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UBC Theses and Dissertations

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UBC Theses and Dissertations

Inversion of horizontal loop electromagnetic soundings over a stratified earth Fullagar, Peter Kelsham

Abstract

A detailed study of electromagnetic induction in a sequence of conductive layers has been completed for the case when the inducing fields are generated by an alternating current in a horizontal loop. The study was undertaken with a view to the development of a computer program to perform automatic inversion of horizontal loop electromagnetic (HLEM) frequency soundings taken over horizontally stratified ground. The program constitutes a new implementation of the general approach of Backus and Gilbert (1967, 1968, 1970). By means of a linearised iterative scheme, it constructs layered conductivities which satisfy a given set of observations to an accuracy consistent with the observational uncertainties. Subsequently, the non-uniqueness admitted by the limited amount of data can be appraised by computing averages of the original constructed model and comparing them with averages corresponding to other dissimilar models which also satisfy the data. In examples the Backus-Gilbert averages faithfully reflect the character of the "true" conductivity in regions of high conductivity, but they are of limited value in delineating resistive zones. The program has been applied successfully to the inversion of real data from Grass Valley, Nevada. A uniqueness theorem is presented for inversion of HLEM frequency soundings. It has been proved that an unlimited quantity of perfectly accurate HLEM frequency soundings (at a fixed receiver location) suffices to completely determine the conductivity as a function of depth. This result, which is believed to be new, enhances the credibility of conclusions based on inversion of HLEM soundings.

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