Page 262 - Physical Principles of Sedimentary Basin Analysis

244 Subsidence

We have already covered in Chapter 5 how the net (porosity-free) amount of rock in each
sedimentary layer can be found, and how it is used to compute the porosity and the (real)
paleo-thickness of each layer. The average basin density at any time t is

b,i (t) z i (t)
i
¯ b (t) = (7.172)
z i (t)
i
where z i (t) is the thickness of layer i, and b,i (t) is the bulk density of the sediments
in layer i. The sums are over all layers in the basin at the actual time. The basin thickness

at time t is simply s(t) = i z i (t), and the porosity φ i (t) gives the bulk density of the
layer at time t as
b,i (t) = φ i (t) w + (1 − φ i (t)) s,i (7.173)

where each layer may have its own matrix sediment density s,i . The thickness of each
layer i is also given by the porosity of the layer as z(t) i = ζ i /(1 − φ i (t)), where the
net amount of the rock in each layer ζ i is constant through the burial history.
Note 7.14 Sclater and Christie (1980) is an early study that applies backstripping as a
procedure for obtaining the tectonic subsidence. They estimated the tectonic subsidence
for several North Sea wells, and compared it with the subsidence of the McKenzie model
in an attempt to estimate the amount of lithospheric stretching. The work of Sclater and
Christie (1980) is an instructive study of tectonic modeling.
Exercise 7.28 Derive the backstripping equation (7.171).

Exercise 7.29
(a) Show that the basin thickness at any time t can be written as

s(t) = (1 + e i (t)) dζ i (7.174)
i
where e i (t) is the void ratio in layer i, and where dζ i is the net (porosity-free) thickness of
the layer.
(b) Show that the average basin density is

i e i (t) w + s,i dζ i
¯ b (t) = . (7.175)
i (1 + e i (t)) dζ i
The only time-dependent property that is needed is the paleo-porosity, because both the
net layer thickness dζ i and the sediment matrix density s,i of each layer are constants
(independent of time).

Exercise 7.30 Assume that the porosity in a basin can be represented as a function of
depth by the Athy function φ = φ 0 exp(−z/z 0 ).
(a) Show that the average basin porosity is

1 s φ 0 z 0
¯ φ = φ(z)dz = 1 − e −s/z 0 (7.176)
s 0 s