Three-dimensional forward modelling and inversion for the CSAMT method using unstructured grids

Kara, Kadir Bahadır (2022) Three-dimensional forward modelling and inversion for the CSAMT method using unstructured grids. Masters thesis, Memorial University of Newfoundland.

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Abstract

Three-dimensional forward-modelling and inversion problems are investigated for the controlled-source audio-frequency magnetotelluric (CSAMT) method and both forward-modelling and inversion codes written. The finite-element (FE) method, which is a numerical method for obtaining approximate solutions to boundary-value problems, is used for forward modelling. A potential formulation, specifically the decomposition of the electric field into vector and scalar potentials for the Helmholtz and the conservation of charge equations, is used. Vector and scalar basis functions are used for the potentials. The equations are discretized using the weighted residual method, which results in a sparse linear system. Modelling domains are subdivided into unstructured tetrahedral grids. The linear system is solved by the direct solver, MUMPS, with LU factorization. A number of examples are presented for the validation of the code. A minimum-structure method with Gauss-Newton iterations is used for the inversion. Iterative preconditioned conjugate gradient and nonpreconditioned generalized minimal residual methods are used to solve the linear systems of equations for the model updates. These solvers do not request explicit calculations of the matrices; therefore, this significantly reduces memory demand. Three benchmark tests are presented to verify the inversion code.

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