Basin Histories and Properties

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Alternative Decompaction Approaches

The compaction corrections we use in constructing geohistory and backstrip diagrams can be a substantial portion of the total corrections we make. The decompaction assumptions and methods we choose significantly influence the shape of resulting curves, particularly within the central portion of geohistory and backstrip diagrams. For example, in decompacting a stratigraphic column, we might use an exponential porosity/depth function with lithology-department constants. We might assume that compaction is progressive and continuous during burial, porosity reduction with depth is due to mechanical compaction only, and that the applied porosity/depth function adequately represents past porosity distributions. Alternative approaches that calculate paleo-porosities differently, or that assume diagenetic reduction of porosity during burial, discontinuous compaction, or a different timing of compaction based on depositional environments may yield more accurate representations of compaction histories.

One approach is to calculate decompacted thicknesses using an exponential porosity/depth function and integrating, porosity within each unit. Angevine et al. (1990) discuss the application and derivation of this method in detail. We can calculate the solid mass of a unit by integrating the solid masses of columns with differential thicknesses, dZ:

$\textrm{Solid mass} = \displaystyle \int \limits _{Z}^{Z+T} (1 - \varphi )\, \textrm{d}Z$ $\quad$ (1)

where T is the thickness of the unit and Z is the depth to the top of the. Equating solid masses of the unit at two different depths, Z₁ and Z₂, gives an expression similar to the equation; $(1 - \phi _{Z_{1}}) \, T_{Z_{1}} = (1 - \phi _{Z_{2}}) \, T_{Z_{2}}$

$\displaystyle \int \limits _{Z_{1}}^{Z_{1}+T_{Z_{1}}} (1 - \varphi )\, \textrm{d}Z = \displaystyle \int \limits _{Z_{2}}^{Z_2+T_{Z_{2}}} (1 - \varphi )\, \textrm{d}Z$ $\quad$ (2)

Substituting the expression $\Phi =\Phi _o \, e^{-cZ}$ (where c is a constant) into Equation 2, integrating these expressions, and rearranging terms gives an expression for decompacted thickness, TZ₂:

$T_{Z_{2}} = T_{Z_{1}} + \left( \dfrac{\phi_0}{c} \right)\left( e^{-cZ_{1}} \right) \left( e^{-cT_{Z_{1}}} \right) - \left( \dfrac{\phi_0}{c} \right)\left( e^{-cZ_{2}} \right)\left( e^{-cT_{Z_{2}}} -1 \right)$ $\quad$ (3)

Notice that TZ₂ occurs on both sides of Equation 3 and cannot be isolated for easier calculation. We can solve this equation by guessing a value for TZ₂, entering our guess on the right side of Equation 3 and calculating a new value for TZ₂. Then, we take the calculated value and enter it into the right side of the equation, calculating another value. We repeat this process until the value for TZ₂ does not change.

Another approach is to assume a porosity/depth function other than an exponential curve. We may determine that another function fits the porosity/depth data for our study area better than an exponential curve. For example, Schmoker & Gautier (1989) concluded that there is less scatter on porosity-versus-TTI (time-temperature index) curves for some areas. Middleton (1981) argued that the following porosity/depth function fit data better, particularly in the shallower parts of sedimentary basins:

$\dfrac{1}{\phi} =\dfrac{1}{\phi _0} + cZ$ $\quad$ (4)

where

ϕ = porosity at depth z,

ϕ₀ = initial porosity, and

c = a lithology-dependent constant

Magara (1980) suggested that an exponential relationship is adequate for shales, but a linear relationship better matches sandstone porosity/depth data:

$\phi = \phi _0 - cZ$ $\quad$ (5)

We present these as examples of empirical functions that have been fit to porosity/depth data. We can use these empirical porosity/depth functions or any other functions that may best fit our data set in a manner similar to the exponential function discussed above to progressively decompact a stratigraphic column.

The goal of correcting a stratigraphic section for compaction is to determine the thicknesses, and thus elevations, of stratigraphic units in the past. Because porosity data are the only estimates of thickness changes as strata are buried progressively deeper, we approximate past porosity/depth distributions using present porosity/depth distributions as proxies. We then apply empirical curves fit to present-day porosity/depth data to stratigraphic depths determined from geohistory and backstrip diagrams.

Geoscientists have also attempted to determine past porosity distributions by relating present distributions to processes of porosity reduction, and then quantitatively separating processes that reduce unit thicknesses from those that do not. Processes that reduce porosity may include mechanical rearrangement of grains, grain deformation, dissolution, and cementation. Mechanical compaction results in porosity and thickness reduction, but cementation processes may result only in porosity reduction and not thickness reduction if the cement source is external. Porosity-reduction processes may be discontinuous, may occur at different times and stratigraphic positions within a basin, and may be strongly controlled by fluid-flow pressure gradients and pathways during the evolution of sedimentary basins. Moreover, the operation of different processes and the amount of compaction may be dependent upon lithology, depositional environment, and the timing of compaction.

For example, a fluvial floodplain mudstone with low porosity may have compacted mechanically soon after deposition while still in its recognizable geomorphological environment, and later cemented during burial. In reality, the thickness of this unit would not change appreciably during burial, but normal application of porosity/depth functions would suggest cumulative compaction on the order of a few tens of percent. By contrast, a lithologically identical marine mudstone may have compacted mechanically, continuously and progressively during burial, and may not have been subjected to significant, externally sourced cementation. The thicknesses we calculate for the marine mudstone unit using an empirical porosity-depth curve might be a good approximation of the actual compaction history.

For most studies, it is impossible to exactly reconstruct past porosity-reduction processes. For constructing geohistory and backstripping diagrams, however, determining average conditions and defining uncertainty limits may be sufficient. Gallagher (1989) discussed methods of determining uncertainties in decompaction studies for both mechanical compaction and cementation models.

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31 minutes read