Mathematical analysis of electrical resistivity tomography - Sim, Zheng Xian (Nanyang Technological University, 2023)
This report is motivated by the rapid development of Singapore's urbanisation and interest in exploiting the underground space to cater to the growing population as stated in the Population White Paper in 2013. Much research has been done to explore the plausibility of creating an underground city however, not much has been done to what constitutes the subsurface distribution and the possibility of future development for that space. Hence, this report analyses the mathematical concepts of Electrical Resistivity Tomography (ERT), specifically the forward modelling of ERT survey which aims to solve Poisson's Equation under some boundary conditions that are dictated by the physical subsurface structure. This is because ERT survey makes use of the electrical properties of geological materials such as minerals, fluid content, porosity, and degree of water saturation to better understand the geological structure beneath the ground. The Finite-Difference method is implemented in the various simulations due to its popularity in solving both linear and nonlinear Partial Differential Equations. In the Finite-Difference Method, the differential operators in the Poisson's Equation are decomposed into discrete stencil points and the solution is obtained numerically. The solution denotes the supposed potential difference distribution of the subsurface structure that is used as a guide in producing the subsurface structure. This report can also further serve as additional material in the planning for future human underground activities in Singapore.