GEOPHYS-624 Problem Set 4
Due: Monday at noon, my office, Nov 3, 2008
Problem 1 (10 pt). For the following moment tensors (given in dyne•cm, 1 dyne =
10-5 Newton)
 M rr

(a) M =  Mθr
M
 φr
M rθ
M θθ
Mφθ
M rφ   −8.5 ×10 24
 
Mθφ  =  1.0 ×10 24
Mφφ   −2.0 ×10 24
€
 M rr

(b) M =  Mθr
M
 φr
M rθ
M θθ
Mφθ
M rφ   −0.03 ×1018
 
Mθφ  =  1.0 ×1018
Mφφ   −0.01×1018
€
 M rr

(c) M =  Mθr
M
 φr
M rθ
M θθ
Mφθ
M rφ   1.2 ×10 24
 
Mθφ  =  0.34 ×10 23
Mφφ   −1.2 ×10 24
€
1.0 ×10 24
0.2 ×10 24
0.5 ×10 24
−2.0 ×10 24 

0.5 ×10 24 
8.3 ×10 24 
1.0 ×1018
0.012 ×1018
0.01×1018
0.34 ×10 24
1.6 ×10 24
−1.1×10 24
−0.01×1018 

0.01×1018 
0.018 ×1018 
−1.2 ×10 24 

−1.1×10 24 
−0.6 ×10 24 
(1) Plot the focal mechanisms by using the program called “momten” (login as user
and type “momten”, enter four input options as 2, 1, 2, 1 for each run to use polar
diagonal-first input and output format) and identify the earthquake as mainly
thrust, normal, or strike slip for each case. A value such as 1.2 x 1024 can be
entered as 1.2e24 on the computer. These are lower-hemisphere projections.
Draw carefully on paper (in scale) if you are unable to print the output.
(2) Use a small solid circle to indicate on the plots where the maximum compressive
axis goes through. Do the same for the dilatational axis (maximum dilatation) but
use empty circle(s). Use vectors to draw on your plot two positions of the
largest S motions.
(3) Report the rough strike direction(s) for each case.
(4) There is one earthquake in this group that is intrinsically different from others in
earthquake faulting. Identify this earthquake and justify your answer.
(5) Note there is usually a P and a T label on the “momten” outputs. Think of why
there is usually one. Draw a beachball (by hand) where you may need to label
two P and two T locations, explain.
Problem 2 (10 pt). In a homogeneous halfspace with density 3.0 g/cm3 of P and S wave
speeds of 7 km/s and 4 km/s, respectively. There is a small region containing the fault
with an area of 50 km2. The fault slips by 20 m (length of slip vector). The fault
geometry shows that strike (φ)= 120°, rake (λ)=10° and dip (δ)=80 °.
(1) From Aki and Richards (Quantitative Seismology, bible of geophysics), we can
obtain a relationship between moment tensor elements between the moment
tensor and the three geometric angles,
M rr = M 0 sin2δ sin λ
M rθ = −M 0 (cos δ cos λ cos φ + cos2δ sin λ sin φ )
M rφ = M 0 (cosδ cos λ sin φ − cos2δ sin λ cos φ )
Mθθ = −M 0 (sin δ cos λ sin2φ + sin2δ sin λ sin 2 φ )
Mθφ = −M 0 (sin δ cos λ cos2φ + 1/2sin2δ sin λ sin2φ )
Mφφ = M 0 (sin δ cos λ sin2φ − sin2δ sin λ cos 2 φ )
Compute the full moment tensor (keep in mind the convention is in dyne*cm).
(2) Plot the moment tensor and identify the faulting type. Also, report the
approximate strikes of the two fault planes and their associated dips.
€
Problem 3 (10 pt). Assume an unknown earthquake of large CLVD (compensated linear
vector dipole) mechanism is the result of the sum of two double couple subevents, with
−5 0 0
one of them being  0 5 0 M 0 , find a candidate moment tensor that can represent the




 0 0 0
second subevent (see CLVD earthquake definition).
a. Assume the scalar moments are the same for these two subevents and they
€ occur in the same region (same material property). If we know that the
ratio of rupture areas for these two subevents is A1/A2=0.5, the slip vector
length of the first subevent is 5 km, find the length of the slip vector of the
second subevent.
b. Assume the scalar moments M0 is1025 dyne.cm, the density of the fault
region is2500 kg/m3, assume a Poisson solid, find the average P velocity
of the surrounding material assuming A = 5000 m2.
c. What is the Moment Magnitude Mw of the earthquake for these
subevents?
Problem 4 (10 pt) (Do this problem last, you will need a figure handout from me on
Tuesday) You are given 3 plots of surface waves of the same event. The difference
between them is that they are filtered differently (meaning they have different frequency
contents), but unfortunately the person who did the filtering didn’t put the frequency
ranges on the plots (that would be me).
a. If you were to use them to find the surface wave magnitude of the earthquake
Ms, which one would you choose and why?
b. The body waves of the same events are shown below the surface wave plots
(Figure d). The time scale doesn’t necessarily start from earthquake origin time.
First, what do you think the phase marked by “??” represents (name two
possibilities that can generate it)?
c. Assume an average P speed is approximately 8 km/s and S speed is 5 km/s,
calculate the source-station distance in degrees from the body waves. Normally
we should use the beginning of a wave to represent arrival times, in this case for
simplicity just use the peak locations as indicators of arrival times.
d. Find the surface wave amplitude Ms of this earthquake. To make life easier, I
have provided the amplitudes in microns.