Estimation of removed sections can often be done by lateral stratigraphic extrapolation, whereby a more complete section is compared with the location where erosion has taken place. Any lateral changes of depositional nature should be taken into account, such as a regional thinning of formations that are not the result of erosion. Thickness changes due to compaction should also taken into account. If the "complete" section is situated at a considerable greater depth, it probably underestimates the amount of removed section at the target location.
A log-based method is the use of sonic plots, or density plots that can indicate whether the section below the un- or dis-conformity was at some time in the past more compacted than the post-erosion section. This becomes apparent, especially on log(delta-t) vs. depth plots of shales ("delta-t is "slowness"). If there is a clear break in the delta-t trend, the pre-erosion section can be shifted downwards with respect to the post-erosion section, until the trends below and above line-up.
Using regression analysis is recommended if enough log data are available. Slowness measured from the sonic logs above and below the gap in the stratigraphy is plotted against depth. If the upper and lower sections give curvilinear trends, it may be advisable to plot the logarithm of the slowness versus depth. Experince shows that the log-linear plot is the better one.
For the estimation by shifting the two sections in such a way that they lie on a single linear trend can be done by hand. But it is also possible to use regression techniques, which allow estimation of the uncertainty as well as the gap. Regression is normally to estinate Y on the basis of X, or estimating slowness as a function of depth. However, here we have no particular reason to select a regression of slowness on depth, or depth on slowness. Therefore, a different regression technique is used which give the principle axis for the upper and lower section. While in normal regression the sum of squared vertical deviations from the regression line is minimized, the principle axis does minimize the sum of squared deviations perpendicular to the principle axis.
It should be kept in mind that the delta-t is not only dependent on the campaction, but also on the "skeleton" pressure of the formation (also called skeleton pressure, grain pressure or effective pressure). The effect of skeleton pressure is to increase sound velocity, hence decreasing delta-t. The effect is discussed by Gardner et al.,(1974). This means that a section that is exhumed (uplifted because of the erosion) will now have a higher delta-t (slower at less skeleton pressure) than at it's maximum depth of burial. So, the lining up of the delta-t trends is slightly in error. The effect is a slight underestimation of the eroded section. Quantification of the skeleton pressure effect is no easy matter. However a rough indication can be obtained from a set of data from Issler (1992).
The Issler data set is a list of core-derived shale porosities, depth and delta-t measurements. The depth range is about 900 to 3500 m. Regression analysis shows that, although the delta-t is strongly and positively correlated with the porosity, there is a highly significant negative correlation (faster) with the depth. This depth effect can be interpreted to be the pressure effect, because other factors such as increased cementation with depth did not arise in this sample of data. The effect is 33 microseconds per km, or 10.6 microseconds per foot. Although other well data show remarkably similar results, the petrophysical process is not fully explaines as yet, and hence the size of a correction for the pressure effect is conjectural.