Page 118 - Physical Principles of Sedimentary Basin Analysis

100 Burial histories

next layer thickness z i , and thereby the real depth to the horizon below, z i = z i+1 + z i .
The thickness ζ i and the porosity gives the real layer thickness

ζ i
z i = (5.15)
1 − φ(z i − z N + z i /2)
which is a function of the wanted layer thickness z i . Equation (5.15) is straightforward
to solve numerically using iteration, where an approximation for z i can be inserted in the
right-hand side to obtain an improved approximation. The iteration scheme can be started
with ζ i as the first guess, and it will converge towards an accurate solution after just a
few iterations.

5.4 Erosion
The preceding sections show how the present-day layer thicknesses give the net amount
of rock in each layer. It is still assumed that porosity is a function of depth from the basin
surface, where depth is either real depth or net (porosity-free) depth. The net formation
thicknesses are wanted because they give the net height (the ζ-coordinates) of the layer
boundaries from the basement. The net thickness of the layers and the ζ-coordinate of the
layer boundaries are constant through the geohistory, and it is the net amount of rock in
each layer that allows the basin to be constructed at each time step through the geohis-
tory. A burial history computation therefore goes through the wanted time steps, and the
following tasks are done at each step:

1. deposit sediments and update the surface ζ-coordinate;
2. make the current porosity;
3. make the current real depths;
4. solve equations for the current temperature and pressure.

This approach to burial history modeling works fine as long as no erosion is involved. The
problem with erosion is that we cannot obtain the net amount of rock in the layers directly
from the present-day layer thicknesses. The porosity of a layer, when it is a function of
depth, decreases with increasing burial. Porosity reduction is an irreversible process, and
the porosity remains constant at the value of maximum burial, when erosion brings layers
up to a shallower depth. The porosity of a layer keeps this minimum porosity until it is
reburied to a depth that is deeper than the previous maximum.
It is therefore not possible to compute the porosity without doing a burial history, but
at the same time it is not possible to compute the burial history without knowledge of the
porosity. A solution to this deadlock is to simulate the full burial history iteratively until a
sufficiently close match against the present-day layer thicknesses is achieved.
An erosion process appears in the present-day stratigraphy as a hiatus. This gap in
the stratigraphy is modeled by first depositing the wanted amount of sediment and then
eroding exactly the same amount of sediment. There may be several deposition and ero-
sion processes that fill the time interval of a hiatus, as long as the net result is zero.