A revised mathematical formulation for induced polarization

Abstract

Researchers involved in induced polarization studies are well familiar with Seigel?s (1959) definition of the chargeability parameter m as the ratio of the secondary potential drop immediately after an infinitely long injected current is turned off, to the primary potential drop that builds up at the end of the current pulse. A major advantage of Seigel?s formulation is that it allows to recover the intrinsic chargeability of the subsurface applying a simple perturbation to the sensitivity matrix of the background resistivity (i.e. not affected by IP effects) model. This important result implies that the chargeability model can be readily obtained after the resistivity model has been recovered, and forms the basis of well established time domain IP inversion techniques (Li and Oldenburg, 2000a; Loke, 1999; Oldenburg and Li, 1994; Sogade et al., 2006). This manuscript aims at showing a fundamental discrepancy between Seigel?s fundamental theory and many different well accepted IP models. While contradicting in practice Seigel?s model, these other models do make use of important mathematical formulation that Seigel derived from his model.