An earthquake occurs at very shallow depth (essentially at the surface of the Ea

Question

An earthquake occurs at very shallow depth (essentially at the surface of the Earth). On a seismometer located directly on top of the earthquake source, PcP (the p- wave reflecting off of the core) arrives at 8 minutes 34 seconds after the earthquake and ScS (the s-wave reflecting off of the core) arrives at 15 minutes 36 seconds after the earthquake. If the earth's radius at this point is 6371 km, and the core's radius is 3471 km, find the average P and S wave velocities in the earth's mantle. Assume both paths are vertical. (Remember it takes time for the waves to travel both down and up!). When would the phase PcS arrive?

Explanation / Answer

As shown in the diagram, the vertical travelling distance is about 2900km where gutenberg discontinuity lies. Thus, by putting value of time and distance one can get the average velocity of p and S wave (if PREM model is not considered) .

Travel time of P wave is : 514 sec

Distance is 2900 km

Average velocity is:

Vp = 2900/514 = 5.6 km/sec

Similarly,

Vs = 2900/ 936 = 3.09 Km/sec

Practically, these calculated velocities are far lesser than the velocities of true earth model due to presence of different temperature pressue and density conditions with depth.

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