Combining spatial components and Hilbert transforms to interpret ground-time-domain-electromagnetic data

Abstract

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.