Resistivity signal partition in layered media

Using a method given by Roy and Apparao (1971), the separate contributions to the measured resistivity sounding curve by the individual layers have been precisely determined for two-layer and three-layer (rho (sub 1) -rho (sub 2) -rho (sub 1) ) models. The substratum in the former, and the middle rho (sub 2) -layer in the latter, constitute the targets in the two models.For the two-layer model, a resistive substratum causes a positive anomaly by contributing higher than normal to the signal measured on the ground surface, while a conducting substratum gives rise to a 'negative' anomaly (resistivity low) by contributing less than its normal share. As the two-layer anomaly develops fully only at infinitely large spacings, it follows that an infinitely resistive basement contributes infinitely although no current flows through it, while a perfectly conducting basement contributes nothing even though it carries the entire current flow.For the three-layer model, the anomaly peak or trough (as the case may be) is formed at intermediate spacings and is contributed to both by the target and the region external to it. Both these regions contribute more than normal for resistive targets and less than normal for conductive targets. At the anomaly peak for high positive values of k = (rho (sub 2) - rho (sub 1) )/(rho (sub 2) + rho (sub 1) ), the contribution from the target dominates and accounts for the bulk of the resistivity high. At the anomaly trough observed for large negative values of k, on the other hand, the fall in contribution from the extra-target region becomes the main cause for the resistivity low.At each spacing and k, the sum of the contributions from the individual layers, of course, is exactly equal to the observed or measured value.