f 3-D Resistivity and IP probability tomography in near-surface geophysics

In a previous paper (Patella and Mauriello, 1998) we extended to resistivity and induced polarization (IP) measurements the principles of probability tomography (Patella, 1997). In this work, we deal with the 3-D case for both types of data and propose a method for a combined tomography, always based on a probabilistic point of view. In the present formulation we start from the tensorial analysis of geoelectric data (Bibby, 1986), now extended to the IP case. In fact, from the apparent resistivity or chargeability tensor it is possible to obtain tensor invariants, which are independent of the direction of the source field and well confined in the neighbourhood of the causative bodies. In particular we focus our attention on the trace tr(A) of the data apparent anomaly tensor. Implementing the mathematical backgrounds reported in the previous paper (Patella and Mauriello, 1998), we write the departure of the measured tensor trace from that calculated on the basis of a reference model as: