## 2 Materials and Methods
\[A_{z}=\frac{iP}{4\pi^{2}}\upmu_{0}C\int\limits_{-\infty}^{\infty}\int\limits_{ -\infty}^{\infty}\frac{e^{-q_{1}|z+h|}e^{i(k_{x}x+k_{y}y)}k_{x}dk_{x}dk_{y}}{( k_{1}^{2}q_{2}+k_{2}^{2}q_{1})(q_{2}+q_{1})}, \tag{6}\]  
where \(C=k_{2}^{2}-k_{1}^{2}\). For a given soil at \(z<\)0 for \(A_{x}\) and \(A_{z}\) we have:  
\[A_{x}=\frac{\upmu_{0}P}{4\pi^{2}}\int\limits_{-\infty}^{\infty}\int\limits_{ -\infty}^{\infty}\frac{e^{-q_{1}}e^{-hq_{2}}}{(q_{2}+q_{1})}dk_{x}dk_{y}, \tag{7}\]\[A_{z}=iP\mu_{0}C\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}\frac{e ^{-a_{2}h}e^{\mu_{1z}}}{(k_{1}^{2}q_{2}+k_{2}^{2}q_{1})(q_{2}+q_{1})}dk_{x}dk_{y} \tag{8}\]  
With the integration of Equations (5)-(8), it is convenient that they are carried out using cylindrical coordinates \(r\), \(\varphi\), \(z\). The connection with Cartesian coordinates is well known [9]:  
\[x=r\cos\varphi;\ \ y=r\sin\varphi;\ \ k_{x}=\gamma\cos\psi;\ \ k_{y}=\gamma\sin\psi.\]  
In cylindrical coordinates, expressions (5)-(8) will take the form [4,6]:  
\[A_{x}=\frac{\mu_{0}P}{4\pi}\int\limits_{0}^{\infty}[e^{-q_{2}|z-h|}+\alpha_{r }e^{-q_{2}(z+h)}]J_{0}(\gamma r)\frac{\gamma d\zeta}{k_{z}},z>0; \tag{9}\]  
\[A_{x}=\frac{\mu_{0}P}{4\pi}\int\limits_{0}^{\infty}\frac{e^{-q_{2}h}e^{\mu_{1 }z}}{(q_{2}-q_{1})}J_{0}(\gamma r)\gamma d\zeta,z<0 \tag{10}\]  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]0  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]1  
To transform (11) and (12), we use the Jacobi-Unger decomposition [9]:  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]2  
where \(J_{m}(x)\) is a Bessel function of the first kind of the \(m\)-th order. Integrate (11) and (12) by \(\varphi\) taking into account (13), then expressions (11) and (12), taking into account (14) will take the form [9]:  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]3  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]4  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]5  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]6  
The conductivity of the bottom soil differs little from the conductivity of seawater due to the humidity of the soil compared to the sea water. Therefore, \(k_{2}^{2}\approx k_{1}^{2},\alpha_{1}\approx\frac{\alpha_{1}-\alpha_{2}}{ \sigma_{1}+\sigma_{2}}=0\) and \(A_{z}=0\), in this case, (9) will take the form [7]:  
\[\frac{\partial A_{x}}{\partial x}+\frac{\partial A_{z}}{\partial z}=i\omega \upmu_{0}\varepsilon_{0}\varepsilon_{2}^{\prime}U. \tag{3}\]7  
that is, the secondary potential of the spheroid is not affected by the lower boundary of the layer. Let us now consider the upper boundary of the seawater-air interface. To do this, in (9), (10), (15), and (16), it is necessary (Figure 1) to perform substitutions: \(h\to H-h\), \(z\to z-H\), \(k_{1}\) replace with \(k_{3}=\omega\sqrt{\varepsilon\mu_{0}}\)--the coefficient of the propagation of the plane homogeneous waves in the air; \(q_{1}\)--the coefficient of the propagation of the plane waves along the \(z\) axis in the air. Moreover, since \(|k_{2}|^{2}>>|k_{3}|^{2}\), then the Fresnel coefficient for the upper interface is \(\alpha_{r}\approx-1\).