Estimating the energy in current signals during electrical sounding: a novel approach

Abstract

Despite the rapidity in the use of electrical sounding/expanding probe technique in the study of hydrology, mineralogy, contamination, and other geophysically based studies over decades, it appears that our ability to identify the relationships between the energy loaded in direct currents injected into the ground between two electrodes at low polarizing frequency is not yet realized and hence the drive for this research. This study is insightfully undertaken to address this problem by establishing the novel links associated with the existing geo-resistivity theories and the two complementary energies, the voltage-driven energy called charging energy and the charge-driven energy called the discharging energy. This was achieved by sorting the resistivity values realized from electrical sounding technique into regimes (trends of resistivities representing certain geologic layers) and plotting each regime in a location against the signal current low polarizing frequency measured from the relationship between power line frequency and the ratio of potential to current separations. The two energies, which are determinable from the slopes of regressed resistivity-period plots and the novel relations established in this work, depend on the dynamic parameters βv and βq, which are respectively called the voltage geometric index of energy and charge geometric index of energy. These indices connect earth resistivity to energy and frequency/relaxation period. Calculating the energy for each sounding at its polarizing frequency, the complementary charging and discharging energies were traced to be dependent on conductivity/resistivity of the geological sequence/regimes. The established equations, graphs, and contour maps give insightful and expanded information on the dependence of energy loaded on injected currents into the ground. The charging energy, which is enhanced in arenaceous layers, has low conductivity and is believed to have high permittivity and low energy loss factor, which is not determined in this work while discharging energy in argillites is high as conductivity and energy loss factor increase at decreasing permittivity. In all cases, the currents and its loaded energy are in comparatively minute magnitudes.