Mass of the Earth
EAS-450 Physics and Chemistry of the Earth
Laboratory exercise - Paleomagnetism
Objective: Understand and manipulate the concepts of virtual
geomagnetic pole and paleomagnetic pole.
1. Mapping a paleomagnetic direction (I,D) at a site (s,s) to a
virtual geomagnetic pole (p,p)
a. Using a stereonet:
i. Assume that the sampling location is at the south pole:
1. Identify the small circle located at an angle:
m = 90 - m = 90 - atan[tan(I)/2]from your sampling location: the
paleomagnetic pole is located somewhere on that circle.
2. Identify the great circle at an angle D.
3. Plot a circle at the intersection of these two circles: this
is the location of the paleomagnetic pole with respect to your
sampling site.
ii. Bring the sampling site to its actual location:
1. Rotate your figure about a pole at (0,90) by 90+s2. Rotate
your figure about a pole at (-90,0) by s3. Read the atitude and
longitude of the VGP
b. Using an analytical procedure:
c. From the paleomagnetic directions (Iobs,Dobs) measured at
sampling locations (s,s), find the latitude and longitude of the
VGP:
Notes:
Problems a to l are trivial (reflection only), m to t are fairly
trivial (reflection plus calculator)
Problems u to y are less trivial (reflection plus
stereoprojection or computer): provide stereonet and computer-based
solution (using Excel).
2. Estimating a paleomagnetic pole.
The so-called Fisher analysis is a method for calculating the
mean direction of a set of vectors. These vectors can be
paleomagnetic directions defined by [I,D], but also VGP directions
defined by [p,p].
Find the cartesian components of unit vector (Ii,Di):
(ni = north component, ei = east component, di = downward
component)
Calculate the vector sun R(Rn,Re,Rd):
The best estimate of the mean directions (IR,DR) is simply the
inclination and declination of R, converted back to spherical
coordinates as follows:
The precision parameter K is given by:
Where N is the number of vectors being averaged and R the length
if vector R given by:
The 95% cone of confidence about the mean vector is usually
apparoximated by:
a. Program the Fisher test in Excel. In order to check your
program, use the following example:
IDID
701088190
753508522
8034989159
821974358
The Fisher analysis should yield:
Rn=1.19938; Re=0.04985; Rd=7.83739
N=8; R=7.92879
IR=81.29 o; DR=2.38 oK=98.30; 95=4.99ob. In the Appalachians you
sample sediments of Carboniferous age (~330Ma) at a site located at
[35oN, 275oE]. The bed you are sampling in is known to have been
folded in the Late Permian. You sample at five sites on the limbs
of a syncline, measure strike and dip of the beds at each location,
and measure the paleomagnetic directions I and D in the lab. The
data are given in the following table:
SiteUncorrected directionsOrientation of bedCorrected
directions
IDStrikeDipID
1-59183060 SE
2-453483525 SE
3-173271205 SW
41932621045 NW
53033520560 NW
i. Find the Fisher mean paleomagnetic direction, K, and 95 for
the uncorrected directions.
ii. Make the tectonic correction for each site.
iii. Find the Fisher mean paleomagnetic direction, K, and 95 for
the corrected directions.
iv. Plot the tectonically uncorrected and corrected data on a
stereonet.
v. Comparing these plots and accounting for your values of K and
95, what can you conclude about the time of magnetization?
vi. Use your results to calculate an apparent paleomagnetic pole
for that time.
vii. What conclusions can you draw about the rotation and
translation of the sampling site?
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