# Functional fits for velocity-depth data

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 4 79 - 140 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 4.12

Given the velocity-depth data shown in Figure 4.12a, what problems would you expect when using simple functional fits in different areas?

Figure 4.12a.  Velocity-depth relations in various areas.

### Solution

The problems are of several kinds. A velocity function involves averaging and thus involves problems wherever the data do not fit the form of the function or where a mixture of data families (lithologies) is involved.

1. A single velocity function cannot represent variations caused by major changes in depositional conditions such as changes from siliciclastic to carbonate deposition or vice versa. An example is the Texas Gulf Coast-2 well: the rocks below about 4.2 km are predominantly carbonate whereas above this they are mainly sand-shale siliclastics. To fit this situation with some sort of average function will give velocities that are too high in the siliciclastic portion and too low in the carbonate section. Problems will also be encountered because of the velocity inversion at about 2.9 km where a thick, low-velocity marine shale is encountered. A thick shale section may also restrict compaction and the release of interstitial water, causing overpressuring and consequent abnormally low velocities. Other areas encounter similar problems.
2. Similar situations are created by major tectonic changes, for example, stresses that produced folding and/or thrusting in a deeper section may have no longer been active during the deposition of a shallower section, resulting in major velocity changes. This is especially apt to be the case where rocks representing some geologic ages are missing because of nondeposition or an erosional unconformity.
3. Velocity functions will also not work well where conditions along the section vary considerably, for example, where an unconformity has removed different amounts of the section, so that the velocity-depth relation changes rapidly in the horizontal direction.
4. Extrapolation of a velocity function beyond the area where the velocity data were obtained will usually give poor results. Consider again the Texas Gulf Coast-2 data and imagine what velocity a function would yield if measurements below some depth (perhaps 2.0 km) had not been available? Functions for all of the areas shown will give unreasonably high velocities if extrapolated well below their data bases. Because the velocity of sedimentary rock is often influenced mainly by compaction and consequent loss of porosity, the rate of increase of velocity with depth should decrease with depth; most velocity functions do not allow for this.
5. Where the functional fit is determined by a least-squares or similar algorithm, the distribution of data will affect the fit.
Figure 4.12b.  Average velocity versus depth.