unsuitable for high rise buildings or compliant towers subject to vibration caused by wind stress, or the movement of elevators etc.

FIGURE 8 Building and tower GPS antenna installations showing schematic methods to monitor the stability of the upper point relative to subsurface, or bed-rock markers.

In installations of GPS antennae in Japan, tiltmeters are fixed to towers to monitor their secular stability (Tsuji et al. 1995). Tiltmeters are suited to tower monuments that are rigid, and that do not experience large short-period accelerations, or diurnal thermoelastic flexure. To monitor the stability of a 6 m steel tower in Cayaco, Mexico, a simple pendulum was arranged to monitor the position of the upper control point relative to a bedrock control point at its base. In this arrangement the flexibility of the tower is immaterial and the presence of short term noise is suppressed by immersing the plumb-bob in oil. The position of the plumb bob is monitored electronically.

A similar method is used to monitor the secular position of fixed GPS antennae relative to existing bed-rock control points in the Himalaya. A permanent antenna monument is constructed in the form of a three-sided brick pillar above the bedrock point. The 0.5-1.5 m high masonry is surmounted with a marble slab (polished and flat) in which a 2 cm diameter hole has been cut. The slab is set precisely horizontal and centered exactly over the fiducial mark and the GPS antenna bolted directly to the slab without additional alignment. A plumb bob is used to align the antenna precisely in position over the bedrock control point. The method provides good stability and permits long term misalignment to be detected and corrected to sub mm precision.

Thus far the discussion of monument stability has been confined to monitoring lateral motions of control points relative to points at depth, partly because GPS vertical accuracies are currently much worse than horizontal accuracies, and partly because horizontal displacements are significantly more of a challenge to suppress or monitor than vertical measurements. Theoretically, the engineered monuments shown in Figure 6 all provide sub-mm vertical stability. The vertical stability of bench marks driven to refusal is reasonably well understood (Floyd, 1998), although measurements of the resulting stability are rare. Where a vertical monument must emerge above the surface it is desirable to use invar (36% Ni alloy with a <1 ppm/°C thermal coefficient). Assuming temperature fluctuations of 50°C in a 2 m exposed tripod the maximum vertical variation is approximately 1 mm for steel and 0.1 mm for invar.

Measurements of vertical position relative to points at depth are fundamental components of long-baseline tiltmeters and strainmeters (Wyatt et al. 1984; Wyatt 1989) and measurements can be made to µm accuracy using laser strainmeters, or invar rods (Figure 9). Recently optic fibers have shown utility in measuring borehole strain (M. Zumberge, personal communication, 1996). Thick glass fiber rods are available commercially