Watson, Francis Maurice
(2016)
*BETTER IMAGING FOR LANDMINE DETECTION: AN EXPLORATION OF 3D FULL-WAVE INVERSION FOR GROUND-PENETRATING RADAR.*
Doctoral thesis, The University of Manchester.

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## Abstract

Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging for landmine detection. Posing the imaging task as FWI means solving the large-scale, non-linear and ill-posed optimisation problem of determining the physical parameters of the subsurface (such as electrical permittivity) which would best reproduce the data. This thesis begins by giving an overview of all the mathematical and implementational aspects of FWI, so as to provide an informative text for both mathematicians (perhaps already familiar with other inverse problems) wanting to contribute to the mine detection problem, as well as a wider engineering audience (perhaps already working on GPR or mine detection) interested in the mathematical study of inverse problems and FWI.We present the first numerical 3D FWI results for GPR, and consider only surface measurements from small-scale arrays as these are suitable for our application. The FWI problem requires an accurate forward model to simulate GPR data, for which we use a hybrid finite-element boundary-integral solver utilising first order curl-conforming N\'{e}d\'{e}lec (edge) elements. We present a novel `line search' type algorithm which prioritises inversion of some target parameters in a region of interest (ROI), with the update outside of the area defined implicitly as a function of the target parameters. This is particularly applicable to the mine detection problem, in which we wish to know more about some detected metallic objects, but are not interested in the surrounding medium. We may need to resolve the surrounding area though, in order to account for the target being obscured and multiple scattering in a highly cluttered subsurface.We focus particularly on spatial sensitivity of the inverse problem, using both a singular value decomposition to analyse the Jacobian matrix, as well as an asymptotic expansion involving polarization tensors describing the perturbation of electric field due to small objects. The latter allows us to extend the current theory of sensitivity in for acoustic FWI, based on the Born approximation, to better understand how polarization plays a role in the 3D electromagnetic inverse problem. Based on this asymptotic approximation, we derive a novel approximation to the diagonals of the Hessian matrix which can be used to pre-condition the GPR FWI problem.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | 3D; BEM; Boundary integral; Computational electromagnetics; Electromagnetics; FE-BI; FEBI; FEM; FWI; Finite element; Full-wave inversion; Full-waveform inversion; GPR; Ground penetrating radar; Helmholtz equation; Hessian; Ill-posed; Imaging; Inverse problems; Inverse scattering; Maxwell's equations; Nedelec elements; Non-linear; Nuisance parameters; Optimisation; Preconditioning; ROI; RWG; Region of interest; Regularization; SVD; Scattering; Sensitivity; Shape sensitivity; Spatial sensitivity; Surface equivalence; TV; Total variation; Vector wave equation; asymptotic; edge elements; l-BFGS; landmine detection; polarizability tensor; polarization tensor |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 90 GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS > 93 Geophysical observations, instrumentation, and techniques |

Depositing User: | Prof WRB Lionheart |

Date Deposited: | 20 Jun 2016 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2486 |

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