## 1 Introduction  
Seismic noise consists of persistent vibrations of the ground generated by a variety of sources: oceanic loading, atmospheric phenomena, and human and environmental activities [1]. Meteo-marine microseism, caused by wind or ocean waves, is particularly energetic near the coast [2, 3, 4]. This microseism, related to the interaction between ocean and crust, is generally characterized by frequencies below 1 Hz [5]. The phenomenon is well-documented in the literature [6]: for example, in the Gulf of Pozzuoli (Italy), it is mainly concentrated in the band 0.1-0.5 Hz and its amplitude depends on the sea/weather condition [4, 7, 8, 9]. In cities, seismic noise, also known as ambient or cultural noise, is due to several processes, such as traffic, flights, trains, industries, etc. [2]. It is generally characterized by shallow propagation and spectral content in the frequency band 1-10 Hz. Another important characteristic is that it shows some specific periodicities: daily changes (night/day alternation) and weekly variation (working days vs. weekends), with a lowering level during holidays (see, e.g., [5]). Due to the persistent nature of seismic noise, continuous recordings acquired by seismometers are affected by this background, which can mask signals such as earthquakes;thus, a general task in Earth science is the extraction of buried relevant waveforms (see, e.g., [10, 11]). The problem is particularly complex in volcanic environments because of the presence of both transient and sustained signals generated by different sources that have a pure volcanic origin or are related to external forcing. Much interest is generally devoted to transients, such as volcano-tectonic earthquakes (VT), long-period (LP) and very-long-period (VLP) events, and explosion quakes, but significant information on the volcanic source is also provided by the investigation of persistent signals such as volcanic and/or hydrothermal tremor. However, both volcanic transients and persistent tremors are very often masked by microseisms and ambient noise, especially when recorded in densely populated areas [2, 12]. The interest in volcanic or hydrothermal tremor comes from the evidence that it represents the seismic signature of magmatic and/or hydrothermal fluids flowing through volcanic structures [13]. Its detection becomes difficult when it is overcome by continuous explosion quakes [14] or by LP swarms, as in the cases of the Deception (Antarctica), Arenal (Costa Rica), and Campi Flegrei (Italy) volcanoes [15, 16, 17]. Often, tremor shares common features with explosion quakes or LP events in both the time and frequency domains, revealing a common mechanism that could explain their generation [15]. The tremor source location can provide indications on the fluid movement, but it is very difficult because of the absence of a clear onset [13], which does not allow the application of standard techniques based on the arrival picking. Tremors are located superficially (<5 km) and observed in several structures such as eruptive craters and conduits [18], gas slug bursts at surface vents [14, 19, 20], lava lakes [21, 22], lava flows [23], shallow dikes [24], and magma-water aquifer interfaces, or due to the coupling between hydrothermal fluid-flow and solid structures [15, 25]. Besides the adoption of well-consolidated methodologies based on the seismological analysis of the waveforms [26, 27, 28], the characterization of typical events occurring on volcanoes, in these last years, has been also performed by using the recent machine learning (ML) techniques, such as artificial neural networks (ANN), multi-layer perceptrons (MLP) [29, 30], convolutional neural networks (CNN) [31], etc. For a review, please consider [32]. These techniques have been applied to obtain detection and classification of transient signals both of tectonic and volcanic origin, such as VT earthquakes, LP events, explosion quakes, etc., from background noise.