Page 263 - Physical Principles of Sedimentary Basin Analysis

7.14 Backstripping and tectonic subsidence 245

0.6 2400
0.5 2200

porosity [−] 0.4 average (basin) porosity average density [kg/m 3 ] 2000

0.3
0.2 1800

0.1
porosity (as a function of depth)
0.0 1600
0 1 2 3 4 5 0 1 2 3 4 5
basin thickness [km] basin thickness [km]
(a) (b)
Figure 7.31. (a) The Athy porosity function and the average basin porosity as a function of basin
thickness. (b) The average basin (sediment) density as a function of basin thickness.

when the basin is s thick. Figure 7.31a shows the Athy porosity function and the corre-
sponding average basin porosity for φ 0 = 0.6 and z 0 = 1350 m.
(b) Show that the average bulk basin density is
¯ b = ¯ φ w + (1 − ¯ φ) s , (7.177)

when the matrix density s is constant (independent of depth). Figure 7.31bshows the
average basin sediment density for the average basin porosity in Figure 7.31a. The water
density and the sediment matrix density are w = 1000 kg m −3 and s = 2650 kg m −3 ,
respectively.
(c) The principle of isostasy (7.3) implies that sediments of thickness s,
( m − w )
s = w, (7.178)
( m −¯ b )
are needed to replace water of depth w, when the sediments have the density ¯ b . What is
the factor ( m − w )/( m −¯ b ) that relates the subsidence s to the water depth w when
the basin is shallow and when the basin is deep? Use the average basin density plotted in
Figure 7.31b and the mantle density is 3300 kg m −3 .(Answer:1.8 and 2.3)
Exercise 7.31
(a) What is the tectonic subsidence as a function of the average basin porosity φ, when the
average sediment density is (φ) = φ w + (1 − φ) s , where w is the water density and
s is the matrix density? Use that the basin thickness is S = ζ 0 /(1 − φ) = ζ 0 (1 + e),
where ζ 0 is the net (porosity-free) amount of sediments in the basin and e = φ/(1 − φ) is
the void ratio.
(b) Chemical processes makes a basin compact as a function of time although there is no
sediment infill. What is the tectonic subsidence from a decreasing average basin porosity
when the water depth is kept constant?