*3.2. Geodetic Survey*

The reference frame is a geodetic network with 10 concrete pillars that surround the 15 check points. Pillars and target points (Figure 2) were set up in 2017. Each target point consists of one Leica 360 reflector (RFL) and one standard target sphere (Ø145 mm) which are rigidly mounted and firmly attached to the rock.

Since their installation had to be undertaken by abseiling, their verticality cannot be taken for granted. The determination of their attitude, which is crucial to transfer coordinates between the center for distances and the center for images, was obtained by photogrammetric methods. Figure 3 shows the photogrammetric data acquisition followed to obtain the vector and thus their attitude between centers.

So far, two geodetic campaigns have been carried out by using a sub-millimetric EDM Kern ME5000 Mekometer (ME5000) [25,26]. For each distance measurement, the meteorological parameters were measured and double-checked by using a traditional Thies Clima Assmann-Type psychrometer (±0.2 K) and a Thommen 3B4.01.1 aneroid barometer (±0.3 hPa) along with a network of 10 Testo 176P1 data-loggers. All the meteorological sensors were previously calibrated at the Universitat Politècnica de Valencia (UPV) calibration laboratory.

Prior to the EDM adjustment, the following corrections were applied: refraction correction [27–29], EDM frequency drift correction and geometric correction [25]. Once these corrections were applied and their corresponding errors computed in order to contribute to the stochastic model, the resulting slope distances were 3D adjusted in the local coordinate system CP2017 (x,y,z) in two steps. In the first step, only distances between pillars were adjusted to provide a solution for the frame. In the second step, distances to check points are included in order to obtain their 3D coordinates. The applied method not only provides coordinates with an overall accuracy of 0.5–1 mm for pillars and 1–3 mm for check points, respectively, but also allows us to monitor the possible displacement of pillars (see Table 1). Finally, the EDM coordinates and their precisions were also converted into geodetic coordinates with ellipsoidal height (ϕ,λ,h) and TM30 with orthometric height (E,N,H) [2].

As it can be seen in Table 2, the differences between the CRP and the EDM coordinates that were obtained in November 2019 are in the range of 1 to 3 cm, which are the expected values and demonstrates that the sub-millimetric EDM-based coordinates are consistent with the CRP-based 3D numeric model that is used as ground truth to validate the accuracy of the CRP survey.
