Probabilistic domain decomposition for the solution of the two-dimensional magnetotelluric problem |
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| Authors: | Alexander Bihlo Colin G Farquharson Ronald D Haynes J Concepción Loredo-Osti |
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| Institution: | 1.Department of Mathematics and Statistics,Memorial University of Newfoundland,St. John’s (NL),Canada;2.Department of Earth Sciences,Memorial University of Newfoundland,St. John’s (NL),Canada |
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| Abstract: | Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell’s equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on the sub-domain boundaries is obtained by evaluating the stochastic form of the exact solution of Maxwell’s equations by a Monte-Carlo approach. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell’s equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function-based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem. |
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