Page 260 - Physical Principles of Sedimentary Basin Analysis

242 Subsidence

at the plot of the erfc-function in Figure 6.24, we see that η h = 1.2 can be approximated
by η h =∞. More than 95% of the area below the erfc-function is covered by η in the
√
∞
range from 0 to 1.2. We can therefore use that erfc(η)dη = 1/ π, and we get the
0
subsidence (7.161) as a function of time.

7.14 Backstripping and tectonic subsidence
It is often of great interest to know the amount of crustal stretching the lithosphere has
undergone. The amount of stretching can be obtained from a subsidence history, which
gives the thickness, age and the lithology of the different layers that constitute a sedimen-
tary basin. We have seen two basic mechanisms that create the accumulation space for the
sediments. The first is the subsidence caused by deposition into a water-filled basin, and the
other is the subsidence caused by stretching and thinning of the crust. The latter subsidence
is called the tectonic subsidence because it is the subsidence from tectonic processes. We
will now see how the sediment load gives the tectonic subsidence.
The (basement) subsidence z(t) of a sedimentary basin is made of three components
at any time t; the water depth w(t), the basin thickness s(t) and the global sea level
change (t)
z(t) = s(t) + w(t) − (t), (7.168)
and it is often denoted total subsidence. Global sea level changes, which are also referred
to as eustatic sea level changes, are distinguished from water depth changes by not being
related to changes in the subsidence. The sea level has changed through geohistory due to
global phenomena like changes in volume of the ocean basins or melting of the polar ice
caps. A positive (t) is a sea level rise.
The tectonic subsidence through the geohistory is found using the principle of isostasy,
assuming that the sediment thickness s(t), the average basin density ¯ b (t), the water depth
w(t) and the (eustatic) sea level change (t) are all known. It is then possible to replace
the isostatic subsidence of the sediments with the corresponding amount of water. A sedi-
mentary basin and its corresponding tectonic subsidence is shown in Figure 7.30. Isostasy
gives that pressures at the same position in the ductile mantle beneath the two columns are
the same

w w(t) +¯ b (t)s(t) + c c + m a 1 = w y(t) + c c + m a 2 (7.169)
where c is the crustal thickness, and where a 1 and a 2 are the thicknesses of a part of the
asthenospheric mantle (see Figure 7.30). The reference level is the present-day sea level
and we have
w(t) − (t) + s(t) + c + a 1 = y(t) + c + a 2 . (7.170)
These two equations give the tectonic subsidence

m −¯ b (t) m
y(t) = w(t) + s(t) − (t), (7.171)
m − w m − w