title: Simulating the gravimetric detection of submarines, calculating high-accuracy terrain corrections using LIDAR elevation data and performing a microgravity survey in the Campsie Fells
Creators: name: Aftalion, Marc
Publisher: name: University of Glasgow
Year: 2023

description: The work in this thesis relates to the field of gravimetry, the measurement of gravitational fields and their variations, which is carried out using highly-sensitive accelerometers known as gravimeters. By using gravimeters to measure the changes in gravitational field strength from place to place, it is possible to detect differences in the concentration of mass around the gravimeter and this has historically been used to monitor geophysical activity (such as variations in groundwater, volcanic activity or glacial mass), for geological exploration (such as searching for mineral or hydrocarbon resources) and many other applications. This work covers a range of topics in gravimetry, starting with the use of computer programs to simulate the gravitational fields that would be generated when a submarine travelled past a stationary gravimeter, or array of gravimeters, situated underwater. This is done with the aim of estimating the efficacy of a new gravimeter known as the ‘Wee-g’ under development at the University of Glasgow at the time of writing and also has applications to the gravitational detection of submarines more generally. The gravitational field of a 100m-long submarine is simulated, using a simplified one-dimensional density profile approximating the real density variations along the length of a large submarine. The simulated gravity field is then compared to the sensitivity of a prototype Wee-g gravimeter of 5µGal/ √ Hz to give an initial estimate of the maximum detection range of such a signal by the Wee-g, which is found to be approximately 20m. Then, synthetic noisy signals are made by combining the simulated gravity signals with real Wee-g sensor noise data and digital signal processing methods are used to try and recover the corrupted signal from the noise in a way that maximises the detection range. Matched filtering is applied which uses foreknowledge of the signal being searched for to significantly increase the signal to noise ratio (SNR) in the noisy data by an order of magnitude, which increases the Wee-g’s detection range of the modelled submarine to ∼ 30m. In addition, computer programs are made that determine a quantity known as the terrain correction at a given gravity survey point using digitised elevation data describing the surrounding topography. Terrain correction is the effect that the presence of surrounding hills and valleys has on the gravitational field strength at a location and, if it is not accounted for, substantial variations in gravity (and hence, potentially useful information) can be partially or completely obscured. Methods already exist to calculate the terrain correction but these are either slow and laborious, inaccurate (in comparison to contemporary gravimeter performance) or both, while the program presented in this work makes use of modern computing speed and high-accuracy elevation maps to improve on these. The terrain correction program presented here analyses terrain out to a distance of 166.735km from the survey point, using 1m-resolution LiDAR elevation data to describe the nearest 2km2 , and can calculate terrain correction values in approximately 9s when run on a computer with 8GB of RAM. Terrain at all distances from the survey point is modelled using many flat-topped rectangular prisms and the gravitational field strength due to each prism is calculated using an already existing analytic solution. An in-depth analysis of the terrain correction computation of the innermost 2km is carried out to compare the accuracy of the method used with simple analytic solutions. This analysis concludes that terrain corrections can be calculated with an uncertainty of 2µGal or less when using 1m2 -resolution elevation data, provided the terrain immediately around the survey point has an incline of less than 10◦ . Finally, two gravity surveys carried out in January of 2020 by the author with a Scintrex CG-5 commercial gravimeter are described: one in the Campsie Fells — a range of hills roughly 10km north of Glasgow — and the second in the cloisters of the Gilbert-Scott building on the University of Glasgow campus. The Campsies survey is compared with a gravimeter survey of the same region carried out in 1969 and discrepancies of up to a few mGal are observed, understood to be due to terrain correction inaccuracies in the older survey. Results from the survey in the cloisters are compared to the gravitational field due to underfloor air ducts described by plans of the building but little correlation is found. This is suspected to be the result of either inaccuracies in the building plans or the impact of environmental noise on the measurements.