GG 304: Physics of the Earth and Planets
Homework 11: Earthquake Seismology
Due Thursday, April 18, 2013
1) During a microearthquake survey in central Turkey, an earthquake was recorded by three
seismometers (see figure below). The P-wave speed is estimated to be α = 5.6 km/s. Calculate
the origin time for this earthquake and locate the epicenter relative to seismometers by using
the following information:
Seismometer 1
P-wave arrival time
S-wave arrival time
Seismometer 2
P-wave arrival time
S-wave arrival time
Seismometer 3
P-wave arrival time
S-wave arrival time
Hours
Minutes
Seconds
13
13
19
20
58.8
4.9
13
13
20
20
2.6
10.8
13
13
19
19
54.5
57.4
Note that Lowrie’s Eq. 3.86 is incomplete. The times it takes P- and S-waves to travel a distance
D are respectively, tP-t0=D/α and tS-t0=D/β. Here, tP is the arrival time of the P-wave at a given
station, tS is the arrival time of the S-wave, and t0 is the time the earthquake occurred. Using
these expressions, Eq. 3.86 is correctly written
tS - tP = D(1/β - 1/α) = (tP - t0)(α/β - 1)= tP(α/β - 1) + t0(α/β - 1).
(3.86)
This is still a line of (tS - tP) versus tP (see Fig. 3.29) and the “y-intercept” or (tS - tP) = 0
represents an imaginary station at epicenter, or when tP = t0 = the time of the earthquake.
The file hw11_start.m (online) shows how to fit a line and determine the slope to an arbitrary
array of Y vs. X. It also shows how to convert time in hrs, minute, and seconds to just hours.
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GG 304: Physics of the Earth and Planets
2) Compare magnitude MS=8.0 events with magnitude MS=7 events:
(a) Assuming MS~ MW, how many times larger is the seismic moment (M0) of a MS=8.0 event?
(b) If both the down-dip extent of rupture area w and the slip displacement D are proportional to
the fault length L, then how much larger is L for the MS=8.0 event?
(c) How many more MS=7.0 events do you expect globally compared to MS=8.0 events?
(d) Compare the total energy released by all MS=7.0 events to the energy released by all the
MS=8.0 events each year. Which is larger and by how much?
3) The map below shows two earthquakes recorded on the mid-Atlantic ridge (double lines
indicate seafloor spreading segments). Focal spheres of the earthquakes 1 and 2 are shown.
(a) Draw fault plane solutions on the focal spheres for both earthquakes. Label the P and T axes.
(b) Describe the fault types that generated earthquakes 1 and 2. From the tectonic setting of each
earthquake, explained how it is possible to infer which plane is likely to be the fault plane,
and which plane is likely to be the auxiliary plane. Estimate the approximate strikes (i.e.,
angle from north) of the probable fault planes and indicate the probable surface displacement
vectors on the map.
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