## 2 Materials and Methods  
### Seismological Overview  
Our study area comprises both hydrothermal systems (such as Campi Flegrei and Ischia) and stratovolcanoes such as Vesuvius and Colima. Campi Flegrei and Ischia belong to the Phlegrean Volcanic District, southern Italy. In both cases, besides transient phenomena, the background signal is characterized by the presence of a persistent hydrothermal tremor, meteo-marine contribution, and anthropogenic noise [36; 37]. The origin of the tremor can be ascribed to the vibrations of the shallow hydrothermal system caused by the fluid motion. Many examples of this mechanism have been found everywhere, each characterized by specific periodicities, from Old Faithful Geyser, Yellowstone (USA) [38] to the Nisyros caldera (Greece), where researchers found oscillations on the order of 40-60 min related to gas instability [39]. Vesuvius is in a quiescent state whose dynamics is constantly monitored to detect eventual variations and/or precursors of eruption [7]. Colima, instead, is in an unrest phase, displaying a variety of eruption styles, from phreatic explosions and major block-lava extrusions, up to large explosive events [27]. The background seismic acquisition at Campi Flegrei is a complex mixture of hydrothermal tremor, meteo-marine microseism, anthropogenic noise, VT swarms and occasionally LP events, and regional earthquakes [9]. Some of these elements can also share the same frequency content, making the discrimination even more difficult. This is the case for the band lower than 1 Hz, in which we find the signature of both meteo-marine microseism and hydrothermal components [36] at specific frequencies of 0.3 Hz and 0.8 Hz, respectively. Instead, anthropogenic noise mainly affects the band above 1 Hz, specifically 4-5 Hz and 10-12 Hz, and it is characterized by the day/night alternation in the amplitude level [40]. The sustained hydrothermal tremor, mainly peaked at 1 Hz, is generated by the shallow geothermal aquifer nearby the Solfatara crater [36; 41]. Here, there is a consistent flux of hot fluids mixed with meteoric water coming from the boiling mud pools and the Pisciarelli fumaroles [42; 43]. Moreover, LP events appear to be the enhancement of the hydrothermal tremor under suitable conditions, sharing the same polarization patterns [15; 44]; they are associated with the vibrations of the shallow branched hydrothermal system, induced by well-sustained fluid circulation. On Ischia Island, the background seismic acquisition is composed of hydrothermal tremor, meteo-marine microseism, anthropogenic noise, and rare VT earthquakes. The hydrothermal tremor appears as a continuous whisper with the fundamental mode at 1 Hz and the first higher odd mode at 3 Hz [9; 25]. In this case, the identification is quite difficult because the higher frequency falls into the range of anthropogenic noise, 1-10 Hz. The hydrothermal whisper has been interpreted as self-sustained vibrations of the shallow system made of a network of channels, continuously excited by the circulating fluids. The latter are a mixture of sea and meteoric water, and the thermal fluids of the hydrothermal reservoir [9; 25]. Vesuvius is a stratovolcano located in the south of Italy, whose last destructive eruption occurred in 1944. Since then, it is in a quiescent state broken by a few volcanic/hydrothermal phenomena. In particular, the recorded transient events are, generally, VTs that can have deep (1-6 km) or shallow (few hundred meters a.s.l) localization, the former with magnitudes up to 3.6, the latter with much lower magnitudes (see, e.g., [45] and reference therein). Occasionally, the seismicity reveals the presence of LP and low-frequency (LF) events related to the dynamics of the deep hydrothermal reservoir [46]. The continuous and persistent background is, instead, dominated by microseism composed of Rayleigh waves, which have been interpreted as being due to an interference phenomenon between incident and reflected sea waves at the southern part of the Gulf of Naples [7].