In an earthquake, both S (transverse) and P (longitudinal) waves propagate from

Question

In an earthquake, both S (transverse) and P (longitudinal) waves propagate from the focus of the earthquake. The focus is in the ground radially below the epicenter on the surface. Assume the waves move in straight lines through uniform material. The S waves travel through the Earth more slowly than P waves (at about 5 km/s versus 8 km/s). By detecting the time of arrival of the waves at a seismograph, (a) how can one determine the distance to the focus of the earthquake? (b) How many detection stations are necessary to locate the focus unambiguously?

Explanation / Answer

TOAs=d/vs

TOAp=d/vp

TOAs - TOAp = d ( 1/vs - 1/vp )

d = vsvp ( TOAs - TOAp ) / ( vp - vs )

By measuring the time between two waves (from the time of arrival of the primary to the time of the arrival of the secondary wave) and from the above equation, we can measure the distance of focus from the station.

Since, we have only the distance, and not the direction, we need at least two stations to determine the location of the focus unambiguously. This can be achived by drawing circles centered at the stations with a radius equal to the corresponding distance obtained from the above equation. The intersection of the two circles will be the focus.

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