Seismic Wave Triangulation — 2D Epicenter Location

Earthquake

Magnitude M6.0

Playback speed 1.0×

Station readings (S − P)

Station A

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Station B

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Station C

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Model time

0.0 s

Triangulated epicenter (vs. true)

not yet located

How the triangulation works

Every earthquake radiates two body waves from the epicenter at once: fast compressional P-waves (V_P ≈ 6.0 km/s in typical continental crust) and slower shear S-waves (V_S ≈ 3.5 km/s) — P-waves arrive first at any station roughly 1.7× faster.

A seismograph station never measures distance directly. Instead it measures the S − P interval — how much later the S-wave arrives than the P-wave — and converts that into distance using the two known wave speeds:

distance = [ Vp·Vs / (Vp − Vs) ] × (t_S − t_P)

That formula gives the radius of a circle centered on the station — the epicenter lies somewhere on it, but a single station can't say where. With three stations you get three circles; in the absence of measurement error they intersect at exactly one point, which this simulation solves for algebraically (the standard trilateration solution for three known circle centers and radii) rather than guessing.

Click anywhere on the map to relocate the epicenter and re-run the rupture. Watch each station's inset seismogram: a small P wiggle arrives first, then a larger S wiggle. Once all three stations have recorded both arrivals, their computed circles are drawn and the gold star marks the triangulated location — compare it to the true red epicenter to see the method's accuracy.

click map to set epicenter

P-wavefront S-wavefront Triangulated epicenter