Self-potential (SP) soil monitoring tool by numbers and vectors characteristic
Authors: Di Fiore Vincenzo , Bianco Francesca , Cavuoto Giuseppe , Milano Girolamo , Pelosi Nicola , Punzo Michele , Tarallo Daniela , Tizzani Pietro , Iavarone Michele , Scotto di Vettimo Paolo , Di Gregorio Costantino 
Published: March 2020

&lt;p&gt;This paper attempts to provide a contribute to electric field monitoring on soil by Self-potential (SP) survey utilizing matrix determinant and eigenvalues. SP is connected to the electrical conductivity of soil that is an indirect measurement and correlates very well with several physical and chemical properties. The purpose of this method is to map the electrical potential to reveal one or several polarization mechanisms at play in the ground. In some cases, the self-potential signals are monitored with an electrodes network which provides the possibility to discriminate between various sources.&lt;/p&gt;&lt;p&gt;Our study provides synthetic and experiment cases that carried out a semi-quantitative method to estimate the variation of the electric field vector in the soil starting from the measurement of the SP. The experimental case is referred to a site located in the Campania Region in southern Italy. SP measurements can be performed by array dipoles oriented N-S, E-W and vertical direction. In this way, we can define the contribution of the electric field in both time and spatial domain. Now, if we denote with V(t) the potential difference between two electrodes, for each dipole, we will have 3 values&amp;#160; V&lt;sub&gt;x&lt;/sub&gt;(t&lt;sub&gt;n&lt;/sub&gt;), V&lt;sub&gt;y&lt;/sub&gt;(t&lt;sub&gt;n&lt;/sub&gt;) and V&lt;sub&gt;z&lt;/sub&gt;(t&lt;sub&gt;n&lt;/sub&gt;) relative to the dipoles in the three directions. Assuming that the electric currents associated with the potentials are continuous or in any case at very low frequency, we can with good approximation assume that the resulting electric field associated with such currents is conservative. Remembering that in the case of a conservative field the electric field vector, we can be expressed as a gradient of the scalar potential V. The SP data were obtained using an Arduino acquisition system with internal voltmeter impedance of 10 MOhm and resolution of 0.1 mV. In order to provide reliable SP measurements, the impedance of the voltmeter needs to be substantially higher than the impedance of the soil between the electrodes because of the small bias current used to measure the voltage. The electric potentials were measured between each electrode and a reference electrode was connected by ground. The electrode consisted of 8 electrodes spaced 1m and arranged in a cross array which form 6 dipoles. The cross array was orientated in N-S and E-W direction.&lt;/p&gt;&lt;p&gt;Because the SP depend on the electrical conductivity of the soil and therefore on the sources and the medium, any variation of the chemical-physical soil variation implies a variation of the SP. We calculated the determinant and the eigenvalues of the matrix whose columns consist of the components of the measured electric field and therefore, by such parameters it was possible to observe the variations of the electric field in the time domain.&amp;#160;&lt;/p&gt;