## 2 Materials and Methods  
When an object enters the field of spreading currents of the transmitting EA, the conductivity of which differs from the conductivity of the environment, the primary field will be distorted. For an infinite homogeneous space, an exact solution to the secondary field of a conducting elongated spheroid at a direct current is known, as is the decomposition of this solution into a Taylor series with the analytical continuation of the first dipole term of this series into the frequency domain [1]. The solution to the problem of a non-conducting elongated spheroid is reduced to replacing the dipole moment with an equivalent dipole, which can be obtained from the known exact solution of a non-conducting elongated spheroid at a direct current [6]. Let the spheroid move at a distance \(h\) from the bottom parallel to the boundaries of the layer depth \(H\). The transmitting and receiving EA are located at the bottom at right angles (Figure 1). In this case, the secondary field of the spheroid can be represented as a sum of the field equivalent to the horizontal and vertical dipoles relative to the boundaries of the layer [4]. Figure 1: The layout of the electrode antennas and the spheroid in the layer. The determination of the horizontal electric dipole field in the Cartesian coordinate system (Figure 1) is determined by two components of the vector potential \(A_{x}\) and \(A\)--satisfying inhomogeneous and homogeneous Helmholtz levels [3,4]:  
\[ \begin{array}{l}\Delta A_{x}+k_{2}^{2}A_{x}=-\upmu_{0}j_{x},\\ \Delta A_{z}+k_{2}^{2}A_{z}=0,\end{array}  \tag{1}\]  
where \(\Delta\) is the Laplace differential operator in the Cartesian coordinate system; \(j_{x}\) is the density of the equivalent current of the secondary field of the spheroid. The potential of the electric field \(U\) is determined by the known Lorentz calibration condition for the harmonic field [3,4]:  
\[\mathrm{div}\overset{\rightarrow}{A}-i\omega\upmu_{0}\varepsilon_{0} \varepsilon_{2}^{\prime}U=0, \tag{2}\]  
where \(\mathrm{div}\overset{\rightarrow}{A}\) is the divergence of the vector potential in the Cartesian coordinate system; \(\upmu_{0}=4\pi\cdot 10^{-7}\) Gn/m is the magnetic constant; \(\upmu_{2}=1\) is the relative magnetic permeability of seawater; \(\varepsilon_{0}=\frac{1}{36\pi}\cdot 10^{-9}\) F/m is the electric constant; \(\varepsilon_{2}^{\prime}=\varepsilon_{2}-i\frac{60\lambda\sigma}{\varepsilon_ {0}}\) is the complex permittivity of seawater; \(\varepsilon_{2}\) is the relative permittivity of water; \(\lambda\) is the wavelength of electromagnetic radiation; \(\sigma\) is the specific electrical conductivity of seawater. Taking into account (1) and (2), Equation (3) will take the form:  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]  
Equation (3) satisfies the boundary conditions [4,7]:  
\[\sigma_{1}\frac{\partial U_{1}}{\partial z}=\sigma_{2}\frac{\partial U_{2}}{ \partial z}\bigg{|}_{z=0};\quad\quad U_{1}=\left.U_{2}\right|_{z=0}, \tag{4}\]  
where \(U_{2}\) is the potential of the secondary field in seawater; \(U_{1}\) is the potential of the secondary field in the soil; the interface is a smooth plane whose equation is \(Z=0\), \(\sigma_{1}\); \(\sigma_{2}\) are the specific conductivities of the bottom soil and seawater. The solution to the system of Equation (1) for \(A_{x}\) and \(A\) with boundary conditions (3) has the form [7,8]:  
\[A_{x}=\frac{\upmu_{0}P}{8\pi^{2}}\int\limits_{-\infty}^{\infty}\int\limits_{- \infty}^{\infty}\left[e^{-q_{2}|h-z|}+\alpha_{r}e^{-q_{2}|z|+h|}\right]e^{i(k_ {x}x+k_{yy})}\frac{dk_{x}dk_{y}}{q_{2}}, \tag{5}\]  
where \(\alpha_{r}=\frac{q_{1}k_{1}^{2}-q_{1}k_{2}^{2}}{q_{2}k_{1}^{2}-q_{1}k_{2}^{2}}\) is the Fresnel reflection coefficient for homogeneous and inhomogeneous plane waves perpendicular to the plane of incidence; \(q_{1}=\sqrt{\gamma^{2}-k_{1}^{2}},q_{2}=\sqrt{\gamma^{2}-k_{2}^{2}}\) are coefficients of the propagation of plane waves along the \(z\) axis.