# Maximum porosity versus depth

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 5 141 - 180 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 5.1

What physical fact determines the “limit-of-porosity” line in Figure 5.1a? What is implied for measurements to the right of this line?

### Background

The porosity ${\displaystyle \phi }$ of a rock is the pore volume per unit volume. The pore space is generally filled with salt water except near the surface, where air may be present, and in petroleum deposits, where the pore spaces contain oil and/or gas.

Pore spaces are usually sufficiently interconnected so that the fluid pressure approximates that of a fluid column extending to the surface; this is called normal pressure. The weight of the rock column exerts an overburden pressure. The differential, effective, or net pressure on the rock matrix is the overburden pressure less the interstitial fluid pressure. However, if there is no communication between the pore spaces and the surface, the interstitial fluid pressure may be greater than the normal pressure causing the differential pressure (and velocity) to be lower than usual for a given depth—a situation known as overpressure.

Figure 5.1a.  Factors affecting velocity (after Ziegler and Spotts, 1978).

### Solution

The line marking the limit of porosity is fixed by the strength of the rock matrix that is presumed to be carrying the major part of the weight of the overburden. The overburden weight is partially supported by the interstitial fluid; in overpressured formations the effective stress on the rock’s matrix structure will be smaller than normal, equal to the stress that would be experienced at a shallower depth. The porosity and velocity will thus be that at the shallower depth and such points may fall to the right of the line.

Figure 5.2a.  S- and P-wave velocities (after Pickett, 1963).