5 - Forward and Inverse Modelling

Summary

In this chapter, we introduce the concepts of forward and inverse modelling of resistivity and induced polarization (IP) measurements.We provide a comprehensive account of the elements that form the majority of modern techniques for resistivity and IP modelling. 1D forward modelling is discussed, building on analytical approaches presented in Chapter 4.For 2D and 3D forward modelling, numerical (discrete) approaches are required, typically adopting finite difference or finite element methods. Inverse modelling, which provides the spatial (or spatio-temporal) variation of a property of interest, is essential for interpretation of resistivity and IP data.We detail various inverse modelling approaches for resistivity and IP data. We illustrate how a priori information can be used to enhance an inverse model and show how data errors can impact on the computed model of electrical properties. Extension of the inverse modelling to treat time-lapse data is explained.Various methods for inverse model appraisal (including model uncertainty) are presented. We illustrate alternative inverse modelling approaches that are based on probabilistic approaches. The inverse modelling of spectral IP data for recovery of relaxation parameters is also discussed.