness difference works out to exactly $1/8$ s per kilometre, so distance in kilometres is simply eight times the S–P gap in seconds. That "times eight" is the rule of thumb, and it is accurate enough for a first pass anywhere in continental crust. A twenty-second gap puts the epicentre about 160 km away.

What a single station gives you is a circle, not a point — the earthquake is somewhere on a ring of that radius. Three stations give three circles that intersect at the epicentre, which is the classic classroom exercise with a compass and a map, and it is still conceptually what a modern location algorithm does with dozens of stations and a least-squares fit. Two honest limits: the velocities are path averages through a layered Earth, so a single pair of numbers is a straight-ray approximation that degrades beyond a few hundred kilometres and needs a real travel-time model past that; and the answer is EPICENTRAL distance, measured along the surface, while the rupture started at the hypocentre below it. For a deep event the true source is farther away than this returns.