INDUCED POLARIZATION RESPONSE OF A HORIZONTALLY MULTILAYERED EARTH WITH NO RESISTIVITY CONTRAST *

A bstract The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present‐day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole‐pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three‐layered earth and dipole‐dipole array for a four‐layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth‐of‐penetration”of a given array. For field induced polarization data that fits reasonably well to the no‐resistivity‐contrast model, this simple approach facilitates quantitative interpretation.