EAS 217-S2020

1. Lab 3. The Floating Lithosphere: Isostasy
Isostasy is a fundamental concept in the Geology. It is
the idea that the lighter crust must be floating on the
denser underlying mantle. It is invoked to explain
how different topographic heights can exists on the
Earth's surface. Isostatic equilibrium is an ideal state
where the crust and mantle would settle into in
absence of disturbing forces.
1
👉🏾 Therefore, understanding the dynamics of
isostasy helps us figure out more complex
phenomena such as mountain building, sedimentary
basin formation, the break-up of continents and the
formation of new ocean basins.
The waxing and waning of ice sheets, erosion,
sedimentation, and extrusive volcanism are examples
of processes that perturb isostasy. The physical
properties of the lithosphere (the rocky shell that
forms Earth's exterior) are affected by the way the
mantle and crust respond to these perturbations.

2. PREVIEW 👀
• Slide 9 solves the same problem using algebra.
• Slides 10-12 ask you to develop a spreadsheet that applies the algebraic solution from Slide 9 to
find the difference in elevation of the top of two floating blocks.
• Slides 13 and 14 you will adapt this spreadsheet to two different conceptual models that try to
duplicate the 4.6-km difference in floating levels of continental and oceanic crust.

3. 9
An alternative approach
Then --
ZT = ZU + ZL
PA =ice g ZT
PB = water g ZL
PA = PB
So, at equilibrium ZL / ZT = ice / water
Let ZT = total thickness.
Let ZU = the upper part (above water level).
Let ZL = the lower part (below water level).
Q2. What is the fraction of
the block that lies below the
water level? Does it agree
with what you found in your
spreadsheet? 🤔
💡 This says that pressure is
the same along the depth of
compensation
🌟 Sometimes the easiest thing to do is to use a little algebra!
ZT
ZU
ZL

4. 10
Q3. What is the difference in elevation of the top of two blocks of floating ice, one 5 m
thick and the other 7 m thick? Use the equations of the previous slide and make a
spreadsheet that calculates this.
This is a preview of Airy isostasy:
mountains are higher than plains
because they have roots.
🗻 Continents are higher than ocean
basins because continental crust is
thicker than oceanic crust 🌊
Two blocks of ice floating in a bucket of water
Note: although the depth of compensation is drawn in the figure, it isn’t used in the calculation in
this spreadsheet.
B C D E F
2 Two blocks of ice
3
4 Fluid density 1.025 g/cm3
5
6 Block A density 0.917 g/cm
3
7 Thickness (Z T ) 5 m
8 Root (Z L ) m
9 Top (Z U ) m
10
11 Block B density 0.917 g/cm3
12 Thickness (Z T ) 7 m
13 Root (Z L ) m
14 Top (Z U ) m
15
16 Topographic difference m
*Not to scale

5. Change the numbers in your spreadsheet to calculate the difference in elevation
between the top of a 5-cm-thick block of copper and a 5-cm-thick block of lead, both
floating in liquid mercury. The densities are 8.94 g/cm3, 11.37 g/cm3, and 13.6 g/cm3
for the Cu, Pb, and Hg, respectively. Q4. What is the difference in elevation? 📊
This is a variation of Pratt isostasy:
mountains are higher than plains
because they are less dense. Thus,
continents are higher than ocean
basins because continental crust is
less dense than oceanic crust.
Two blocks of metal floating in a bucket of mercury
B C D E F
2 Blocks of Cu and Pb in Hg
3
4 Fluid density (Hg) 13.6 g/cm3
5
6 Block A density (Cu) 8.94 g/cm
3
7 Thickness (Z T ) 5 cm
8 Root (Z L ) cm
9 Top (Z U ) cm
10
11 Block B density (Pb) 11.37 g/cm3
12 Thickness (Z T ) 5 cm
13 Root (Z L ) cm
14 Top (Z U ) cm
15
16 Topographic difference (A -B ) cm
*Not to scale
11

6. Change the numbers in your spreadsheet of Slide 10 to calculate the difference in
elevation between the top of a 28-km-thick block of granite (density 2.67 g/cm3) and a
7.9-km-thick block of gabbro (density 2.99 g/cm3) both floating in a fluid with density
3.3 g/cm3. Q5. What is the difference in elevation? 🤔
Compare your calculated topographic
difference to the difference between
continents and ocean basin averages
cited in the first slide. What do you
think of this conceptual model as an
explanation for the topographic
difference between continents and
ocean basin? 👨🤔🏫
Two blocks of crust floating in a bucket of asthenosphere
B C D E F
2 Blocks of granite and gabro
3
4 Fluid density (asthenosphere) 3.3 g/cm3
5
6 Block A density (granite) 2.67 g/cm
3
7 Thickness (Z T ) 28 km
8 Root (Z L ) km
9 Top (Z U ) km
10
11 Block B density (gabbro) 2.99 g/cm
3
12 Thickness (Z T ) 7.9 km
13 Root (Z L ) km
14 Top (Z U ) km
15
16 Topographic difference (A -B ) km
*Not to scale
12

7. B C D E F
2 Blocks of granite and gabro
3
4 Fluid density (asthenosphere) 3.3 g/cm
3
5
6 Block A -- continental crust
7 density (granite) 2.67 g/cm
3
8 Thickness (Z C) 28 km
9
10 Block B -- oceanic crust
11 density (gabbro) 2.99 g/cm
3
12 Thickness (Z O) 7.9 km
13
14 Thickness Z M 15.50 km
15
16 Structural difference ( H) 4.6 km
An alternative picture: Together, the blocks cover the entire
surface so that the asthenosphere, which the blocks are
floating on, does not reach the surface.
Isostasy
ZC = thickness cont. crust
ZO = thickness oceanic crust
ZM = thickness upper mantle
DH = difference in elevation.
Rethink your spreadsheet. Recall depth of compensation.
Do you still like the conceptual
model? Think
ρO ZO + ρM ZM = ρC ZC
ZO + ZM + DHd = ZC
🏾You should have gotten this result in
the previous spreadsheet.
Not to scale
(These equations are equivalent to
equations 1 and 2 on the last page
of the Isostasy Reading. Check that
out if you don’t see where they
come from.)
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8. Isostasy “for real”
You shouldn’t, because (oops!) we forgot the ocean!
So, add a second layer (seawater)
to the ocean-basin block.
*Not to scale
14

9. Isostasy Assignment
Pre-Lab 3 file must contain excel file with:
• Answer Q1 on Slide 6
Lab file 3 must contain excel file with the following tabs (sheets):
• Answer Q2 on slide 9
• Answer Q3 on slide 10
• Answer Q4 on slide 11
• Answer Q5 on slide 12
PART 2:
• Answer the questions on BB
Remember to show your work. Due next week on Blackboard