Page 214 - Physical Principles of Sedimentary Basin Analysis

196 Subsidence

sea level
ρ ρ ρ ρ
c
c
c
c
ρ 0 ρ 1 ρ 2 ρ 3

(a) (b)
Figure 7.3. (a) Airy isostasy (b) Pratt isostasy.

asthenosphere to a common depth before and after loading is a 1 and a 2 , respectively. The
pressure is the same at the depth (7.1) in the asthenosphere

w w 1 + l l + a a 1 = w w 2 + s s + l l + a a 2 . (7.2)

Equation (7.1) for equal depths gives that a 2 = a 1 + w 1 − w 2 − s, and when a 2 is inserted
into equation (7.2) for equal pressures we get the subsidence
( a − w )
s = (w 1 − w 2 ). (7.3)
( a − s )
If all the water is replaced by sediments, w 2 = 0, we get a sediment thickness s that is the
initial water depth w 1 multiplied by the factor f = ( a − w )/( a − s ). The factor is
greater than 1 because sediments have a higher density than water ( s > w ), and therefore
makes the lithosphere float deeper. If we let w = 1000 kg m −3 , s = 2300 kg m −3 and
a = 3300 kg m −3 we get the factor f = 2.3. A water-filled basin becomes more than
twice as deep when filled with sediments. This kind of subsidence, which is caused by a
lithosphere floating on the asthenosphere, is called Airy isostatic subsidence. Isostasy is
the same as hydrostatic equilibrium, which means that the difference in pressure between
any two points is equal to the difference in hydrostatic fluid pressure.
There is an alternative model of isostatic subsidence, which assumes lateral density vari-
ations in such a way that the base of the crust remains at the same depth. See Figure 7.3.
This model is called Pratt isostasy. The depth of the base of the crust is b at the lateral posi-
tion where the crust is at sea level, and 0 is the crustal density at this position. Hydrostatic
equilibrium implies that the weight of all columns in Figure 7.3b have the same weight.
The crustal density is denoted p at the position where the crust has a height h above sea
level. We have that p (b + h) = 0 b, and the crustal density becomes

b

p = 0 . (7.4)
b + h
The lateral density of the crust is therefore a function of the crustal height above sea level.
In a similar way, if the crust is at a depth h below sea level the weight of the columns are
p (b − h) + w h = 0 b, which gives
0 b − w h
p = . (7.5)
b − h