Three-dimensional numerical modelling of gravity and electromagnetic data using unstructured tetrahedral grids

Jahandari, Hormoz (2015) Three-dimensional numerical modelling of gravity and electromagnetic data using unstructured tetrahedral grids. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

This thesis investigates the forward modelling of gravity data and electromagnetic (EM) data on unstructured tetrahedral and Voronoï grids. Unstructured grids allow efficient local refinement of the mesh at the locations of high field curvature. These grids also provide the flexibility required for representing arbitrary topography and geological interfaces. For the forward modelling of gravity data, finite-element and finite-volume methods are employed, and for the modelling of electromagnetic data the finite-volume method is used. The main application of the presented gravity schemes is to minimum-structure inversion methods which use gradient-based minimization techniques. The main application of the presented electromagnetic schemes is for total-field modelling approaches. The unstructured schemes that are presented here are novel in the field of geophysics. In the finite-volume modelling of gravity data, tetrahedral grids and their dual Voronoï grids are used for deriving cell-centred and vertex-centred schemes, respectively. In the finite-element modelling of gravity data, tetrahedral grids are used and linear and quadratic schemes are developed. The capabilities of the four schemes are illustrated with both simple and realistic synthetic examples. The results of accuracy studies show that the quadratic finite-element scheme is the most accurate but also the most computationally demanding scheme. The best trade-offs between accuracy and computational resource requirements are achieved by the linear finite-element and the vertex-centred finite-volume schemes. In the finite-volume modelling of electromagnetic data, staggered tetrahedral- Voronoï grids are used. The two main variants of the governing equations are discretized and solved: the direct EM-field formulation is used for modelling controlledsource and magnetotelluric data, and the EM potential formulation is used for modelling controlled-source data. To verify the controlled-source schemes, two examples are presented which show the computation of the total and secondary fields due to electric and magnetic sources in halfspaces that contain anomalous bodies. The results show good agreement with those from the literature. To demonstrate the versatility of the approach, an example is also included in which helicopter-borne data synthesized for a realistic model show good agreement with real data. The magnetotelluric scheme is verified using two benchmark COMMEMI models and the solutions are compared with those from the literature. Accuracy studies show the relatively higher accuracy of the potential scheme compared to the direct EM-field scheme. The potential scheme performs more efficiently with iterative solvers while the direct method works better with sparse direct solvers. The potential scheme is also used for studying the relative contribution of the inductive and galvanic affects to the observed electromagnetic data.

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