Browsing by Author "Desmarais, J.K."

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Approximate semianalytical solutions for the electromagnetic response of a dipping-sphere interacting with conductive overburden
(Society of Exploration Geophysicists, 2016-06-06) Desmarais, J.K.; Smith, Richard S.
Electromagnetic exploration methods have important applications for geologic mapping and mineral exploration in igneous and metamorphic terranes. In such cases, the earth is often largely resistive and the most important interaction is between a conductor of interest and a shallow, thin, horizontal sheet representing glacial tills and clays or the conductive weathering products of the basement rocks (both of which are here termed the “conductive overburden”). To this end, we have developed a theory from which the step and impulse responses of a sphere interacting with conductive overburden can be quickly and efficiently approximated. The sphere model can also be extended to restrict the currents to flow in a specific orientation (termed the dipping-sphere model). The resulting expressions are called semianalytical because all relevant relations are developed analytically, with the exception of the time-convolution integrals. The overburden is assumed to not be touching the sphere, so there is no galvanic interactions between the bodies. We make use of the dipole sphere in a uniform field and thin sheet approximations; however, expressions could be obtained for a sphere in a dipolar (or nondipolar) field using a similar methodology. We have found that there is no term related to the first zero of the relevant Bessel function in the response of the sphere alone. However, there are terms for all other zeros. A test on a synthetic model shows that the combined sphere-overburden response can be reasonably approximated using the first-order perturbation of the overburden field. Minor discrepancies between the approximate and more elaborate numerical responses are believed to be the result of numerical errors. This means that in practice, the proposed approach consists of evaluating one convolution integral over a sum of exponentials multiplied by a polynomial function. This results in an extremely simple algorithmic implementation that is simple to program and easy to run. The proposed approach also provides a simple method that can be used to validate more complex algorithms. A test on field data obtained at the Reid Mahaffy site in Northern Ontario shows that our approximate method is useful for interpreting electromagnetic data even when the background is thick. We use our approach to obtain a better estimate of the geometry and physical properties of the conductor and evaluate the conductance of the overburden.
Combining spatial components and Hilbert transforms to interpret ground-time-domain-electromagnetic data
(Society of Exploration Geophysicists, 2015-06-19) Desmarais, J.K.; Smith, Richard S.
We have developed a method for displaying or imaging data from a ground-time-domain electromagnetic system and for extracting the geometric parameters of a small conductor. The parameters are determined directly from the data using combinations of the spatial components of the secondary fields and their Hilbert transforms. The position of the target coincides with the peaks of the energy envelope (EE) or the 𝑇-component of the response. Here, the EE is the square root of the sum of the squares of the three spatial components and their Hilbert transforms, whereas the 𝑇-component response is an analogous quantity that excludes the Hilbert transform terms. Studies on synthetic models indicate that the 𝑇-component response is sharper than the EE in most possible target orientations. Once the position of a body has been determined using the peak of the 𝑇-component response, the dip of the target can be quantified using the ratio of the full-width at half-magnitude (FWHM) of the 𝑇-component response and the 𝑇-component Hilbert transform response, which is analogous to the EE but excludes the untransformed quantities. Finally, once all other geometric parameters have been determined, the depth of the target can be evaluated using the FWHM of the 𝑇-component response. The proposed modeling method was tested over an anomaly acquired at the Coulon field site during an InfiniTEM survey in the Abitibi greenstone belt of Quebec. The extracted geometric parameters were consistent with the available geologic information.