GEO 1011: Exercises in seismology, chapter 19.

Exercise 1:

The radius of the Earth is 6371km.

Estimate the time it takes a P-wave to reach the other side of the Earth.

The same for an S-wave, for a surface wave, for a tsunami, and for a sound wave in the atmosphere. Use the following mean velocities in the Earth:

P waves: 12 km/s

S waves: 8 km/s

Surface waves: 4.4 km/s

Tsunamis: 0.4 km/s in deep water

Sound speed: 330 m/s

Exercise 2:

Use copies of seismograms to evaluate the distance from Oslo of two earthquakes.

For the first one, use crustal velocities, that is a P-wave velocity of 5.6 km/s and an S-wave velocity of 3.4 km/s. For the second one, use mantle velocities, that is a P-wave velocity of 8.0 km/s and an S-wave velocity of 4.6 km/s.

Exercise 3:

Assuming P and S waves traveled through the crust at 5.6 km/s and 3.4 km/s, respectively, estimate the epicentral location (North and South, in km) of the earthquake which was registered at 3 seismological stations as indicated in the following table

Seismograph location / Arrival time
North in km / East in km / P wave / S wave
0 / 0 / 13:19:58.9 / 13:20:04.7
4 / 49 / 13:20:02.6 / 13:20:10.8
-68 / 24 / 13:19:54.5 / 13:19:57.4

Exercise 4:

The seismic moment of an earthquake is given by M0=μAD where μ is the rigidity of the material, A is the rupture area (fault length multiplied by width) and D is the average amount of slip. The moment magnitude is then Mw= (2/3)*log10M0 – 6.06, where the seismic moment M0 is given in Nm.

An earthquake caused an average of 2.5m slip over an 80km long and 20km deep portion of a fault. Assuming that the rock rigidity is 2x104 MPa (1 MPa=106 Pa and 1Pa=1N/m2), estimate the seismic moment and the moment magnitude of the earthquake.