*4.1. Estimation Based on "In Situ" Field Measurements*

Due to the time variation of the magnetic field rms value, tracing the transversal and longitudinal values is difficult to achieve using only one instrument. The objective of this paper is to obtain an estimation of the magnetic field at each point of a rectangular mesh beneath the OPL at a particular moment of time. This estimation is realized using the values of B obtained with the two instruments MILTS and MISM and then applying a correction to the values obtained at successive moments in time. In this way, all the values for B in each profile are estimated at the same moment of time as if simultaneous measurements were made in 61 points for the transversal profile and 95 points for the longitudinal profile.

Figure 8 presents three estimations of B for the transversal profile near the pillar at moments tTi, tTj and tTk (11 a.m., 12 a.m. and 1 p.m.), determined from the successive measurements recorded in PT, performed with MISM and estimated according to relation (3). In Figure 8, the data from PT (represented in Figure 3) are also included in order to observe the possibilities of the proposed method.

**Figure 8.** Transversal profiles near the pillar estimated at times tTi, tTj and tTk, compared to the results from spot measurements.

Using the same method, estimations for the longitudinal profile were also made at the moments tLi, tLj and tLk (11 a.m., 12 a.m. and 1 p.m.). The estimated longitudinal profiles, as well as the original profile, are presented in Figure 9. As may be seen, the original large variations of B from Figure 4 are corrected, and the estimation results present a rather smooth variation.

In order to verify the proposed estimation method, similar estimations were made for the transversal profile PTM (corresponding to z = d/2) for the chosen moments tTMi, tTMj and tTMk (11 a.m., 12 a.m. and 1 p.m.). The resulting plots, as well as the original profile PTM, are presented in Figure 10.

**Figure 9.** Estimated longitudinal profiles at times tLi, tLj and tLk compared to the results from spot measurements.

**Figure 10.** Transversal profiles at the mid-distance between the pillars, estimated at the moments tTMi, tTMj and tTMk, compared with the experimental profile.

As mentioned before, the transversal profile PTM was traced for z = d/2, but similar transversal profiles can be determined experimentally and then estimated according to (3) for any value z ∈ [0, d].

Figure 11 presents two plots that estimate the transversal profile for B in z = d/2 at the same moment tk (in the considered case at 1 p.m.), using two separate sets of experimental data, namely:


**Figure 11.** Estimated transversal profile at the mid-distance between two towers, based on two different sets of data correlated with the continuous recording of BLTS.

Comparing the two plots in Figure 11, a relative deviation of under 9% is observed in the conditions in which the range of the recorded values for B is from 724 to 1375 nT, and other factors, such as instrument error (under 5%), terrain oscillations, small errors in positioning the instrument MISM, etc., affect the measured values of B.

In a similar manner, the transversal profiles for any value of z can be obtained using one transversal profile (PT) measured at a fixed point z0, the longitudinal profile PL and the time recordings for B conducted with MILTS.

Using this method for estimating the magnetic field in transversal direction for any z∈ [0, d], maps of the magnetic field in a rectangular region beneath the OPL can be obtained for any of the 17,530 moments of time for which recordings of B performed with MILTS exist (Table 1).

Figures 12 and 13 represent a map of |B| in the region z∈ [0, d], x∈ [−xmax, xmax], with d = 282 m, xmax = 30 m, in two cases: for a time tX when the estimated value of B is equal to the maximum value obtained in the long-time survey, and for a time ty when the estimated value of B is equal to the minimum recorded value of B. These maps can be obtained using only one longitudinal and one transversal profile, resulting in a significant reduction of the number of spot measurements.

**Figure 12.** Magnetic flux density map for the maximum recorded value of B.

**Figure 13.** Magnetic flux density map for the minimum recorded value of B.
