12.005
Lecture Notes 8
Assertion:
most of the stress tensor in the Earth is close to "lithostatic,"
τ
ij
~ 
ρ
gd
δ
ij
,
where
ρ
is the average density of the overburden, g is gravitational acceleration, and d is
the depth of the point under consideration.
Consider the following table of the lithostatic pressure at various points of interest:
depth
(km)
Pa
bars
ocean ridge crest
2.5
25 MPa
250
abyssal plain
4
40 MPa
400
deep sea trench
12
120 MPa
1.2 kbar
base of crust
30
1 GPa
10 kbar
transition zone
600
20 GPa
200 kbar
Coremantle bndry
2900
140 GPa
1.4 Mbar
Center of Earth
6400
360 GPa
3.6 Mbar
Assertion:
Typical "tectonic" stresses have magnitudes in the range 0.3  300 MPa (3
3,000 bars).
Conclusion:
In considering tectonic problems, it is usually useful to subtract some
isotropic reference state of stress.
There are 2 common choices  the lithostatic stress,
which leaves the nonlithostatic stress tensor, and the pressure field, which leaves the
deviatoric stress field.
But since we need to know the actual stress tensor in order to
calculate the pressure, which requires knowing the solution to the problem in advance, it
is most common to use the lithostatic stress field as the reference.
In order to place these comments in context, let's look at the situation described in T&S
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 Fall '10
 ywn
 Force, center of Earth, MIT OCW, mbar, Southern California Transverse Ranges

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