“3-D Forward Modeling and Inversion of Geo-magnetic Data Using Gauss Legendre Quadrature and Correlation Tomography Methods"

Abstract

Thesis presented a new method for 3-D forward modelling of the magnetic effects of the hexahedral (trilinear) element using the Gauss-Legendre Quadrature (GLQ) method. Remanent magnetization is not assumed in the computer program so the calculation is restricted to induced magnetization only. The complete magnetic effect has been evaluated by looking at the summation of the point dipole’s effect that fills the volume. The 3-D volume is divided into smaller prisms using an appropriate number of nodes. The algorithm is tested on different synthetic examples and the results are compared against calculated data from a common program developed at the University of British Columbia – Geophysical Inversion Facility (UBC-GIF), all tests show positive results. Similarly, the program is applied to different field data. Using this program with hexahedral prisms facilitates the calculation of magnetic anomalies for complex shapes and terrain with spatially variable magnetic susceptibility. Interpretation of the results show that the three dimensional constructed models are successful in recovering the shape and location of the true model. Subsurface magnetic susceptibility distribution is considered a powerful method in the interpretation process. This thesis provides a simple methodology for imaging magnetic susceptibility from three dimensional correlation tomography of magnetic data. This methodology can be used for deriving a quick evaluation of 3-D magnetic dipole distribution in the subsurface, especially when powerful commercial programs are not available. In correlation tomography, the subsurface space is divided into 3-D regular grid, and then the cross correlation between the observed total magnetic field anomaly and the calculated total magnetic field anomaly due to a point dipole is calculated. The resultant correlation coefficient can be used to describe the equivalent magnetic dipoles distribution in a probabilistic sense.