Page 201 - Physical Principles of Sedimentary Basin Analysis

6.20 Temperature transients from sediment deposition or erosion 183

Benfield’s temperature (6.299) solves the convection–conduction equation (6.298)
assuming that the temperature gradient is constant at infinite depth. We recall from
Section 6.12 that we have already obtained a Fourier series solution of equation (6.298),
but then for a model with a finite depth. The boundary condition at the surface is the
same for these two solutions, but the second boundary condition is a fixed temperature at
a given depth for the Fourier series solution – for instance at the base of the lithosphere.
Note 6.14 shows how it is possible to apply the Fourier series solution (6.166) to thermal
blanketing. A condition for the validity of this solution is that the depth to the base of the
lithosphere is much larger than the thickness of the deposited sediments. The Fourier series
solution (6.166) and Benfield’s solution (6.299) are then completely overlapping under this
condition.
The reduction in temperature from a recent and rapid deposition process may have an
impact on the vitrinite reflectance. This is exemplified with a numerical study shown in
Figure 6.39a, where deposition of 1000 m of sediments took place over a period of 1.5Ma
in the Pliocene (from 3.5 Ma to 2 Ma). There was also a rapid deposition process in
the Cretaceous, where 600 m is deposited over 9 Ma (from 85 Ma to 79 Ma), and the
depression of isotherms is clearly seen. The thermal transient from the deposition of the
formation Naust in the Pliocene is shown in Figure 6.39b. We see that the thermal depres-
sion increases linearly with depth as expected from the geotherms in Figure 6.38a. The
◦
deposition rate is 667 m/Ma and the depression in the temperature becomes 20 Catthe
depth of 3 km, which is reasonable according to Figure 6.38a. Figure 6.40a shows that
the difference in the computed vitrinite reflectance is noticeable between stationary and
transient temperature solutions. The stationary solution is insensitive to deposition pro-
cesses and it overestimates the temperature, and the corresponding vitrinite reflectance is
therefore also overestimated. The necessity of transient temperature solutions in thermal
studies of sedimentary basin were observed already in early work that included vitrinite

C P E O M P Q P Q
0.5 Nordland−fm 0.5 10 Nordland−fm
10
20 20
1.0 30 1.0 30
40 Naust−fm 40 Naust−fm
1.5 50 1.5 50
60 60
70 Kai−fm 70 Kai−fm
2.0 2.0
80 90 Brygge−fm 2.5 90 80 Brygge−fm
Tare−fm
Tare−fm
depth [km] 3.0 100 110 120 Springar−fm depth [km] 3.0 100 Springar−fm
Tang−fm
Tang−fm
2.5
Nise−fm
Nise−fm
110
120
Kvitnos−fm
Kvitnos−fm
3.5
130
140
140 3.5 130
4.0 Lysing−fm 4.0 Lysing−fm
Lyr−fm
Lyr−fm
150
Garn−fm 150 Garn−fm
4.5 Not−fm 4.5 Not−fm
160 Ile−fm Ile−fm
Ror−Tofte−fm 160 Ror−Tofte−fm
5.0 5.0
5.5 5.5
−150 −120 −90 −60 −30 0 −10 −8 −6 −4 −2 0
time [Ma] time [Ma]
(a) (b)
Figure 6.39. (a) A burial history that has a deposition of nearly 1000 m of Pliocene sediments (the
formation “Naust”). (b) The thermal transient is shown for the deposition of the formation “Naust.”