borehole can be re-occupied to mm accuracy and measured to a tilt accuracy corresponding to 0.01 horizontal-mm per vertical- m. Random errors in measuring the lateral deflection of a borehole increase as 0.6ÃL mm, where L is the depth in km (Bilham, 1993). The horizontal accuracy down-hole is thus comparable to the vertical accuracy obtained with first order spirit-leveling on the surface.

A study in Colorado (Figure 4) revealed that significant attenuation of lateral displacements below 8 m occurred in a vertically bedded shale overlain by boulder clay. A more recent study in a clay-sand environment in California, showed no such simple suppression of noise with depth (Figure 5). The data in Fig.5 are somewhat unusual in that they are obtained within 7 m of a creeping fault that slipped 24 mm during the 3 year time interval of the measurements. Noise in the east borehole (squares) falls in the first two meters but increases briefly at 23 m. Noise in the west borehole (filled circles) is low in the uppermost and lowermost 5 m but doubles between 5 and 7 m depth, decaying to low values where the vertical borehole pierces the 75° SW dipping fault.

FIGURE 4 Attenuation of lateral noise in repeated measurements of a 30 m deep borehole at Table Mountain, Boulder, 1991-4. Below 8m the data appear relatively noise free.

FIGURE 5 Mean lateral deviations at subsurface increments in two 28-m-deep boreholes. The data represent ten-sample-averages of lateral offset in contiguous 0.5 m segments of each hole 1993-7. The two boreholes are vertical (±1°), 30 m apart, and 7 m from the surface expression of the Hayward fault in Fremont, California. The west borehole intersects the Hayward fault at 21±2 m depth.

The inclinometer borehole examples cited offer little guidance for general conclusions concerning the decay in noise with depth. However, the inclinometer method potentially provides a way to measure the lateral stability of geodetic control points. In principle, an inclinometer borehole can be incorporated into engineered monuments at little extra cost, and can be periodically measured to monitor long-term fluctuations relative to its base. Sub mm measurement accuracies can be obtained for boreholes less than 50 m deep.