Model for high-frequency Strombolian tremor inferred by wavefield decomposition andreconstruction of asymptotic dynamics

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.