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 0.23002 0.7150 0.26003 0.7660 0.84004 0.7710 1.03005 0.8090 1.95006 0.8440 2.69207 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 143Nd/144Nd 147Sm/144Nd1 0.5105 0.12002 0.5122 0.18003 0.5141 0.24004 0.5153 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 10.1For 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.

A

B

C

5.6

1.3

5.6

Figure 4: Plate tectonic map for problem 8.

X

Z

2.25cm

0.74cm

A

-55

+30

X

Z B

2.25cm

0.74cm -55

+30

Figure 5: Finite strain ellipse for Problem 10.