# Transient Responses in Shallow Depth Electromagnetic Studies

- Authors
- Type
- Published Article
- Journal
- Izvestiya, Physics of the Solid Earth
- Publisher
- Pleiades Publishing
- Publication Date
- May 01, 2021
- Volume
- 57
- Issue
- 3
- Pages
- 425–437
- Identifiers
- DOI: 10.1134/S1069351321030022
- Source
- Springer Nature
- Keywords
- Disciplines
- License
- Yellow

## Abstract

Abstract—Current turn-off processes in ungrounded antennas used in shallow depth transient electromagnetic (TEM) investigation have been studied theoretically and experimentally. Single-turn antennas in the form of a square loop laid on the Earth’s surface are analyzed as the systems with distributed electrical parameters. The theoretical calculations are based on the results following from two-wire transmission line (TWL) theory. Transient processes in loops with sizes ranging from 6 m × 6 m to 50 m × 50 m and TWLs with sizes 50 m × 1 m and 100 m × 1 m have been studied in the field experiments in the nanosecond and microsecond time range. It is shown that current turn-off ramps in TEM antennas develop in the same way as in the TWLs short-circuited at the output without losses and are described by time-descending step functions. The duration of steps is determined by the electromagnetic wave transit time along the antenna perimeter, and the amplitude of the steps decreases exponentially with the denominator depending on the resistance ratio of the damping input resistor and the input impedance of the antenna Z0. Based on the voltage and current turn-off waveforms, per-unit-length inductances and capacitances are calculated for copper wire antennas with wire cross-section 0.35–1.0 mm2. The input impedance Z0 reaches ~1000 Ω if the antennas’ and TWLs’ wires do not contact vegetation and soil and decreases to Z0 = 400–500 Ω for the antennas placed on the ground. The duration of the current turn-off ramp in the A × A (m × m) square antennas is at most Toff (ns) ≤ 150×A, which determines the depth of the dead zone of soundings \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H({\text{m}}) \leqslant 0.25\sqrt {\rho {\text{A}}} $$\end{document} where ρ (Ω m) is the effective resistivity of the near-surface layer with thickness H. Within this depth interval, layer-by-layer interpretation of transient responses is impossible; however, a robust estimate can be obtained for longitudinal conductance S = H/ρ. The transient responses measured by the TEM system in small antennas after final current turn-off t > Toff demonstrate inconsistency between the theory and the experiment. In antennas smaller than 25 m × 25 m, the induction effects with the intensity and duration depending on the wire thickness are observed. We present physical interpretation of these effects which are related to the relaxation of the induced currents within the open wire circuit. It shows that at the time the transmitter’s turn-off ramp, the decaying magnetic field induces a volume closed current vortex in a wire body, similarly to what takes place in local conductors (conducting medium). The relaxation time of these currents depends on the conductivity and cross-section area s (mm2) and is τCu ≈ (1.4–1.6)×s (µs) for copper wire. The induction effects in antenna wires can be reduced by using a special stranded wire (litz wire). In the case of the combined 12 m × 12 m to 25 m × 25 m receiver–transmitter antennas made of 127-core litz wire, the depth of the dead zone does not exceed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H({\text{m}}) \leqslant 1.5\sqrt {\rho {\text{A}}} $$\end{document}.