The vertical gradient of gravity in vertical and near vertical boreholes

The vertical gradient of gravity is the rate of change of gravity in the direction of the plumb line. For a vertical borehole interval, it is approximated by the ratio of the gravity difference to the height difference as measured between the end points of the interval. The borehole vertical gradient is strongly affected by the densities of the rocks laterally adjacent to the well. Because of this useful effect, vertical (gravimetric) density profiles of the rooks adjacent to the borehole can be calculated from the borehole vertical gradients. A second useful effect, termed the "anomalous" vertical gradient, is caused by non-level equal-density surfaces related to the local and regional geology. The anomalous vertical gradient can enhance exploration beyond the confines of the borehole although it is a small and commonly negligible effect. These two useful effects are not determinable with absolute accuracy from observed borehole vertical gradients without independent subsurface rock density and (or) surface gravity information.

In this study observed vertical gradients from high-precision, detailed gravity surveys made in seven shallow oil wells that penetrate a late Cenozoic sequence of marine and non-marine rocks in the Midway-Sunset Oil Field, California, are interpreted to obtain vertical density profiles. These gravimetric density profiles are adjusted 1) for anomalous vertical gradients calculated from surface gravity maps end, alternatively, measured on a portable tower and 2) for small extraneous effects of surface topography. The unadjusted and adjusted density profiles are compared with density measurements of core samples.

The unadjusted density profiles of six wells are on the average systematically greater than core densities by .05 g/cm³. Adjusted profiles for the same wells agree with core densities to within .01 g/cm³ on the average. Densities of an adjusted profile of a seventh well are .15 g/cm³ less than those of the unadjusted profile and are in better agreement with core densities by that amount. However, residual systematic discrepancies between core and gravimetric densities for this seventh well indicate a measurable variation of the anomalous vertical gradient with depth and (or) lack of representative core density data.

Topographic effects and anomalous vertical gradients in boreholes are usually small and change slowly with depth but, in some instances, may be comparatively large and change rapidly with depth. In the former case, gravimetric density profiles unadjusted for these effects can be in error by as much as about .05 g/cm³ and, in the latter case, by as much as several tenths of a g/cm³. In both cases, relative errors between neighboring parts of the density profiles are much smaller.

In cases where the anomalous vertical gradient changes appreciably with depth, it cannot be reliably estimated in the borehole from surface gravity measurements or from tower gradient measurements, which are especially sensitive to very shallow local density irregularities. At any borehole depth the anomalous gradient can be estimated from the difference between core and gravimetric densities of the same borehole interval. The core densities must be highly accurate and representative of the interval and the gravimetric density must he adjusted for topographic effects.

Measured borehole vertical gradients have precisions of .00025 to .00050 mgal/ft (8 to 16 Eotvos units) for vertical intervals as small as 10 feet (3 meters); this meets the most stringent requirements of recognized applications for borehole gravimetry. An ideal borehole density logging device would be an in-motion continuously recording vertical gravity gradiometer.