Efficient Electromagnetic Induction Modelling : Adaptive mesh optimisation, advanced boundary methods and iterative solution techniques

Abstract: Forward modelling of electromagnetic induction data simulates the electric and magnetic fields within a computational domain for a given distribution of electromagnetic material properties and a given source of the electromagnetic field. The quantities of interest are the fields at receiver locations at the Earth's surface. Reliable results require high accuracy solutions at the receivers.  First and foremost, numerical computations need to be accurate, but ideally they are also resource efficient, i.e., as fast and cheap as possible. Run time and memory demand mainly depend on the size of the numerical problem to be solved. This thesis addresses specific steps within the forward modelling procedure of electromagnetic induction data in order to improve the solution accuracy of forward modelling as well as to reduce computational resources. The solution accuracy is strongly influenced by the spatial discretisation of the computational domain, which directly correlates with the numerical problem size. To optimise the solution accuracy while keeping the numerical problem size as small as possible, a goal-oriented adaptive mesh refinement scheme for three-dimensional controlled-source electromagnetic models is developed. In addition, this thesis investigates the influence of different types of boundary methods on the solution accuracy at the receivers. To replace inhomogeneous boundary conditions in magnetotelluric total-field modelling by perfectly-matched layers (PML), a domain decomposition approach (the total and scattered field decomposition) is adapted for Earth models. By reducing boundary effects, the approach yields superior solution accuracy for specific types of models. The fastest and most memory-efficient way to solve large numerical problems are iterative solution methods. Iterative solvers, however, work poorly for numerical systems arising from domains bounded by PML. In this thesis a preconditioned iterative solution framework that efficiently solves PML-bounded magnetotelluric models is proposed.