Page 179 - Physical Principles of Sedimentary Basin Analysis

6.15 Cooling sills and dikes 161

10

5

z [−] 0 8 4 2 1 1/2 0
^

−5

−10
0.0 0.2 0.4 0.6 0.8 1.0
^
T [−]
Figure 6.27. The temperature of a cooling sill at ˆ t = 0, 1/2, 1, 2, 4 and 8.

ˆ t = 4 the temperature has decreased further to T ≈ 0.25. The decrease in temperature at
ˆ
the center of the sill is then as follows for a longer time span:

ˆ t ˆ T
0 1
1 5.2 · 10 −1
10 1.8 · 10 −1
100 5.6 · 10 −2
1000 1.8 · 10 −2
10 4 5.6 · 10 −3
10 5 1.8 · 10 −3
10 6 5.6 · 10 −4

We see that we have to wait more than 1000×t 0 before the dimensionless temperature falls
◦
to less than 2% at the center of the sill. A sill emplaced with the temperature T 0 = 1000 C
has then the temperature 18 C. The table below shows how long time t 0 is for sills of
◦
different thicknesses:

Sill thickness a t 0
1 m 1/2 m 2.9 days
10 m 5 m 289 days
100 m 50 m 79 years
1000 m 500 m 7927 years