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UBC Theses and Dissertations

Linearized inverse theory applied to direct current resistivity measurements Plenderleith, Donald H.


Layered resistivity models have been constructed from the potential difference measurements made in direct current resistivity soundings using Backus and Gilbert's linearized inverse theory in a manner similar to that of Oldenburg (1978). The efficiency of the original method has been improved by approximating the one-dimensional structure with a finite number of layers, and by computing the Hankel transforms used in evaluating the Frechet kernels, and solving the forward equation, with a digital filter. Also, the surface resistivity is no longer required thus making the method fully automatic. The constructed model's representation of a hypothetical resistivity structure was tested, varying the starting model, adding up to 20 percent noise to the synthetic data, and decreasing the data density. In all cases the hypothetical structure was recognizably reproduced. With the program's ability to reproduce this structure verified, six Schlumberger soundings in the Anahim Volcanic belt in British Columbia were inverted. Although the setting was not ideal, models which fit the data according to the chi-squared criterion were constructed. A standard deviation of 10 percent was assigned to the data to account for measurement errors, and invalidity of the flat one-dimensional earth approximation made in solving the potential equation. From the models constructed and the known near-surface geology, three integrated interpretations were made. The first is a purely geological interpretation of the low resistivity zones. In the second, they are attributed to increasing temperatures with depth and to the north, and a heat source north of the survey region is hypothesized from an observed north-south resistivity gradient. The third is the most probable interpretation. In it, the heat source to the north is retained because it is inferred from a trend of decreasing average resistivities indicated by the four northernmost soundings, but one of the remaining southern anomalies is questioned, and a geological explanation is given for the other. There was not enough information in this data set to favor either the hot-spot, or the edge effect hypothesis for the genesis of the Anahim Volcanic belt. The two soundings most important to the heat-source-to-the-north hypothesis were linearly appraised. Average models have been constructed with a predetermined standard deviation and, on the basis the low resistivity zones being present, it can be said that the features which form the basis of this hypothesis are resolvable.

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