Wittke, Jan (2017). Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion. PhD thesis, Universität zu Köln.

[img]
Preview
PDF
WittkeDissFinal.pdf - Published Version

Download (3MB)

Abstract

The first part of thesis presents new meshless methods for solving time harmonic electromagnetic fields in closed two- or three-dimensional volumes containing heterogeneous materials. This new methods will be used to simulate magnetotelluric experiments, when an Earth conductivity model is given in advanced. Normally, classical approximation methods like finite elements or finite differences are used to solve this task. The algorithms here in this thesis, only need an unstructured point sampling in the modelling domain for the discretization and is able to gain a solution for the partial differential equation without a fixed mesh or grid. This is advantageous when complex model geometries have to be described, because no adapted mesh or grid need to be generated. The meshless methods, described here in this thesis, use a direct discretization technique in combination with a generalized approximation method. This allows to formulate the partial differential equations in terms of linear functionals, which can be approximated and directly form the discretization. For the two-dimensional magnetotelluric problem, a second-order accurate algorithm to solve the partial differential equations was developed and tested with several example calculations. The accuracy of the new meshless methods was compared to analytical solutions, and it was found, that a better accuracy can be achieved with less degrees of freedoms compared to previously published results. For the three-dimensional case, a meshless formulation was given and numerical calculations show the ability of the scheme to handle models with heterogeneous conductivity structures. In the second part of this thesis, the newly developed two-dimensional simulation method will be used in an inversion scheme. Here, the task is to recover the unknown Earth conductivity model with the help of data gained from a magnetotelluric experiment. Due to the previously developed meshless approximation algorithm, some numerical tasks during the inversion can be simplified by reusing the discretization defined on the point sampling from the forward simulation. The newly developed meshless inversion algorithm will be tested with synthetic data to reconstruct known conductivity anomalies. It can be shown, that the inverse algorithm produces correct results, even in the presence of topography.

Item Type: Thesis (PhD thesis)
Creators:
CreatorsEmailORCID
Wittke, Janwittke@geo.uni-koeln.deUNSPECIFIED
URN: urn:nbn:de:hbz:38-79072
Subjects: Mathematics
Physics
Earth sciences
Uncontrolled Keywords:
KeywordsLanguage
magnetotellurik, nummerik, partielle Differentialgleichung, gitterfreie Methoden, InversionGerman
magnetotellurics, meshfree methods, partial differential equations, inversionUNSPECIFIED
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Institut für Geophysik und Meteorologie
Language: English
Date: 29 November 2017
Date of oral exam: 16 November 2017
Referee:
NameAcademic Title
Tezkan, BülentProf. Dr.
Spitzer, KlausProf. Dr.
Michael, BeckenProf. Dr.
Full Text Status: Public
Date Deposited: 08 Dec 2017 10:52
Refereed: Yes
Status: Published
URI: http://kups.ub.uni-koeln.de/id/eprint/7907

Downloads

Downloads per month over past year

Export

Actions (login required)

View Item View Item