## Decompaction

Decompaction is the process of estimating the thickness of formations at different, often shallower depth in geological history. An important concept in such estimation is the "solidity" of the formations, i.e. 1 - porosity, where porosity is a fraction. In other words the ratio of the solid material (grains) to the bulk rock volume. During compaction, the solidity increases gradually to a certain maximum value, theoretically to 1, if all pore space has vanished. Basing decompaction on this concept only means that we neglect the effect of cementation brought in from outside the rock volume studied and that we neither take any elastic compression of the grains themselves into account. This program assumes that the bulk of the compaction effect is related to the increase in solidity, and hence is only an approximation to the complex processes that determine compaction. Solidity can be estimated roughly by standard relationships with depth for formations that have only subsided, not uplifted.

Three equations of the same type have been derived for three lithologies.

1. Shale: The original equation of Baldwin & Butler (1985), translated into solidity:

S(z)=0.258z0.1575

2. Carbonates: The equation of Schmoker & Halley (1982) re-fitted to a log/log relationship between solidity and depth.

S(z)=0.290z0.1371

3. Sandstones: The average of the Maxwell (1964) envelope and the Sclater&Christie (1980) curves combined to give for solidity:

S(z)=0.207z0.1672

The advantage of these equations is ease of integration. The decompaction is based on the fact that, without removal or addition of solids, the amount of solids in a section of rock will remain the same during compaction. The solidity (1 - porosity) is a measure of compaction. It runs from, say about 0.50 to 1.00, although the lower end will depend very much on the lithology. For instance clay may have porosity up to 80%, so that S0 = 0.20. Now the solidity times the thickness is a constant during compaction, because it only expresses the "solid thickness":

S1T1 = S2T2
for a given formation at depth 1 and depth 2.

For a given interval between z1 (top) and z2 (base) the mean solidity can be calculated as follows. First we express the solidity/depth relationship in a general form:

S(z) = β0zβ1
The values of the two β's will depend on the lithology (see above).

The mean solidity between base and top is found by integration of the S(z) equation:

The constant solid thickness is obtained by multiplying both sides of the above equation by the depth difference between base and top (thickness), hence:

Now assume that the top of an interval is known: ztop. For decompaction w need to know the depth of the base zbase. This means that we need to know the average solidity for the same interval. but now with the top at a new depth ztop.

Multiplying again both sides of this equation with (zbase - ztop), we get:

Fortunately we can solve zbase from the above equation, as it is the only unknown:

The ST product refers to the present solidity and thickness. The restored thickness is the difference between zbase and ztop.

The first problem to solve, if only approximately, is to obtain solid thicknesses for the input intervals. The user is assumed to base his thickness estimates largely on well data. If there are no unconformities in the sequence, the cumulative thickness of the layers down to the base of a given layer is also the depth of the base of that interval. This can be used to get the solid thickness for each interval, taking the lithology class into account.

In the case of erosion, the section below this interval will be "exhumed". This reduces the depth at which it is found, but here it is assumed that compaction is simply irreversible. In reality there may be a little "rebound", especially in the case of shales, but this effect is neglected here. The irreversability of compaction complicates the calculation to some extent, because the maximum state of compaction has to be remembered by the program. For the solid thickness estimation, the maximum burial depth for each interval-top is calculated. Then the solid thickness is calculated for that depth position.

It should be noted that erosion amounts should not exceed the cumulative thickness given for the intervals below the erosion interval. If this were the case, it would mean that the target interval, i.e. the bottom of the lowest, earliest interval, cannot be present! With a number of intervals present and a number of erosion intervals, such inconsistent input might be made. The validation in the program will return a fatal error if this occurs. Even more so, the last (lowermost or oldest or "target") interval cannot be an erosion period.

Decompaction of a number of intervals has to proceed by taking the top one at top-depth zero. Then the depth of the base is estimated by formula for zbase above. This is then the top depth of the second lower interval. Then calculate the depth of the base of the second interval, etc. For each interval that is added to the overburden, the depth top has to be checked against the maximum depth it ever attained. So for each interval the "minimum thickness" of the interval is to be updated in an array. The thickness of the decompacted layer to be added cannot be more than the minimum thickness it had attained before. In this way the irreversible nature of compaction is taken into account.

Although compaction is due to the "skeleton" pressure, or "grain pressure" of the overburden, and not due to the water column in the overburden, this program does not take waterdepth into account in the decompaction process. This means that a given layer is decompacted by putting the top to zero depth, rather than to the prevailing waterdepth.The reason is that the decompaction curves derived from various publications do not appear to take this effect into account. It could be argued that the compaction curves take an unspecified "average waterdepth" into account. For most overburden layers this will not matter very much.