Page 267 - Physical Principles of Sedimentary Basin Analysis

7.15 Subsidence of the Vøring margin, NE Atlantic 249

and the β-factor for rift phase i in a column is denoted β i . The product of the β-factors for
each rift phase is the total (or cumulative) β-factor

β 1 β 2 β 3 β 4 = β max . (7.184)
This is the previous equation (7.89). The initial thickness of the crust (7.181) can be
rewritten as an expression for the thickness of the crust at any time t
c(t) = c 0 − f w w(t) − f (t)s(t) (7.185)

where w(t) is the paleo-water depth, s(t) is the sediment thickness, s (t) is the average
sediment density. The coefficient f (t) = ( m − s (t))/( m − c ) is the factor f N+1 as a
function of time. The knowledge of the crustal thickness c(t) gives the cumulative amount
of crustal stretching during the geohistory as
c 0 c 0
β max (t) = = . (7.186)
c(t) c 0 − f w w(t) − f s (t)s(t)
Alternatively, the cumulative amount of stretching (7.186) can be written
c 0
β max (t) = (7.187)
c 0 − f w s T (t)
when expressed by the tectonic subsidence

s T (t) = w(t) + f T (t)s(t) (7.188)
where f T is the factor f T (t) = ( m − s (t))/( m − w ). The time of the beginning of rift
phase number i is denoted t i (and the number of rift phases is N). The time t N+1 denotes
the present time although no rifting is necessarily beginning at this time. The cumulative
amount of crustal stretching at the beginning of each rift phase i becomes

β max,i = β max (t i ) (7.189)
which makes the β-factor for the ith rift phase
β max,i+1
β i = for i = 1,..., N. (7.190)
β max,i
The cumulative stretching is initially β max,1 = 1, because there is no crustal thinning
before the first rift phase, and β max,N+1 is the present-day (maximal) β-factor. The
β-factors (7.190) obviously give the product (7.184) when multiplied together. We notice
that expression (7.190) is based only on information for the times for the beginning of the
rift phases and the present time. If we have some knowledge about the water depth w(t i ),
then we get the remaining data, the average basin density s (t i ) and the basin thickness
s(t i ) from the burial-history modeling (or backstripping) of the basin. We can use a
constant mantle density at the times t i when the time interval between the rift phases is
sufficiently long for the thermal uplift to have died out. The periods between the rift phases
are often quite long (more than 50 Ma) and the modeling of the burial history therefore
gives us important estimates for the β-factors. Figure 7.32c shows such estimates for