[1] We study the volcanic tremor time series recorded by a broadband three-component seismic network installed at Stromboli volcano during 1997. By using decomposition methods in both frequency and time domains, we prove that Strombolian tremor can be described as a linear combination of nonlinear signals in time domain. These ''components'' are similar to those obtained for explosion quakes, with the only difference being the amplitude enhancement. We characterize each of these nonlinear signals both in terms of their wavefield properties as well as dynamic systems. Moreover, we take into account the complex processes of magma flow and turbulent degassing, looking at time and amplitude modulation of tremor on a suitable scale. The distribution of tremor amplitudes is Gaussian while the intertimes between the maxima in a suitable scale are described by a Poisson clustered process. Starting from these analyses, a first approximate model for volcanic tremor field can be deduced. The recorded signals, i.e., the elastic vibrations at a point, can be described by a nonlinear equation which gives limit cycles (different observed ''nonlinear modes''). This equation is governed by a time-dependent threshold which represents the variability of bubble flux. We take into account some inelasticity in the medium perturbing the elastic potential with a Gaussian function on a suitable scale. It acts as a radiance function modulating the frequency of the limit cycle. This proposed model is able to reproduce waveform, Fourier spectrum, and phase space dimension of one of the extracted nonlinear wave packets.

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[1] Long continuous seismic data recorded at five broadband seismic stations during 2006 at Campi Flegrei caldera have been analyzed. Introducing a coarse-grained method, we evaluate the time evolution of amplitude and polarization of the seismic noise in the frequency band common to long-period events. The series are modulated on tidal time scales: the root-mean square is basically dominated by solar contribution, while the azimuth of the polarization vector shows lunar diurnal and semidiurnal constituents. In addition, we find that in the frequency band common to long-period events the azimuths are polarized toward a specific area, suggesting that these persistent oscillations can be induced by the activity of the shallow geothermal reservoir.Components: 6,271 words, 5 figures, 1 table.

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Abstract. We analyse tiltmeter time series recorded from April 2015 to March 2019 at three borehole instruments installed at Campi Flegrei caldera (Italy). We evaluate the crustal response in terms of ground tilting to external excitations of medium/long-period tidal constituents by applying a polarization analysis. The azimuths of the tilt vectors show well-defined polarization directions and the ground tilting planes oscillate with the periodicity of the corresponding tidal constituents. For two of the three tiltmeters, the average ground oscillation pattern related to the monthly Mm and fortnightly Mf constituents show seasonal variations, which can be ascribed to rainfall-induced tilting. In addition, for the same two instruments, a clear seasonal amplitude modulation of the diurnal S1 constituent appears in the time series, revealing the occurrence of site thermoelastic effects. The results indicate that the tidal tilting is mainly controlled by the local stress field distribution and rheology; in addition, seasonal exogenous factors like rainfalls play a role in modulating the ground deformation.