Geodynamics
Flexure of the lithosphere
Lecture 6.5 - Examples of flexure of lithospheric plates
Lecturer: David Whipp
[email protected]
Geodynamics
www.helsinki.fi/yliopisto
1
Goals of this lecture
•
Look at two examples of flexure of the lithosphere beneath
the Hawaiian island chain:
•
•
Solid elastic plate
“Broken” elastic plate
2
Bending of the lithosphere beneath Hawaii
Depression
Figs. 3.28, 3.29, Turcotte and Schubert, 2014
Peripheral bulge
•
As we’ve previously seen, the Hawaiian island chain acts as a
load on the oceanic lithosphere, deflecting it downward
•
Here we consider two different options for modeling this
deflection, and how they’re useful for understanding the
lithosphere
•
First, we will treat the volcanoes as a line load on the
lithosphere 𝑉0 at and assume 𝑞a(𝑥) = 0 and 𝑃 = 0
•
With this, we can simplify our general equation for deflection
of the oceanic lithosphere to be
d4 w
D 4 + (⇢m ⇢w )gw = 0
dx
3
Bending of the lithosphere beneath Hawaii
•
•
For a solid elastic plate, the resulting deflection of the oceanic
lithosphere is
⇣
⌘
x
x
w = w0 e x/↵ cos + sin
↵
↵
In this version of the equation, 𝑤0 is the maximum deflection,
given by
V0 ↵ 3
w0 =
8D
and 𝛼 is known as the flexural parameter

1/4
4D
↵=
(⇢m ⇢w )g
4
Bending of the lithosphere beneath Hawaii
Fig. 3.30, Turcotte and Schubert, 2014
•
•
Here we can clearly see a significant depression and
much smaller (though significant) forebulge
The height of the forebulge is given by
wb =
w0 e
⇡
at location
xb = ⇡↵
5
When should the lithosphere be treated as a
solid elastic plate?
•
In general, the lithosphere can be modelled as a solid elastic
plate whenever its mechanical strength is not significantly
lowered by fracture zones, volcanism and/or major faults
•
Some examples of these scenarios include
•
•
•
Loading of stable continental interiors by ice sheets
Seamounts and oceanic islands*
Loading by river deltas
6
Bending of the lithosphere beneath Hawaii
Fig. 3.31, Turcotte and Schubert, 2014
•
If we think that volcanic activity may have affected the plates
ability to transmit elastic bending stress from one side to the
other, it may be more appropriate to model deflection of a
“broken” plate
•
In this case, the deflection 𝑤 is
x
w = w0 e
cos
↵
where the maximum deflection 𝑤0 is
x/↵
V0 ↵ 3
w0 =
4D
7
Bending of the lithosphere beneath Hawaii
Fig. 3.32, Turcotte and Schubert, 2014
•
The results are somewhat similar, though the form of the
deflected plate is clearly different at 𝑥 = 0
•
In this case, the height of the forebulge is 3⇡
3⇡/4
w
=
w
e
cos
b
0
4
at location 3⇡
xb =
↵
4
8
When should the lithosphere be treated as a
broken elastic plate?
•
In general, the lithosphere can be modelled as a broken elastic
plate whenever its mechanical strength is significantly lowered
by fracture zones, volcanism and/or major faults
•
Some examples of these scenarios include
•
•
•
Deep sea trenches at subduction zones
Seamounts and oceanic islands*
Foreland basins
9
Let’s see what you’ve learned…
•
If you’re watching this lecture in Moodle, you will now be
automatically directed to the quiz!
10