Page 266 - Physical Principles of Sedimentary Basin Analysis

248 Subsidence

a discussion of the different possibilities for the LCB. The simplest alternative is used in
the following, where the LCB is Caledonian crust. It has therefore been a part of the crust
through the entire geohistory.
We also assume that we have modeled (or backstripped) the burial history, and that
we have the load of the sedimentary basin through the geohistory. (See Chapter 5 and
Section 7.14.) The load is known by means of average sediment density s (t) and the thick-
ness s(t) of the sedimentary basin at any time t. We also assume that we have the
paleo-water depth, and we will use the same water depths as in Wangen et al. (2007).
The paleo-water depth is a highly uncertain piece of input, and Exercise 7.32 gives some
simple sensitivity estimates of how the results depend on the water depth.
We need the initial (Devonian) thickness of the crust in order to compute the crustal
stretching in terms of β-factors and subsidence. The use of Airy isostasy, knowledge of the
present-day state of the profile in terms of the water depth (w N+1 ), thickness of the basin
(s N+1 ), average sediment density ( N+1 ), and thickness of the crust (c N+1 ), gives that the
initial thickness of the crust is

(7.181)
c 0 = c N+1 + f w (w N+1 − w 0 ) + f N+1 s N+1
where w 0 is the initial water depth. The number of rift phases is N and the index N + 1
denotes the present day. (This indexing turns out to be convenient.) The water depth w 0 is
for simplicity set to zero in the following. The factors

m − w m − N+1
f w = and f N+1 = (7.182)
m − c m − c
are made from the mantle density m , the average crustal density c , water density w
and the present-day average basin sediment density N+1 . Figure 7.32b shows both the
present day thickness of the crust and its initial thickness. The present day crust is thin
underneath Træna basin, the deepest depo-center. Other local minima of the present day
thickness of the crust coincide with the depocenters of the other sub-basins. The initial
crustal thickness (7.181) is roughly 35 km across the profile, and it gives right away the
maximum (present day) crustal thinning

c 0 w N+1 s N+1
β max = = 1 + f w + f N+1 (7.183)
c N+1 c N+1 c N+1
when we look away from eventual thermal uplift from the last rift phase. The modeling
of the rifting phases is based on the initial crustal thickness (7.181) because it is the crust
(without sediments and water) that is in isostatic equilibrium with the present day litho-
sphere. It is also possible to make other choices, for example a constant 35 km initial
thickness, since we know very little about the upper lithosphere at the beginning.
The lithosphere along the 2D profile is now represented by a row of columns, where each
column becomes stretched with its own β-factors (one for each rift phase). The β-factors
are therefore piecewise constant along the profile, and the columns have vertical sides that
remain vertical during the extension process. The columns have had periods of extension