The secondary voltage associated with time-domain induced polarization data of disseminated metallic particles (such as pyrite and magnetite) in a porous material can be treated as a transient self-potential problem. This self-potential field is associated with the generation of a secondary-source current density. This source current density is proportional to the gradient of the chemical potentials of the [Formula: see text]- and [Formula: see text]-charge carriers in the metallic particles or ionic charge carriers in the pore water including in the electrical double layer coating the surface of the metallic grains. This new way to treat the secondary voltages offers two advantages with respect to the classical approach. The first is a gain in terms of acquisition time. Indeed, the target can be illuminated with a few primary current sources, all the other electrodes being used simultaneously to record the secondary voltage distribution. The second advantage is with respect to the inversion of the obtained data. Indeed, the secondary (source) current is linearly related to the secondary voltage. Therefore, the inverse problem of inverting the secondary voltages is linear with respect to the source current density, and the inversion can be done in a single iteration. Several iterations are, however, required to compact the source current density distribution, still obtaining a tomogram much faster than inverting the apparent chargeability data using the classical Gauss-Newton approach. We have performed a sandbox experiment with pyrite grains locally mixed to sand at a specific location in the sandbox to demonstrate these new concepts. A method initially developed for self-potential tomography is applied to the inversion of the secondary voltages in terms of source current distribution. The final result compares favorably with the classical inversion of the time-domain induced polarization data in terms of chargeability, but it is much faster to perform.
3D time-domain induced polarization tomography: a new approach based on a source current density formulation
