Revisiting the issue of contactless measurements in the resistance method: Mathematical simulation data

Background. The resistivity method of electromagnetic survey has a long-recognized problem associated with the need for reliable grounding of measuring electrodes, which is difficult or impossible in conditions of permafrost, rocky soils, snow cover, or artificial surfaces. Contactless measurements solve this problem and speed up the survey process. However, the theoretical justification for this approach is historically based on approximate methods rather than rigorous solutions.

Aim. To theoretically substantiate the technique of contactless measurements in the resistance method using rigorous forward solution of electrodynamic equations. The study aims to analyze the components of the electromagnetic field and determine the optimal conditions for the correct assessment of the specific electrical resistance (SER) of soil.

Materials and methods. The study is conducted using the mathematical simulation of two medium models: two-layer (air–conductive half-space) and three-layer (air–intermediate layer–conductive half-space). The simulation is performed for a low-altitude dipole-axis array at an AC frequency of 16 kHz. The field calculation is based on a rigorous solution to the system of electrodynamic equations. The amplitude of the total electric field strength Ex and the modulus of the reactive component Re Ex are analyzed.

Results. The standard approach using the amplitude of the total field E_x to calculate the apparent SER (ρ_a) at small spacings gives anomalously high values independent of ρ₂ due to the field effect of charges at the ends of the current dipole. In contrast, the calculation of ρa based on the reactive component Re Ex excludes this effect. For a two-layer model, an optimal spacing of 8—10 m was established to provide the best match between ρ_a and ρ₂. For a three-layer model, the high-SER layer is equivalent to an increase in the height of instrument lift, while the layer with low resistivity significantly complicates the interpretation.

Conclusion. An advanced approach to contactless measurements in the resistance method using the reactive component of the electric field is developed and substantiated. This approach increases the reliability of determining the specific electrical resistance of underlying rocks. The results of the study open up prospects for the development of effective equipment and methods for contactless electromagnetic survey applicable in complex grounding conditions.

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