GY305 Geophysics
Final Exam
Problem 1.
Given the below information, calculate the linear velocity and azimuth of relative plate
motion for point X on the plate boundary between the Eurasian and Pacific plate:
λP
+61.1°
φP
85.8°
λX
+50.0
φX
+158.0
ω
9.0x10-7 deg/yr
R
6371 km
Linear velocity:__________________ cm/yr
Azimuth:___________________
Solve this problem with an Excel spreadsheet. Print out your solution on a single sheet
of paper to turn in with test.
Problem 2.
Given the following information from an un-deformed basalt flow:
Sample present day latitude & longitude (X , X ): 40°N, 20°W
Present day inclination of remnant magnetism (I): 50°
The present day magnetic declination of the remnant field (D): -60
Turn in the spreadsheet used for calculations and fill in the below answers:
Original latitude of the rock ():______
Latitude & Longitude of the paleo-magnetic pole (P , P ):______, _______
Problem 3.
Given the following seismic reflection data solve for the depth to the reflector at the
ends of a 24-geophone seismic line. Also calculate the dip angle of the reflector
assuming the seismic reflection line is perpendicular to strike:
Shot point offset: 50 feet
Geophone spacing: 100 feet
Layer velocity: 7500 ft./sec.
2-way travel time recorded by geophone #1: 133.5 msec
2-way travel time recorded by geophone #24: 379.1 msec
Ray path distance to geophone #1=: _________
Depth to reflector @ geophone #1: __________
Ray path distance to geophone #24: _________
Depth to reflector @ geophone #24: _________
Dip of reflector: ____________________
Problem 4.
Using the diagram in Figure 1 that contains 1st motion readings (filled circles =
compression; open circles = dilation):
1. Plot the nodal planes and list the strike and dip of the nodal planes:
a. Strike and dip = ________________
b. Strike and Dip = ________________
2. Using the fact that the seismic data was collected from eastern Japan:
a. Fault strike and dip = _______________
b. Type of Fault = _________________
Problem 5.
Seismic P-waves travelling through the lower continental crust of density 2.7 encounters
upper mantle of density 3.9 at the crust/mantle interface. If the incident angle is 35
degrees, what is the incident angle when the ray path is refracted? What angular
change in ray path does this produce? Use Figure 2 to estimate seismic velocities.
1. Incident angle in lower layer = ______________
2. Angular change = __________________
Problem 6.
Given the below whole-rock data obtained from a mass spectrometer from a granite
pluton in Colorado:
Sample 87Sr/86Sr 87Rb/86Sr
1
0.7120
0.2300
2
0.7150
0.2600
3
0.7660
0.8400
4
0.7710
1.0300
5
0.8090
1.9500
6
0.8440
2.6920
7
0.8830
3.1600
Construct a spreadsheet that will solve for the age of the Rb/Sr isochron. The
spreadsheet should have both mathematical formulas and a graphical plot. Fill in the
below info and plot the spreadsheet to turn in with this test:
Isochron age (Ma): __________________________
Correlation coefficient (R): _______________________
a. Initial 87Sr/86Sr ratio: ______________________
b. Does the magma that formed the pluton have a mantle or crustal source?
__________________________
Problem 7.
Calculate the Rf and  values for the finite strain ellipsoid using the photo in Figure 3:
Rf: ___________________
 : ___________________
Turn in the measurements of Rf and  in a spreadsheet for the strained pebbles in the
photograph. Also turn in the hyperbolic net plot used to find the finite strain ellipse Rf
and .
Problem 8.
Given the map in Figure 4, calculate the relative plate motion of B relative to C and
subduction rate for plate B:
Linear relative plate motion velocity and azimuth of B relative to
C:___________________
Subduction rate of plate B:________________
Turn in the drawing used to graphically calculate the relative plate velocity with this test
with a scale bar.
Problem 9.
Given the below Sm/Nd isotopic data taken from a peridotite:
Sample
1
2
3
4
143Nd/144Nd
0.5105
0.5122
0.5141
0.5153
147Sm/144Nd
0.1200
0.1800
0.2400
0.2800
Calculate the below values in a spreadsheet:
Slope of linear regression:________________
143Nd/144Nd initial ratio:________________
Isochron Age: _________________Ma
Correlation Coefficient (R): _________
Turn in a printout of the spreadsheet used to calculate the above values.
Problem 10.
For the lines (A) and (B) that are elliptical diameters to the strain ellipse in Figure 5,
with θd angles of +30̊ and -55̊ respectively, calculate the following values:
Calculate:
(1) λ (quadratic elongation): (A)_________, (B)___________
(2) S (stretch): (A)_________, (B)___________
(3) γ (shear strain): (A)_________, (B)___________
(4) ψ ( angular shear): (A)_________, (B)___________
(5) α (angle of internal rotation): (A)_________, (B)___________
Show all calculations for problem 10 below:
Figure 1: Seismic 1st motion data from Japan.
Figure 2: Seismic velocities for common rocks at (a) 6km, (b) 18, and (c) 30 km depth. Filled circles = crystalline rocks, open
circles = sedimentary rocks.
Figure 3: Vadito group metaconglomerate with cleavage direction parallel to green line.
1.3
C
A
5.6
5.6
B
Figure 4: Plate tectonic map for problem 8.
Z
0.74cm
B
-55
2.25cm
+30
A
Figure 5: Finite strain ellipse for Problem 10.
X