you know that the hypocenter lies on the surface on an imaginary
sphere, centered on the seismometer, with that distance as its radius.
Once you have determined the distance from a seismometer to an earthquake's
hypocenter, you have two constraints placed upon the time and location
of that hypocenter. First, you can easily determine its origin time
by dividing the distance by either of the body wave velocities, and then
subtracting that answer from the appropriate arrival time. Second,
you know that the hypocenter lies on the surface on an imaginary
sphere, centered on the seismometer, with that distance as its radius.
This constraint on location assumes equivalent wave velocities in all
directions for which the sphere intersects solid ground (you can
automatically eliminate the sky as an earthquake source!). This
assumption is rarely, if ever, completely valid. Wave velocities tend
to increase with depth, meaning that if the earthquake originated directly
underneath the seismometer, the waves probably travelled faster
(and thus farther) than they would have had the earthquake originated
near the surface. The correct way to phrase our constraint upon
the location of the hypocenter is to say that it lies on the surface
of an irregular, spheroidal solid, centered on the seismometer, with
the surface at a radially variable distance defined by the travel-time
difference multiplied by the velocity factor
Now, think back through the steps we've used to arrive at our
travel-time sphere: picking P-wave and S-wave arrivals on a waveform,
calculating the travel-time difference, and computing the distance from
the recording instrument to the hypocenter. We now know that the
earthquake was located somewhere on the outer surface of that
sphere. Suppose you did this for another seismogram of the same
earthquake, recorded by an instrument at a different location.
What would this tell you?
