Some methods of analysis of geodetic data and their applications to the measurement of crustal deformation

Abstract

This thesis reviews methods of analysing geodetic data with the aim of detecting and quantifying deformation of the Earth's crust. All the methods of analysis are founded on the theory of least squares. The relationship with least squares theory is illustrated with a detailed discussion of the methods of analysis of distance and horizontal angle observations of lines of sight between well defined points or 'stations' on the surface of the Earth. These methods estimate the coordinates of the stations on a plane approximating the Earth's surface. Relative weighting of different observations according to accuracy and type is discussed. Estimates of station displacements due to crustal deformation can be found by comparing separate estimates of coordinates each calculated with observations made at different times. By using standard techniques, mathematical models can be fitted to the displacements. The methods of analysis of data sets consisting only of distance and horizontal angle observations can be extended to deal with a much greater variety of geodetic data including astronomical observations of latitude, longitude and azimuth, gravimetric measurements, levelling circuit observations, vertical angle observations and various kinds of satellite data. The methods of 'operational geodesy' are outlined with emphasis on one particular method. These methods are able to use all types of geodetic data to estimate both the coordinates of stations in three dimensions and parameters characterising the field of gravity above the Earth's surface. Modifications of these methods enable estimates of three dimensional deformation parameters and rates of change of gravitational field parameters to be made from observational data repeated at different times. The problem of a rank deficient system of observation equations is discussed and various means of overcoming this problem are outlined. Changes in the 'horizontal' coordinates of stations interact only weakly with changes in station heights. For many data sets accurate estimates of horizontal deformation parameters can be made assuming that the station heights are constant with time. A variety of methods for estimating parameters of horizontal deformation are discussed with special attention paid to methods using a spheroidal system of coordinates. One of these methods is applied to data collected from the region lying between Gisborne and Raglan. The data consisted of horizontal angle observations made during the first order geodetic survey between 1923 and 1936, and horizontal angle observations and electromagnetic distance measurements made during the Earth Defomation Study survey of 1976. The mean rate of principle shear strain, γ and the direction of the axis of maximum compression, β were estimated for each of five separate networks which span the region. The largest rate of deformation was found in the East Cape region and is (3.3±.5)x10 -7 rads/year. The quoted error is an estimate of the standard deviation in γ. The direction of the axis of maximum compression was estimated at 40° ±4° east of north. Values of γ for the other four networks were smaller and estimates of β were less well defined but close to 40°. The thesis concludes with a discussion of the methods suitable for future use in New Zealand and recommends a method for analysing the results of the proposed resurvey of the Raglan-Gisborne region in 1986.