Page 199 - Physical Principles of Sedimentary Basin Analysis

6.20 Temperature transients from sediment deposition or erosion 181

6.20 Temperature transients from sediment deposition or erosion
The deposition of sediments may cause a suppression of the surface heat flow and the tem-
perature in a sedimentary basin. In order to see this we will consider the following case –
let a sedimentary layer be deposited instantaneously. The temperature in the layer is the
same as on the surface, and the temperature underneath the layer is unchanged. The ther-
mal state of the subsurface is shifted downwards by the thickness of the layer, since it has
not had time to adapt to the new surface. This effect is often called “thermal blanketing.”
The blanketing effect is enhanced by the low heat conductivity of uncompacted sediments
near the surface. (The heat conductivity of pores filled with brine is “low” compared to the
sediment matrix.) The thermal gradient is zero in the layer right after deposition and it then
starts to increase as the temperature moves towards a new stationary state. The deposition
of sedimentary layers is not instantaneous, but may take millions of years. We will in this
section see that the suppression of the thermal gradient is controlled by the deposition rate
and also by the time span of the deposition period.
In order to handle the effect of deposition on the temperature we must first find a tem-
perature equation that describes the process. We have that the heat flow by conduction is
in a coordinate system that is attached to the sediments and therefore follows the burial
∗
during deposition. The z-coordinate in this system is now denoted z and the temperature
∗
equation along the z -axis is
2
∂T ∂ T
− κ = 0. (6.295)
∂t ∂z ∗2
We would like to work in a coordinate system with the z-axis attached to the surface,
where the surface remains as z = 0 during deposition. The transformation between these
two coordinate systems is
∗
z = z + vt (6.296)
where v is the deposition rate. We then have that z = 0 corresponds to z = vt during
∗
burial, and that the two z-axes overlap at t = 0. Differentiation with respect to time along
∗
the z -axis gives

∂T ∂T ∂T ∂z ∂T ∂T
= + = + v (6.297)
∂t z ∗ ∂t z ∂z ∂t ∂t z ∂z
when it is transformed to the z-axis. The temperature equation along the z-axis is therefore

2
∂T ∂T ∂ T
+ v − κ = 0 (6.298)
∂t ∂z ∂z 2
where a convection term represents the thermal effect of deposition. Compaction of the
sediments is for simplicity ignored in the following, and burial is therefore at the same
rate as deposition. We need two boundary conditions before we can solve (6.298), where
one is a constant temperature at the surface. We will look at two alternatives for the other
boundary condition, which will be either (1) a constant thermal gradient at infinite depth