P travels faster than S, so the gap between them grows with distance. Time the gap and you have the distance — from a single station, which is why it was the first thing seismology could do and still the first thing to do with a record.
6.0 and 3.46 km/s are ordinary continental crust, and their ratio is √3 — the value for a Poisson solid, which most crystalline rock nearly is. In sediment both fall and the ratio rises, so a basin gives a longer gap for the same distance and the answer reads too far. This assumes direct waves through one layer; beyond a few hundred kilometres the first arrival has refracted through the mantle and this stops being the right sum.
One station gives a circle. Two give two crossings. Three settle it — and if the three circles do not meet in a point, that gap is telling you something about your velocities.
A magnitude read off an instrument depends on that instrument and where it stands. Moment magnitude does not: it comes from how much rock moved, how far, over what area — which is exactly what a geologist can measure in a trench or map on the ground.
Intensity is not magnitude. One earthquake has a single magnitude and as many intensities as it has places — and intensity is what damaged the building, so it is the number that matters where somebody is standing.
| MMI | what people and buildings did |
|---|
The Modified Mercalli scale is an observation, not a measurement — it is assigned from what happened, which is why it can be recovered from newspapers and letters centuries after the event, and why historical seismicity exists at all.
A rupture that reaches the surface leaves a scarp to map and a trench to log — and the shaking it caused is what Geotechnical means by a seismic coefficient. Slope stability under earthquake loading is a different calculation from static, and the difference is usually the failure.