Geophysics - Geology 310
Homework assignment - Paleomagnetism
Name____________
Problem 1.
The magnetic moment of the Earth’s geocentric dipole is 7.76741022 A m2. Assuming an
axial dipole, calculate and plot the total geomagnetic field intensity as a function of
latitude. What is the field intensity here in Philadelphia?
Problem 2.
Magnetic measurements have been made on some lavas found in N. America at 60o N,
90oW. The angle of inclination I of magnetization is measured to be 37o.
a) At what latitude were these lavas erupted?
b) The declination of magnetization is measured to be 75o. Calculate the position (λp,φp)
of the paleomagnetic pole.
c) What do the above results imply about how North America moved since the time
these lavas erupted?
Problem 3.
A paleomagnetic site from a single Oligocene welded ash flow tuff was collected at site
location λs = 35°N, φs = 241.2°E. The site-mean ChRM data are N = 8, Im = –17.9°, Dm =
232.6°, k = 320.0.
a) From these data, calculate the site-mean VGP for this site. Note: The magnetic
colatitude, p, must be a positive number (it is the great-circle distance from the site to the
pole). If you obtain a negative number for
⎛ 2 ⎞
⎛ tan I m ⎞
⎟⎟
p = cot −1 ⎜
⎟ = tan⎜⎜
tan
I
⎝ 2 ⎠
m
⎠
⎝
Then
⎛ 2
p = tan −1 ⎜⎜
⎝ tan I m
⎞
⎟⎟ + 180 o
⎠
b) Estimate the semi-axes (dp, dm) of the ellipse of confidence about this VGP.
Problem 4.
Vector component diagrams illustrating progressive demagnetization data for two
paleomagnetic samples are shown in Figures below. The numbers adjacent to data points
in the figures are temperature steps in degrees Celsius for (a), and indicate AF field in mT
in (b); open symbols are vector end points projected onto a north-south oriented vertical
plane; solid symbols are vector end points projected onto the horizontal plane; numbers
on axes are in A/m. These samples are from volcanic rocks containing magnetite as the
dominant ferromagnetic mineral.
a) Using a protractor to measure angles of line segments in Figure below, estimate the
direction of the ChRM revealed by this progressive demagnetization experiment.
b) Applying the same procedure to the Figure below, estimate the direction of the
secondary component of NRM that is removed between AF demagnetization levels 2.5
mT and 10 mT. What is apparent about the remanence of this sample?
\
c) The following remanence vectors were measured during the thermal demagnetization
of a specimen.
Sample
ex5-1
ex5-1
ex5-1
ex5-1
ex5-1
ex5-1
ex5-1
ex5-1
ex5-1
Temp
20
150
250
350
450
500
525
550
575
Int. (10−4 emu)
41.99
48.34
54.53
59.78
64.00
65.25
59.50
29.27
3.83
Dec.
16.1
18.6
19.8
21.1
22.1
23.4
23.9
23.7
30.1
Inc
-2.3
-14.8
-23.4
-27.1
-30.8
-32.5
-34.5
-34.1
-22.0
--- Either by hand or using matlab, python, excel or some other graphical programming
language plot the projection of the vector onto the horizontal plane and the projection
onto the plane containing N-S vertical plane. Use different symbols on the same plot for
the two different projections. What is the direction of the low stability component of
magnetization? the high stability component of magnetization? What is the most likely
remanence carrying mineral in this sample?
Problem 5.
Sometimes rocks are exposed to elevated temperatures for long periods of time (for
example during deep burial). The grains with relaxation times (at the elevated
temperature) shorter than the exposure time will have acquired a so-called thermoviscous remanence. In order to demagnetize this remanence, we need to know the
blocking temperature on laboratory time scales.
Use these curves (from Pullaiah et al. 1975) to determine the laboratory blocking
temperature of a:
a) VRM acquired since the last reversal (0.78 Ma) by a rock remaining at 20◦ C for
magnetite and hematite.
b) Do the same for a rock buried for 30 Ma to a depth at temperature 250 C.
c) Hydrothermal activity elevates the temperature of a red sandstone to 225°C for a time
interval of 1000 yr and results in formation of thermoviscous remanent magnetization
(TVRM). If hematite is the exclusive ferromagnetic mineral in this red sandstone,
approximately what temperature of thermal demagnetization is required to unblock
(remove) this TVRM? The time at maximum temperature during thermal
demagnetization is approximately 30 min.