Download Homework Set 1

Geol 344: Earthquakes and Seismic Hazards
Spring 2006
Homework Set 3: Fault Friction, Seismogenic Faults, and Seismic Waves
1. Measurements of principal stresses at two different depths in the Earth's crust at a
hypothetical location indicate the following stress magnitudes (in megaPascals, MPa):
Depth:
5 km
10 km
1
115 MPa
240 MPa
3
14 MPa
54 MPa
(i) Use this data to construct Mohr circles on a  vs n graph (shear stress versus normal
stress) for the two depths shown. Important: you MUST use graph paper because the
vertical () and horizontal (n) scales must be exactly the same in order for this to work
properly. Label each axis in increments of MPa.
(6)
(ii) Assuming that these Mohr circles define the strength of the rock at the given depths,
construct a Mohr envelope that is tangent to both circles. What is the general equation of
this line?
(3)
(iii) Use the Mohr envelope to deduce the inherent shear strength of the rock (So) (i.e., the
y-intercept) and the coefficient of friction of the rock () (i.e., the slope of the line or in
other words, the tangent of the angle of slope of the line).
(4)
(iv) At a depth of 10 km, what is the normal and shear stress acting on a fault that is oriented
at an angle  of 30 to 3? (read your answer directly off the graph using the angle 2) (4)
(v) Would the fault in question (iv) be able to produce an earthquake? How can you tell? (2)
(vi) At a depth of 10 km, what would the angle  need to be for a fault to be optimally
oriented for failure? Explain your reasoning.
(4)
(vii) How much pore pressure would need to be added to the system at a depth of 5 km in
order for the Mohr circle to touch the failure line and potentially create an earthquake? (3)
(viii) Which fault orientation would be prone to producing earthquakes for the situation in
question (vii) (i.e., what  value?).
(2)
(ix) If 1 represents the vertical principal stress at this location, what type of faults would we
expect to be active in this region, and why?
(3)
2. On 27 June, 1988, a magnitude 5.4 earthquake was recorded at three Californian
seismograph stations (BKS, JAS, and MIN), as shown on the attached map. The difference
Geol 344: Earthquakes and Seismic Hazards
Spring 2006
between P and S wave arrival times are shown in the table below, along with the calculated
epicentral distances based on the S-P time interval.
California Seismograph Station Data
Station
S-P
(sec)
Distance
(km)
BKS
21.0
190
JAS
20.4
188
MIN
12.9
105
(a) Use this data to determine the location of the earthquake epicenter on the attached map.(8)
(b) Use your determined epicenter location to determine why this earthquake occurred
where it did and when it did. Be sure to refer to the Coulomb failure criterion in your answer
(i.e., provide a reason for the earthquake based on the physics of fault failure).
(6)
3. Could a seismograph attached to a buoy just below the ocean surface detect the seismic
waves from an earthquake that occurred below the ocean floor? Also, would the distance to
the earthquake be calculable? Explain your reasoning in each case.
(5)
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Geol 344: Earthquakes and Seismic Hazards
Spring 2006