PSI - Issue 44

Caprino Amedeo et al. / Procedia Structural Integrity 44 (2023) 1578–1585 A. Caprino et al./ Structural Integrity Procedia 00 (2022) 000 – 000

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• Analysis of interferometric displacement data; • Comparison of interferometric displacement rate with environmental parameters.

The first step involves the interferometric process that enables to identify MP from SLC (Single – Look-Complex) satellite images through the PSInSAR technique. Once MP are retrieved, the analysis of satellite data begins by examining the mean satellite’s line -of-sight (LOS) displacement velocity, expressed in mm/year, of the AOI (Area Of Interest). Due to the high number of MP, the irregular pointwise distribution is converted into a continuous map through the spatial interpolation method IDW (Inverse-Distance-Weighting) approach (Lu and Wong, 2008; Shepard, 1968). As the displacements are expressed along the LOS, expressions (1) and (2) are employed to convert LOS measurements into vertical and horizontal displacements: = ( , ) ⁄ −( , ⁄ ) (ℎ ) ⁄ −(ℎ ⁄ ) (1) ℎ = ( , ℎ ⁄ )− ( , ℎ ⁄ ) ( ℎ ⁄ ) − ( ℎ ⁄ ) (2) where V LOS, desc and V LOS, asc are the mean LOS displacement velocity respectively for the descending and the ascending orbit, while h and e are the horizontal and vertical directional cosines of the respective orbit (Floris et al., 2019). After the urban scale evaluation, a deeper analysis of displacement relative to Scrovegni Chapel is retrieved by selecting MP located on the Chapel itself and its closest surroundings. Later, displacement time series of the same MP are compared with environmental parameters collected by both the monitoring system installed on the monument and a meteorological station in the city centre of Padova. MP time series are resampled to fill the existing gaps in the satellite acquisitions and to achieve a weekly estimation of LOS displacement through a linear regression. The comparison between LOS displacement and environmental parameters is carried out using the Pearson correlation coefficient r xy (Hair et al., 2014; Lee Rodgers and Nicewander, 1988), defined by: (3): = ( , ) (3) where x and y are respectively the resampled displacement time series of a MP and one of the environmental parameters, while σ x and σ y are the standard deviation of the two analyzed parameters. 2.3. Data sources The analysis of Scrovegni Chapel is performed through the combination of both satellite and in situ data. The satellite interferometric assessment is developed through two 10-year-long CSK stocks of SLC images, deriving from ascending and descending satellite acquisitions described in Table 1. The SLC images are processed through PSInSAR technique by means of SAR data processing software SARscape (sarmap, 2022), available under ENVI platform (ENVI, 2004) provided by HARRIS Geospatial Solutions. During the processing phase, a coherence threshold is set to select the best MP possible for following analysis of the Chapel.

Table 1. CSK datasets ’ parameters

Acquisition mode

Revisiting time

Incidence angle

Monitoring period 24/03/2012 – 30/12/2021 17/04/2012 – 06/12/2021

Satellite images

Reference date

Coherence threshold

Orbit

Satellite

139

16/02/2016

0.75

Ascending

26.86°

Stripmap (3 m resolution)

COSMO SkyMed

16 days

156

21/10/2016

0.70

Descending

28.86°

The satellite data are compared with in situ environmental data deriving from the monitoring system installed for assessing the monument’s health condition: data from two thermocouples measuring temperature and humidity, inside and outside the Chapel, are analyzed. The sensors provide hourly acquisitions, starting from 21/10/2013 with good regularity and only few missing data; their main characteristics are summarized in Table 2.