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

采矿业对加拿大经济至关重要，寻找更多的矿床对该行业的未来至关重要。许多矿体及其伴生的矿化具有良好的导电性。因此，一种寻找矿化带的方法是使用电磁（EM）场来感应电流在导电矿化物内流动，并测量由这些电流产生的磁场。该项目的工业合作伙伴Nova Mining Exploration Solutions开发了新的软件，用于对此类调查中获得的数据进行建模，并将该软件作为勘探行业的服务提供。EM勘测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。为了提取这些信息，需要使用计算机建模技术。存在考虑地下的一般模型的建模技术。这些都是有用的，但计算成本很高。然而，矿化带的形状往往像一个扭曲的，有折痕的床单，即，它们的高度和水平范围可达数十米或数百米，但厚度为厘米。此外，寄主岩石的电导率通常很低，实际上为零。对于这些方法，它是可能的，以描述的2-D功能，只存在于矿化带，而不是在寄主岩石的感应电流。这种方法的实施以前已经开发假设矿化带的形状像一个矩形板。这种方法已被证明是有用的，因为它是快速计算和充分近似的更简单的勘探方案。然而，矩形板对于许多情况来说过于简单。拟议的研究将调查现有方法的新适应，包括一个新的数学映射，将允许矩形板的数学转换为任意板的数学。这种方法的计算速度仍然很快，但现在应该允许计算更真实的矿化区的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，从而提高其竞争优势。

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.