## 2 Methods  
### SPV and HT Data Collection and Imaging Procedure  
The sonic investigations exploit propagation in the material of elastic compression waves generated by a short elasto-mechanical impact on the surface to investigate the conditions in which the material is in its interior or to localize any inhomogeneities, voids, and defects in the investigated section [3; 4; 5; 6; 18].  
The SPV is dependent on the physical-mechanical characteristics of the investigated material. Internal defects, voids, and lower density result in lower velocity values, indicating a poor state of conservation. On the contrary, high velocities indicate good characteristics and high homogeneity of the material.  
The test involves the generation of elastic waves by using an instrumented impact hammer with a frequency range of 20 Hz-20 kHz through a punctual mechanical impulse, which is then read by an accelerometer. The value obtained in a sonic test is the time-of-flight (ToF), which is the time interval taken by the wave to pass through the material investigated. From the ToF and the length of the path investigated (L), the velocity of the wave (v) is estimated.  
The instrumentation used for this study is a Novasonic U5200 CSD of IMG Ultrasound SrI, consisting of a hammer with a load cell in the impact head, the source of the acoustic wave. The time-amplitude function of the force applied in the impact is recorded through a detection system directly connected to the hammer [3; 7].  
The sonic test is performed in indirect mode; see Figure 1a in which the hammer and the accelerometer are placed on the same face. SPV was performed according to a specific survey scheme on the same regular grid of points (Figure 1b), following a horizontal line. The mechanical impulse point is kept fixed, moving the accelerometer horizontally at progressively increasing distances from the hammer.  
By collecting measurements in a regular grid of points, SPV maps can be visualized to identify possible critical areas. These SPV maps represent velocity distribution. From the reference velocity of the investigated material in a good state of preservation, it is possible to consider the state of degradation of the frescoed masonry by comparing zones at different velocities. Since the SPV test involves acquiring large data, a management system for data collection and analysis on-site has been designed, adapting it to the specific survey campaign [3] (Figure 1c). Moreover, collected data were processed through GIS software for the graphical representation of the velocity distribution maps.  
Likewise, hygrometric tests (HT) of the area were performed punctually, following the SPV measurement scheme and data processing. HT was carried out using the instrument Protimeter MMS2 BLD8800 of Allemano Instruments, set on the \"pin mode\", to measure the surface moisture of the painting layer. The instrument measures the moisture content in WME% in non-conductive solid materials [19]. HT maps were generated by imaging the punctual values collected to highlight moisture distribution in the frescoed masonry. The environment measurements were conducted in the study area, with an indoor temperature of 7-12 \({}^{\circ}\)C and a relative humidity of 55-60%.  
SPV and HT investigations were performed on the frescoed walls of the apsidal conch of St. Panfilo Church, selecting four areas (panels A, B, D, and E), widely described in [20].