Further Advances In Prospecting By Electric Transients

EXPLANATIONS of the basic procedure for making earth-conductivity studies by the Eltran method have already appeared in several places.1,2,3 In its essentials, this method consists of applying step functions of voltage to one pair of earth grounds and measuring the transient potential resulting at a separate pair of ground points. As previously pointed out,4 the transient potential resulting from a suddenly applied steady voltage is the indicial transfer function of Carson,5 which has been extensively studied in network theory. [ ] The discussion here, with one special exception, will ignore the problem of how the physical configuration of the earth affects the transient response voltage; it appears that this phase of the problem has been solved in only a few special cases having any direct bearing on the prospecting problem. Entirely distinct from the potential theory aspect of the conductivity problem is the interesting material that can be had from studying the well-known network relations between cause and effect in linear circuits, and thus deducing criteria for the application of the several experimental methods available. To do this, only one assumption need be made about the nature of the earth. The earth is to be considered a linear conductor within the tolerance of ordinary measurements. The discussion will be restricted to collinear electrode configuration like that of Fig. I, since this is the only type of spread practical for use with driving currents that vary with time. Here one pair of grounds carries the driving current, and in line with these and external to them is a [ ] pair of potential probes. The problem will be to consider the relation between the different voltages appearing between the potential circuit terminals when various types of driving voltage sources are inserted in the current circuit. Suppose that the grounding points G1 and G2 make good contact with the earth, and that a battery of sufficient voltage to produce one ampere of direct current is introduced into the current circuit by the closing of a switch. The potential transient response to such a voltage can be measured by taking an oscillogram at the potential circuit terminals, giving the time function that has been called A(t).4 This time function has been solved for analytically in the case of a homogeneous earth,6,7 and the