UBC Theses and Dissertations
Forward modelling and inversion of time-domain electromagnetic geophysical surveys in the presence of chargeable materials Belliveau, Patrick
The work described in this thesis examines transient geophysical electromagnetic forward modelling and inversion in the presence of induced polarization (IP) effects. The thesis introduces a new method of modelling IP using stretched exponential relaxation. A three-dimensional (3D) forward modelling algorithm taking full account of the coupling of IP and electromagnetic induction is developed. The stretched exponential modelling algorithm has been implemented using efficient numerical methods that allow it to tackle large-scale problems and are amenable to use in inversion. In particular, a parallel time-stepping technique has been de- veloped that allows transient electric fields at multiple time steps to be computed simultaneously. The behavior of the stretched exponential model is demonstrated by applying it to synthetic numerical examples that simulate a grounded source IP survey with significant electromagnetic induction effects and a concentric-loop airborne electromagnetic sounding over a polarizable body. An inversion algorithm using the stretched exponential model was developed that is able to recover the 3D structure of physical properties of the earth related to IP from transient geophysical electromagnetic data. The method is tested on a simple synthetic example problem. The thesis finishes with the development of a novel stochastic parametric level-set inversion algorithm, which could be useful in applying stretched exponential inversion to real world problems in the future. The algorithm addresses some of the shortcomings of the simple inversion approach used for stretched exponential inversion earlier in the thesis. The stochastic parametric inversion algorithm is used to solve shape reconstruction inverse problems in which the object of interest is embedded in a heterogeneous background medium that is known only approximately. Shape reconstruction is posed as a stochastic programming problem, in which the background medium is treated as a random field with a known probability distribution. It is demonstrated that by using accelerated stochastic gradient descent the method can be applied to large- scale problems. The capabilities of the method are demonstrated on a simple 2D model problem and in a more demanding application to a 3D inverse conductivity problem in geophysical imaging.
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