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