| 1. |
- Buntin, Laura M.
(författare)
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Efficient Electromagnetic Induction Modelling : Adaptive mesh optimisation, advanced boundary methods and iterative solution techniques
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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.
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| 2. |
- Rulff, Paula
(författare)
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Three-dimensional forward modelling and inversion of controlled-source electromagnetic data using the edge-based finite-element method
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Electromagnetic geophysical methods are applied to investigate anomalous subsurface structures exhibiting contrasts in electrical resistivity, as for example in mineral exploration or geothermal areas. When evaluating electromagnetic data, one big challenge is to account for full three-dimensional measurement setups and subsurface scenarios. To address this challenge, this work seeks to report on the development of a three-dimensional forward modelling code for controlled-source electromagnetic data and its integration into an inversion framework to enable the computation of three-dimensional resistivity models of the subsurface.This thesis outlines the technical details of the developed forward and inverse modelling routines and describes synthetic tests to verify their effectiveness. The implemented forward modelling routines, based on the linear edge-based finite-element formulation on tetrahedral elements, consist of a standalone code containing a goal-oriented mesh refinement option. The forward modelling code was included with several modules into an existing inversion framework. Electromagnetic field components or impedance tensors and vertical magnetic transfer functions serve as input data for the inversion. Data gradients, required for the used non-linear conjugate-gradient inversion algorithm, were implemented for all input data types. Furthermore, regularisation options were employed and tested. The aforementioned forward and inverse modelling codes were applied for different field settings: A forward modelling study of an ore deposit in central Sweden aimed at finding an adequate receiver distribution for the field measurements. In another modelling project, the mesh design for subsurface models containing steel-cased wells was investigated. Finally, an inversion of controlled-source electromagnetic data collected on a frozen lake in Stockholm for a tunnel-project complemented previously obtained two-dimensional resistivity models with a three-dimensional model. The benefit of the presented research is twofold: First, the new modules added to the inversion framework can be used by the academic community to obtain improved resistivity models. Second, the reported models and field settings provide detailed information for measurement design, meshing of three-dimensional domains and local resistivity distributions of the subsurface allowing to answer geological, hydrological and geotechnical questions of selected field sites.
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| 3. |
- Weiss, Michael, 1990-
(författare)
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Implementation of the spectral element method and iterative solution techniques for 3D controlled-source electromagnetic modelling
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Controlled-source electromagnetic methods are imaging techniques applied at/on the surface of the Earth which record the electromagnetic field in order to assess the electrical conductivity distribution of the Earth’s subsurface, along with anomalies in this material property, as well as to characterise and interpret structures in Earth’s crust. Extracting information from the recorded electromagnetic data requires inverse modelling algorithms. A key component of inverse modelling is the reverse process, namely, forward modelling, that is numerically simulating the electric and magnetic fields for a computerised model using discretisation techniques, appropriate boundary conditions and efficient solution methods. The forward problem for 3D models constitutes a computationally challenging and expensive task. Hence, cost effective forward modelling algorithms are crucial to limit the computational resources in terms of time and memory needed for realistic large-scale models. This thesis investigates numerical aspects of forward modelling problems encountered in frequency-domain land-based controlled-source electromagnetic methods. It presents the mathematical framework and the implementation of a 3D forward modelling algorithm based on the spectral element method which merges the high accuracy and the favourable convergence properties of the spectral method with the geometrical flexibility of the finite element method. Further, it introduces the total field formulation to the spectral element method. On the basis of the developed code, a cost-effective, efficient and robust iterative algorithm using the generalised conjugate residual method preconditioned with an efficient block-based PREconditioner for Square Blocks (PRESB) is implemented in order to reduce time and memory requirements of the modelling routine. Two core findings of this thesis, is that the efficiency of the iterative algorithm hinges on the efficiency of the solution of the two inner linear systems of equations which arise through applying preconditioner PRESB, and that the auxiliary-space Maxwell preconditioner AMS represents a highly efficient preconditioner for the aforementioned inner systems. To expand the scope of application of the iterative algorithm, this thesis investigates a block lower-triangular preconditioner based on either the Schur complement or its element-by-element approximation and finds that the AMS-preconditioned solver used to solve systems with the Schur complement or its approximation is not well suited for either. Only the Schur complement based preconditioner is shown to work for relevant problems.
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