Investigation of geophysical electromagnetic computer modelling approaches for infinitesimally thin conductors of curved, complex shapes

矿业对加拿大经济很重要，找到更多的矿藏对这个行业的未来至关重要。许多矿体及其伴生的矿化都能很好地导电。因此，寻找矿化带的一种方法是使用电磁场来诱导电流在导电矿化中流动，并测量这些电流产生的磁场。该项目的工业合作伙伴Nova矿业勘探解决方案公司开发了新的软件，用于模拟在此类调查中获得的数据，并将该软件作为服务提供给勘探行业。EM调查的数据包含有关导电矿化带的位置、深度、大小和组成的信息。要提取这些信息，需要使用计算机建模技术。存在考虑地下一般模型的建模技术。这些方法很有用，但计算成本很高。然而，矿化带的形状往往像翘曲的折痕薄片，即它们的高度和水平范围可达数十或数百米，但厚度可达厘米。此外，主岩的电导率往往很低，实际上为零。对于这些方法，可以用只存在于矿化带而不存在于主岩中的二维函数来描述感应电流。以前已经开发了这种方法的实现，假设矿化带的形状像矩形板。这种方法被证明是有用的，因为它计算迅速，并充分接近较简单的勘探情景。然而，矩形平板对于许多情况来说过于简单化。拟议的研究将研究现有方法的新改编，其中包括一种新的数学映射，该映射将允许将矩形平板的数学转换为任意薄板的数学。这种方法应该仍然计算得很快，但现在应该可以计算出更现实的矿化带的EM响应。开发的软件将使Nova能够提供处于EM建模能力前沿的新服务，从而提高他们的竞争优势。

Mining is important to Canada's economy, and finding more ore deposits is critical to the future of this industry. Many ore-bodies, and the associated mineralization, can conduct electricity well. A method for finding mineralized zones is therefore to use electromagnetic (EM) fields to induce electric currents to flow within the conductive mineralization, and to measure the magnetic field generated by these currents. The industrial partner for this project, Nova Mining Exploration Solutions, develops new software for modelling the data acquired in such surveys, and offers this software as a service to the exploration industry. The data from EM surveys contain information about the location, depth, size and composition of conductive mineralized zones. To extract this information requires the use of computer modelling techniques. Modelling techniques exist that consider general models of the subsurface. These are useful, but are computationally expensive. However, mineralized zones are often shaped like a warped, creased sheet, i.e., they can have heights and horizontal extents of tens or hundreds of metres, but have a thickness of centimetres. Also, the conductivity of the host rocks can often be so low that it is effectively zero. For these approaches it is possible to describe the induced currents in terms of 2-D functions that exist only in the mineralized zone and not in the host rocks. An implementation of this approach has previously been developed assuming the mineralized zone is shaped like a rectangular plate. This approach has proved to be useful as it is fast to compute and adequately approximates the simpler exploration scenarios. However, the rectangular plate is too simplistic for many scenarios. The proposed research will investigate a new adaptation of the existing approach that includes a new mathematical mapping that will allow the mathematics for the rectancular plate to be transformed to those for an arbitrary sheet. This approach should still be fast to compute, but should now allow for the EM responses of much more realistic mineralized zones to be calculated. The software developed will allow Nova to offer a new service that is at the leading-edge of EM modelling capabilities, thus improving their competitive advantage.