## 2 Analytical Methodology for the Calculation of Electric Field Strength
On the \"right\" part, the electrode is at a distance \(d_{r3}\) from the soil, provided the respective depth is ensured. The angle formed with the ground plane is \(\theta_{g}\). The following assumptions stand: 1. The electromagnetic field theory requires the continuity of the tangential electric field strength, as well as of the vertical current density, on the dividing surfaces. 2. The non-radial currents on the surfaces \(r=d_{r1}\), \(r=d_{r1}\), and \(r=d_{r3}\) are ignored. 3. The infinite layer of seawater-dam-soil has a constant active thickness \(L\), while in reality, it grows significantly, e.g., at short distances, it has a thickness of the order of meters, as much as the height of the electrode, while at long distances, it is tens or hundreds of meters (making it too conservative and unsuitable for the far-field). 4. The seawater resistivity \(\rho_{w}\), dam resistivity \(\rho_{d}\), and soil resistivity \(\rho_{s}\) are considered constant, while in reality, they change (especially that of the soil). If the most unfavourable values are taken (e.g., considering the ground resistivity as infinite), the most conservative result is obtained. 5. The materials of soil, dam, and seawater segments do not form uniform surfaces; their shape varies in different directions, as shown in Figure 1. However, it is a quite satisfactory approach. From the respective solution in cylindrical coordinates, as presented in detail in SS2.3 of [2], the radial components of the electric field strength in the ground \(E_{rs}\), in the dam \(E_{rd}\), in the water in general \(E_{rw}\), and in the water in the \"left\" \(E_{rw,J}\) or in the \"right\" part \(E_{rw,J}\) are derived, given the total electrode current \(I_{el}\), as follows:  
\[E_{rw,l}=E_{rs}=\frac{I_{el}}{r\times L\times\left(\frac{2\times\pi-\theta_{g} }{\rho_{w}}+\frac{\theta_{g}}{\rho_{s}}\right)}\ :r>max\{d_{r2},d_{r3}\}\ \text{or}\ d_{r3}<r<d_{r1} \tag{4}\]  
\[E_{rw}=\frac{\rho_{w}\times I_{el}}{2\times\pi\times r\times L}\ :r<min\{d_{r1},d_{r3}\}\ \text{or}\ d_{r2}<r<d_{r3} \tag{5}\]  
Figure 1: Simplified model regarding the positioning of an electrode on the shore or in near-shore sea, assuming a linear electrode, in cylindrical coordinates and incorporating a dam–soil surface (based on model “C” and Figure 6, as in [2]). \[E_{rw,r}=E_{rd}=\frac{I_{el}}{r\times L\times\left(\frac{2\times\pi-\theta_{g}}{ \rho_{d}}+\frac{\theta_{g}}{\rho_{w}}\right)}\ :d_{r1}<r<min\{d_{r2},d_{r3}\} \tag{6}\]  
\[E_{rs}=E_{rd}=\frac{I_{el}}{r\times L\times\left(\frac{2\times\pi-\theta_{g}}{ \rho_{d}}+\frac{\theta_{g}}{\rho_{s}}\right)}\ :max\{d_{r1},d_{r3}\}<r<d_{r2} \tag{7}\]  
For the far-field, a point curvature is considered (method \"B\" of [2], which is identical to \"A\" outside the dam). Practically unifying the considerations of CIGRE B4.61 675: 2017 [1], SS5.5.3.1 and Figure 5.35 and IEC TS 62344: 2013 [27], SS6.1 and Figure 5, the dam is added according to Figure 2, where an electrode is placed on the shore (or on the seabed, in shallow waters), at the centre of the coast. The bottom of the sea is considered to be inclined, with respect to the horizon, forming an angle \(\theta_{w}\). The electrode is at a distance \(d_{r1}\) from the dam, while the depth of the dam is \(t_{d}\). Therefore, the exterior radius of the dam is \(d_{r2}=d_{r1}+t_{d}\) as in the near-field calculation method. The ground has an angle \(\theta_{s}\), while the remainder is occupied by air. In addition to assumptions 1, 2, 4, the following are also made:  
* The soil does not form a wedge and the water is also not a uniform wedge, with its shape varying in different directions. Nonetheless, this approach is better than those of IEC TS 62344: 2013 and CIGRE B4.61 675: 2017. * The electrodes are situated in areas that are protected, such as a shore or a cave, while the exposed side of the sea is limited to an angle \(\varphi\) (rad) smaller than \(\pi\) rad. The analysis can be improved using the multiplier \(\pi/\varphi\) to the calculated distance of the remote earth.