Title:

High precision relative and absolute gravity in Britain

Tide gauge observations suggest current rates of uplift of the land with respect to mean sea level of a few millimetres per year ranging from +1.6 at Lerwick to 3.2 at Southend. The measurement of absolute heights separates the land movements from changes in mean sea level. 10 mm of uplift causes a change in gravity of about 2 μgal (1 μgal = 10^{8} m s^{2}) so a precision of 5 μgal detects a differential rate of 5 mm per year in about 10 years. The British Precise Gravity Network 1993 (BPGN93) was established by the author to provide a datum from which future reobservation could identify vertical crustal movements. It consists of 58 sites spaced about 100 km apart over mainland Britain. They were observed with three specially calibrated LaCoste & Romberg gravity meters and controlled by observations measured with FG5 absolute gravity meters at Edinburgh, Birkenhead, Teddington and Taunton. Very high accuracy relative gravimetry depends on the calibration of the instrument and maintaining reproducible instrumental drift characteristics, correctly modelling environmental disturbances such as Earth tides and developing robust and appropriate statistical models. A search for periodic errors in the micrometer screw of the unique doubledial instrument D145 appeared to find a period of about 400 coarse dial turns, four times that expected from the gear ratios. The meter was balanced using the coarse screw at various settings of the fine screw. The sequence of readings every 10 minutes for up to 5 hours detected nonlinear drift caused by changes in the direction of screw turning. Because a linear drift model was analysed using leastsquares, this was initially interpreted as a periodic screw error. The 'spring hysteresis model' explains the anomalous result. SolidEarth tides were calculated using the full CartwrightTaylerEdden expansion but other algorithms agree to better than 0.5 μgal. Inconsistent treatment of the static tide can create discrepancies of about 30 μgal for British latitudes. The ocean load tide is only important near the margins of continents, and in particular in SW England, but was implemented for all relative and absolute gravity data. This thesis describes improved analysis techniques for absolute gravimetry, with a detailed study of three corrections, for vertical gradient, datum height and system response, which were incorrectly treated in the manufacturer's software. The vertical gradient of gravity was measured at the eight absolute gravity sites locations in the UK where the absolute gravity has been observed to correct the new data. The FG5 absolute gravity meter measures the position and time of a freely falling cornercube reflector using fringes produced by laser interferometry, and estimates gravity by fitting them to an equation of motion. Ignoring the vertical gradient of gravity in the equation of motion estimates gravity at the 'effective measurement height', but it is shown that theoretical predictions relating this position to the top of the drop are incorrect because of fringe counting errors. Thus the equation of motion used must include the vertical gradient of gravity, determined by relative gravimetry, so as to estimate gravity estimate at a definite height for comparison with other instruments.
