The problem of determining optimal measurement setups that improve the resolution of reconstructed images is well known in several inverse problem applications such as magnetic tomography, electrical impedance tomography, and electrical resistivity tomography. In electrical resistivity tomography, for example, several optimisation strategies have been proposed, their aim being to collect "optimal datasets", which when inverted , should give tomographic resolutions close to that obtained from “comprehensive datasets" comprising all possible linearly independent measurements. While these optimisation strategies are useful, there has been no conceptual framework developed for finding optimal measurement setups within the context of inverse problems. Electrical resistivity tomography is an ill-posed inverse problem, and components of the inversion process influence the nature of reconstructions obtained. Such a framework would incorporate within its optimisation process important components of the inversion process. This research describes the development of sl1ch a meta inverse framework. The framework incorporates within its optimisation process important ingredients of an inversion process such as choice of regularisation parameter, nature and size of data error, and a priori knowledge on solutions. As a first example, 'the framework is implemented for an acoustic source reconstruction linear problem, the aim being to find optimal acoustic receiver locations at which best reconstructions of the acoustic source strength can be obtained. To improve the quality of acoustic source strength reconstructions, a framework adaption algorithm is developed for use with the meta inverse framework The adaption algorithm uses successive measurements to improve the quality of reconstructions. Numerical results from implementing the meta inverse framework illustrate its success at finding optimal locations at which best reconstructions of the acoustic source strength can be obtained. The results also show that the framework adaption algorithm can be successfully implemented to improve the quality of reconstructions. To implement the meta inverse framework for electrical resistivity tomography, new forward and inverse solvers were developed. The forward solver is based on the finite integration technique (FIT), the inverse solver is called the domain search algorithm. The FIT solver generates the 'simulated data for an assumed resistivity model of the subsurface; the domain search inverse solver searches to find a resistivity model that gives an acceptable fit to the simulated data. Numerical results from implementing these solvers show that they are successful in simulating and reconstructing the resistivity distribution in electrical resistivity tomography. To find optimal electrode locations from which best reconstructions can be obtained for a 2D 'resistivity tomography problem, the meta inverse framework is incorporated into the forward and inverse solvers. Numerical results from implementing these algorithms show that the meta inverse framework is successful in finding optimal electrode locations at which best reconstructions can be obtained.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603521 |
| Date | January 2013 |
| Creators | Usdosen, Ndifreke |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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