368 Seismology and Plate Tectonics
(b) Sketch the force–slip diagram for two different spring constants, and use the sketch to explain how the slip and force
drop in a slip event change and why.
(c) For the slider block model, formulate a quantity analogous
to an earthquake’s seismic moment, and explain why it
depends on each term. What is the major difference between
this quantity and the seismic moment?
(d) Recall the observation (Fig. 4.6-11) that earthquake stress
drops are similar for a wide range of earthquakes. If the
slider block model is relevant, what does this imply?
(e) What conditions might correspond to aseismic slip, which
could be viewed as the limit of a continuous series of very
small slip events?
Computer problems
C-1. (a) Write a subroutine to compute the rate and azimuth of plate
motion at a point, given the location and an Euler vector in
the form (pole latitude, longitude, magnitude).
(b) Use the Euler vector in Table 5.2-1 to test your program on
the San Andreas and Aleutian site examples in Section 5.2.1.
C-2. (a) Find the rate and azimuth of Cocos–North America plate
motion at 18.3°N, 102.5°W.
(b) This location is the epicenter of a large 1985 Mexican earthquake, whose mechanism had nodal planes whose strike and
dip are (127°, 81°) and (288°, 9°). Infer from the tectonics of
the Middle American trench which plane was the fault plane.
Using the methods of Section 4.2, determine the azimuth of
slip during the earthquake. How does this compare to your
predicted azimuth?
C-3. (a) Write a subroutine to add and subtract two Euler vectors
given in the form (pole latitude, longitude, magnitude). The
output should be a Euler vector in the same form.
(b) Use your program to determine the absolute Euler vector for
the Pacific plate using Table 5.2-1.
(c) Determine the rate and azimuth of absolute plate motion at
Hawaii (Fig. 5.2-7). Compare the direction to the Hawaiian–
Emperor seamount chain.
C-4. Write a program to plot the temperature distribution in the
oceanic lithosphere as a function of age using the cooling halfspace thermal model (Eqn 5.3.4). Compute erf(s) (Eqn 5.3.3)
using either available software or numerical integration as
discussed in problem 4C-6.
C-5. (a) Write a program to plot the temperature distribution in a
subducting slab using the analytic thermal model (Eqn 5.4.3).
Compute it for a plate subducting at 80 mm/yr at an angle of
45°. Make assumptions that seem reasonable and justify them.
(b) Change the program to make the age of the subducting plate a
parameter and generate temperature fields for different slabs,
as in Fig. 5.4-6.
(c) Using the results of (b) and Fig. 5.4-4, estimate a temperature
above which deep earthquakes are not observed.
(b) Sketch the force–slip diagram for two different spring constants, and use the sketch to explain how the slip and force
drop in a slip event change and why.
(c) For the slider block model, formulate a quantity analogous
to an earthquake’s seismic moment, and explain why it
depends on each term. What is the major difference between
this quantity and the seismic moment?
(d) Recall the observation (Fig. 4.6-11) that earthquake stress
drops are similar for a wide range of earthquakes. If the
slider block model is relevant, what does this imply?
(e) What conditions might correspond to aseismic slip, which
could be viewed as the limit of a continuous series of very
small slip events?
Computer problems
C-1. (a) Write a subroutine to compute the rate and azimuth of plate
motion at a point, given the location and an Euler vector in
the form (pole latitude, longitude, magnitude).
(b) Use the Euler vector in Table 5.2-1 to test your program on
the San Andreas and Aleutian site examples in Section 5.2.1.
C-2. (a) Find the rate and azimuth of Cocos–North America plate
motion at 18.3°N, 102.5°W.
(b) This location is the epicenter of a large 1985 Mexican earthquake, whose mechanism had nodal planes whose strike and
dip are (127°, 81°) and (288°, 9°). Infer from the tectonics of
the Middle American trench which plane was the fault plane.
Using the methods of Section 4.2, determine the azimuth of
slip during the earthquake. How does this compare to your
predicted azimuth?
C-3. (a) Write a subroutine to add and subtract two Euler vectors
given in the form (pole latitude, longitude, magnitude). The
output should be a Euler vector in the same form.
(b) Use your program to determine the absolute Euler vector for
the Pacific plate using Table 5.2-1.
(c) Determine the rate and azimuth of absolute plate motion at
Hawaii (Fig. 5.2-7). Compare the direction to the Hawaiian–
Emperor seamount chain.
C-4. Write a program to plot the temperature distribution in the
oceanic lithosphere as a function of age using the cooling halfspace thermal model (Eqn 5.3.4). Compute erf(s) (Eqn 5.3.3)
using either available software or numerical integration as
discussed in problem 4C-6.
C-5. (a) Write a program to plot the temperature distribution in a
subducting slab using the analytic thermal model (Eqn 5.4.3).
Compute it for a plate subducting at 80 mm/yr at an angle of
45°. Make assumptions that seem reasonable and justify them.
(b) Change the program to make the age of the subducting plate a
parameter and generate temperature fields for different slabs,
as in Fig. 5.4-6.
(c) Using the results of (b) and Fig. 5.4-4, estimate a temperature
above which deep earthquakes are not observed.