Automatic forward modelling of two-dimensional problems in electromagnetic induction




Poll, Helena Eva

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A finite difference algorithm for solving the forward modelling problem of geo-electromagnetic induction in two-dimensional (2D) structures has been developed in this thesis. The governing equations have been modified to solve for the anomalous field by separating out the 'host' field which is assumed to be the field generated by the one-dimensional (1D) conductivity distribution on the left hand side of the model. This was done to prevent the small anomalous fields being masked by the much larger host field due to the finite length of the computer word. One of the most important features of this program is an automatic gridding subroutine which greatly reduces the amount of time required to design a suitable grid for a model and removes the human element from such grid design. Up to 20 periods can be submitted to the model at one time and specific locations (e.g. the locations at which field data are available) can be added to the automatically generated grid. Integral boundary conditions at the surface and bottom (z = d) of the model eliminate the need to extend the grid above the earth's surface or down into the half-space underlying the model. The program has been used to perform a 2D inversion of magnetoteliuric data from a NS profile in Sardinia. The magnetoteliuric responses from two sites along this profile indicated that the structure underneath them could not be considered to be solely 2D. To examine the conductivity anomalies perpendicular to the profile indicated that are affecting the results at these two sites, 2D inversions were performed on the data to obtain their EW conductivity models. The apparent resistivity curves from the models fit the data fairly well at both sites especially at short periods. Many features of the models were in agreement with the 2D model along the profile obtained by Peruzza et al. (1990) and they also provided insight into the geological structure of the area. A study was made of the behaviour of 2D induction arrows over a buried conductivity contrast. Although the general trend of in-phase arrows is to point towards the regions of high electrical conductivity, some investigators have found small amplitude in-phase arrows that point away from these same regions. Reversals such as these, which do not behave according to the general trend, can cause confusion and erroneous interpretation of the in-phase induction arrows. Using a model with two semi-infinite conducting plates, one at the surface and one buried at a depth d in a layered half space, it was found that the period at which a reversal in the in-phase induction arrow direction occurs was a function of the apparent resistivity of the layered host. Anomalous behaviour was found in the short period in-phase arrows from which the coast effect had been removed. The problems in interpretation of such arrows was discussed. Finally a 2D inversion scheme was discussed in which a 2D forward modelling program was incorporated with a minimization routine MTNDEF. First an investigation was made into the relative merits of using the impedances ZTE, ZTM, Zave and Zeff to calculate the ID inversions that are combined to form starting models for the 2D inversions. A subsequent 2D inversion of the North American Central Plains (NACP) anomaly results in a best fit model whose responses show good agreement with the field data from 20 sites. Tests have been performed to ensure that an oversimplification of the starting model is not responsible for the lack of certain features found by other authors. It is concluded that the incorporation of these features in the model is not required in order to obtain a good fit to the field data.



Electromagnetic induction, Magnetic induction, Geomagnetism