Detectability of Intermediate conductive and resistive layers by time‐domain electromagnetic sounding

Abstract

An analysis in the time domain has been made of the detectability of an intermediate layer in a three‐layer earth model by the horizontal coplanar loops (system I) and loop‐wire element (system V) electromagnetic (EM) sounding systems for a train of half‐sinusoidal and square waveforms of alternating polarity. The studies involve conversion into the time domain by a Fourier series summation of the matched complex mutual coupling ratios, computed by the digital linear filter method, of the layered‐earth models. The three‐layer earth models considered here have the following resistivity distribution: [Formula: see text], [Formula: see text] for the conductive case, and [Formula: see text], [Formula: see text] for the resistive case (subscripts 1, 2, and 3 represent the first, second, and third layer in the three‐layer sequence; ρ is the resistivity). The intermediate‐layer thickness varies over a wide range. The responses of the three‐layer earth models have been compared with that of a homogeneous earth with the resistivity of the top layer in the three‐layer sequence. The measurement error is assumed to be of the order of 3 percent, and an rms difference of 10 percent between the responses for the three‐layer and the homogenous earth is defined as the detectability level. On the basis of this definition, it is observed that the horizontal coplanar loops system (system I) is better than the loop‐wire element system (system V) in detecting the thin intermediate layer, which may be either conductive or resistive. For a transmitter‐receiver separation (R) of 1000 m by square‐pulse excitation, a conductive intermediate layer as thin as 1/14 of the top layer can be detected by system I and as thin as 1/6 by system V. For the resistive intermediate layer, the corresponding thickness ratios are 0.6 for system I and 1.25 for system V. The detectability is lower in the case of half‐sinusoidal pulse excitation. Instead of normalizing the mutual coupling of the layered earth to the free‐space coupling, the detectability is enhanced markedly if the normalization is done to the coupling over a homogeneous ground. For system V, it is observed that an intermediate layer as thin as 1/100 in the conductive case and 1/4 in the resistive case of the top layer can be detected easily by this approach. Some direct comparisons between the time‐domain and the frequency‐domain results also are given.