Lab 3, due before the end of lecture 4/28/15

Name (10 pts):___________________
GSC307: Global Geophysics
Lab 3 (100 pts)
Due before end of next Lecture 4/28/15
PROBLEM 1 (30 pts)
Consider the geometries shown to scale below for Plates A, B and C. For plate
geometry II, the relative motion of plate C with respect to Plate B is 2.2 cm/yr in a direction
of 206 degrees (so: clockwise from North).
For both geometries: create a velocity space diagram (one for each). Place and label all
three plates, and place and label all the plate boundary velocity lines in these diagrams. Use a
different color for each of the plate boundary velocity lines. Then, if possible, mark the triple
junction in velocity space and label it with TJ. Determine whether the triple junction is stable
or not, and clearly label the diagram as stable or unstable.
(I)
(II)
PROBLEM 2 (30 pts)
A velocity diagram of a triple junction not only indicates whether it is stable or not, the
location of the triple junction in the velocity diagram also indicates the velocity and direction
with which the triple junction will migrate (move), just like the plates themselves. You will
use this fact to answer the following questions.
1.
(24 pts) After the Pacific plate made
contact with the North American plate, triple
junctions started to evolve. Analyze the two triple
junctions on either end of the San Andreas Fault in
the bottom map by drawing two velocity diagrams
for the two triple junctions (shown as circles on the
bottom map). Create these diagrams to the same
specifications as in problem 1, but here hold the
North American (N) plate fixed. The velocity on
the San Andreas Fault is 50 mm/yr and the
velocity between the Pacific and Farallon plates is
60 mm/yr. Also explain in a few short sentences
what these diagrams show about the stability of
these two triple junctions and then explain in a few
sentences what these diagrams show in terms of
the direction of migration of each of these two
triple junctions.
2. (6 pts) Due to its continued migration (the
nature of which you determined in 1.) and the
limited size of the plates, the southern triple
F
junction will eventually change in type (try to
visualize the future of the plate boundary using
the answer to the previous question and the
bottom map). Write down the three-letter
combination of the original configuration and that
of the future type of triple junction. Once the
southern triple junction changes its type, will it
subsequently cease to migrate, or change its
migration direction, or maintain its migration
direction, and most importantly: why? (Hint: you
do not need to create an additional velocity diagram to answer this question.)
PROBLEM 3 (30 pts)
CALCULATING ISOSTATIC SUPPORT OF MOUNTAINS
Isostasy is based upon Archimedes principle—that the weight of a floating solid is supported by
the weight of the fluid that it displaces. Archimedes was the ancient Greek scientist who is said to
have made his insights about fluid displacements getting into the bathtub. The reason that an
iceberg with a mass of 100,000 kg does not sink to the bottom of the ocean is that it displaces
exactly 100,000 kg of water. The reason that nine-tenths of the iceberg is below the waterline is that
ice is only nine-tenths as dense as water—100,000 kg of water are displaced by 90,000 kg of ice,
and the remaining 10,000 kg of the iceberg stand above the surface.
A
Airy isostasy:
B Pratt isostasy:
1
H
Crust
2
1
H
Crust
T
ρc
2
ρ c1 T
ρc2
T
ρc1
R
Mantle
ρm
Da
Da
Mantle
ρm
Depth of
compensation
The calculation of isostatic support is based upon the principle that at any given depth within
a fluid, called the depth of compensation, the pressures generated by overlying material are
everywhere equal (see Figure 1). This means that the weights of any two columns of material,
measured down to the depth of compensation, are equal. Given an area of uniform crustal density
(ρ c) and thickness (T), a mountain block with elevation H above the surface, and an arbitrary
distance down to the depth of compensation (Da), we can calculate the mountain-root depth (R)
beneath the base of the crust for Airy isostasy (Figure 1A). Weight (W) equals mass (volume ×
density) times gravity (g). For column 1, through the mountain block
W 1 = (Hρ c + Tρ c + Rρ c + D ρ m) g
(1)
The weight of column 2 equals
W 2 = (Tρ c + Rρ m + D ρ m) g
(2)
The weights of the two columns equal each other, therefore
W 1 = W2
(3)
(Hρ c + Tρ c + Rρ c + D ρ m) g
= (Tρ c + Rρ m + D ρ m) g
(4)
Hρ c + Tρ c + Rρ c + D ρ m
= Tρ c + Rρ m + D ρ m
(5)
Hρ c + Tρ c + Rρ c = Tρ c + Rρ m
(6)
Hρ c + Rρ c = Rρ m
(7)
Rρ m – Rρ c = Hρ c
(8)
R = Hρ c / (ρ m – ρ c)
(9)
1) An iceberg is floating in the ocean as illustrated to the right. Use the information provided to
calculate the height that the iceberg stands above the water line.
H
-
ice density =
800 kg/m3
34 m
water
density =
900 kg/m3
2)
A simple iceberg is floating in water separated by a thermocline, which results in a density
difference. Use the information shown to find the density of the water beneath the
thermocline (ρ).
water
density =
34 m
water
density =
900 kg/m3
ice density =
800 kg/m3
13 m
7.0 m
ρ
3) A stratified iceberg is floating in the ocean as illustrated below. Use the strata thicknesses and
the densities shown to calculate H, which is the height of the iceberg above the water.
H
900 kg/m 3
10 m
700 kg/m 3
5m
800 kg/m 3
20 m
water density =
1000 kg/m 3