The use of constraints in 2D and 3D resistivity modelling

Electrical imaging surveys are now widely used to map areas with complex subsurface geology. The many applications include groundwater exploration, mineral exploration, environmental and engineering studies (Dahlin, 1996; Griffiths and Barker, 1993). While 2D surveys are more commonly used due to time and cost limitations, 3D surveys are also used in very complex areas such as in mineral exploration surveys (White et al., 2001). A cell-based inversion model is normally used to model such complex structures. The subsurface is divided into a large number of rectangular cells and an inversion algorithm is used to determine the resistivity of the cells. The inversion of resistivity data gives non-unique results. Thus some assumptions are made about the subsurface so as to limit the range of plausible models. The regularized least-squares optimization method where constraints can be easily added into the inversion procedure (Ellis and Oldenburg, 1994) is frequently used. The effects of constraints on the inversion results are discussed in the following sections.