Very-Long-Period Volcanic Tremor at Stromboli, Italy

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1 Bulletin of the Seismological Society of America, Vol. 95, No. 3, pp , June 2005, doi: / Very-Long-Period Volcanic Tremor at Stromboli, Italy by S. De Martino, M. Falanga, R. Scarpa, and C. Godano Abstract We analyze a long time space series of Stromboli volcanic tremors. A very-low-frequency content in the range of Hz has been found by using spectral analysis and independent component analysis. Independent component analysis is an entropy-based technique. We observe the occurrence of a component having a period of 30 sec. Polarization analysis shows that the wave field comes mainly from the crater area, well evidenced by seismometers located around the summit ring, whereas the radiation becomes increasingly scattered at stations located around the base of this volcano. Based on its apparent velocity, the 30-sec component appears to be a slow wave, related to inhomogeneities of the source and/or gas-pressure fluctuations inside the shallow plumbing system. Introduction Stromboli is one of the most active volcanoes in the world, characterized by persistent explosive activity superimposed on a background volcanic tremor. During recent years, Strombolian events, particularly at high frequencies ( 0.5 Hz), have been studied by different authors (Del Pezzo et al., 1992; Chouet et al., 1997; Saccorotti and Del Pezzo, 2000; Acernese et al., 2003). Many results have been extracted concerning spectral features, polarization analysis, location, and modeling of the source, leading to the general agreement that tremor and explosions seem to be generated by the same dynamic source process; namely, the source of tremor and explosions at high frequency seems to be located at a shallow depth beneath the active craters. A preliminary study carried out by Neuberg et al. (1994) on broadband observations showed that Strombolian eruptions can produce signals with periods of 10 sec or longer. Moreover, very-long-period events have been revealed on other volcanoes in the world (Rowe et al. 1998; Ohminato et al., 1998). Since then, much attention has been devoted to the study of the broadband nature of Strombolian events and, recently, explosion quakes at low frequency ( Hz) have been analyzed, constraining the geometry and the dynamics of the source (Chouet et al., 1999, 2003); namely, the source associated with explosions (whose time length ranges from 5 to 15 sec) is localized below the same crater area previously recognized for the high-frequency seismograms. On the contrary, the characteristics of tremor at low frequency are still unknown, so the aim of our work is to study a long series of tremors in the range of Hz. This could give new insight into the fluid-dynamic mechanisms involved in magmatic transport (Hagerty et al., 2000). Data We have studied data collected during a field survey performed in 1997, when 21 three-component Guralp CMG- 40T broadband seismometers were deployed on the Stromboli volcano by the U.S. Geological Survey, the University of L Aquila, Osservatorio Vesuviano, and the National Seismic Survey. An accurate description of the network and instrumentation can be found in Chouet et al. (2003). The seismometers were deployed in three rings located around the summit area (top), medium elevation (middle), and the base of the volcano (bottom). In Figure 1, we show the location map of the seismic array. All the signals have been high-pass filtered with a corner frequency at 0.02 Hz to avoid any problem of instability of the broadband seismometers. We have performed spectral analysis by using a standard power spectrum, focusing our attention on the low-frequency content of the recorded signals. Figure 2a shows an example of a normalized power spectrum of ground motion for a three-component signal lasting 12 min. The spectral characteristics exhibit three distinct energy concentrations: the very-well-studied highfrequency region ( 0.5 Hz) where most of the energy is emitted (Chouet et al., 1997); the band centered around a few seconds; and new features appearing at very long periods, characterized by a period of about 30 sec, hereafter referred to as VLP. To confirm this evidence and to show that the result is not affected by the choice of the single station, we have constructed a stacking of power spectra at top sensors, having high signal-to-noise ratios. In Figure 2a, the vertical component at T1 exhibits an amplitude ratio between VLP signals and the high frequencies of about 1/2. Figures 2b and 2c, respectively, for the entire frequency 1186

2 Short Notes 1187 Figure 1. Location map of the 21 threecomponent broadband seismometers located at different levels: top (T), middle (M), and bottom (B). The experiment was performed in September Contour lines represent 200-m contour intervals. The inset shows the location of Stromboli in the Tyrrhenian Sea (TS) in relation to Italy, Sicily (SI), Sardegna (SA), and Corsica (CO). range and for the VLP band, show the stacking of all the top stations, for vertical, radial, and transverse components still normalizing the maximum value to 1. We note that the amplitude ratio for the stacked vertical components exhibits the same 2:1 relationship as for the single-station spectrum (T1) shown in Figure 2a. This confirms that the energy portioning is not site specific but rather is a characteristic of the source. In addition, we can note that about 1/10 of the energy is emitted at VLP (Fig. 2b). For the first time, energy of volcanic tremor in this VLP range is observed at Stromboli. Although the existence of components with periods greater than 10 sec is quite common for transient signals related to explosion phenomena or formation of calderas (Rowe et al., 1998; Arciniega-Ceballos et al., 1999; Kumagai et al., 2001, 2003), only in a few other cases have researchers observed tremor at VLP frequencies, as in the Aso volcano in Japan (Dawson et al., 1998; Kawakatsu et al., 2000). Figure 2. (a) Normalized velocity power spectrum of the vertical component of ground motion recorded at station T1. (b) Normalized stacked spectra of radial (solid line), transverse (dashed line), and vertical (dotted grey line) components of ground motion at top stations. Each north south and east west component has been rotated with respect to the angle inferred from polarization analysis. (c) Normalized stacked spectra of radial (solid line), transverse (dashed line), and vertical (dotted grey line) components of ground motion at top stations in the low-frequency range. Once again, each north south and east west component has been rotated with respect to the angle inferred from polarization analysis. The presence of energy emitted in the VLP band is well evidenced.

3 1188 Short Notes Independent Component Analysis To upgrade our knowledge of the nature of the VLP tremor, we have applied a technique based on information theory, widely used in signal processing and in blind source separation: the independent component analysis (ICA) (Hyvärinen et al., 2001). Let us explain in brief the mathematical setting on which ICA is based. We can suppose to have m different recorded time series x. We hypothesize that the m time series are different linear combinations (mixtures) of n mutually statistically independent unknown signals s. The mixtures are, in general, different because of path, noise, instrumental transfer functions, etc. The mixing has to be linear; nothing is assumed with respect to the component signals, which can be linear or nonlinear. Formally, the combinational model is written as x As l, (1) where l incorporates the presence of an additive noise, which is often omitted in equation (1), because it can be considered as one of the component signals. In addition to the independence of the components, we assume that the number of available linear combinations m is at least as large as the number of independent signals n. Only one of the signals s i is allowed to have a Gaussian distribution, because it is impossible to separate two or more Gaussian distributions (Bell and Sejnowski, 1995; Karhunen, 1996). The ICA goal is to obtain a separating matrix W A 1, such that the vector y Wx (2) is an estimate y s of the original independent signals. Moreover, we hypothesize, as required by ICA, that the combinations are composed of signals propagating with the same velocity. We stress that the separation is achieved on the basis of statistical independence. Independence implies that the joint probability of two or many observation series can be factorized at any statistical order. This is more general than the simple noncorrelation, which implies factorization at the second order. Separation among the signals in this application is achieved on the basis of fourth-order statistical properties. By the central limit theorem, it is well known that the distribution of the superposition of many independent signals is more Gaussian than any of the single constituents. Thus, the extraction of independent components in the linear combinations is achieved maximizing the nongaussianity. Many indicators of nongaussianity exist; one of the most used is the negentropy function defined as follows (Hyvärinen et al., 2001): J(x) H(x ) H(x) (3) gauss where x gauss is a Gaussian random vector of the same covariance matrix C as x and H is the entropy, which can be evaluated as 1 m H(x gauss) log detc (1 log 2p). (4) 2 2 In the following, we shall use the fixed-point algorithm, namely FastICA (Hyvärinen et al., 2001). The FastICA learning rule finds a direction, i.e., a unit vector w such that the projection w T x maximizes the independence of the single estimated signal y. Estimating independence through negentropy by using the definition would require an estimate (possibly nonparametric) of probability density functions. Therefore, simpler approximations of negentropy are adopted. Independence is here measured by the approximation of the negentropy (3) given by T 2 J G(w) [E{G(w x)} E{G(m)}] (5) where w is an m-dimensional (weight) vector, x represents our combinations of signals, E{(w T x) 2 } 1, m is a standardized Gaussian random variable, and G is the approximating contrast function. Maximizing J G permits us to find one independent component or projection pursuit direction. Note, for example, that ICA is able to separate the normal modes of linearly coupled harmonic oscillators or linear combinations of nonlinear modes (Falanga, 2003; Ciaramella et al., 2004a, 2004b). Summarizing, the application of ICA requires stationarity; a hypothesis of statistical independence of basis signals; a number of linear combinations (i.e., recorded signals) greater than the number of independent components to be extracted (m n); and component signals that propagate with the same velocity. In our case, we suppose that seismograms are linear combinations of independent waves, whose weighted sums are determined by the medium between source and stations. The extraction of the time evolution of the independent basis waveforms corresponds to an objective criterion to separate the full spectral content into different, nonoverlapping frequency bands. This can have very important implications for the source of the volcanic tremor. The existence of separated modes, observed at Stromboli, could be caused by the superposition of the normal modes of a single resonator of some specific geometry (cylinder, crack, sphere, etc.) or by the superposition of many tremor sources, distributed within the volcanic edifice. In the latter case, the sources are not connected or linearly interacting. We have observed that VLP tremor, recorded in this experiment, remains stationary in windows lasting hours, allowing the applicability of the ICA method. ICA has been applied to windows of 6-min lengths. We have used the top and middle stations as recording points. The traces are aligned by using the phases of the VLP explosions in all three directions of motion. When time windows contain explosion

4 Short Notes 1189 quakes, ICA extracts an explosion waveform with a period of about 10 sec, that is associated with the explosion envelope, that is, its duration, in agreement with the recent results of Chouet et al. (1999, 2003). In Figure 3 we report the ICA-extracted components related to windows containing tremor at low frequency ( 0.5 Hz) in the vertical direction. As we can see, three components appear in the band sec. To reduce the contribution of some noise, the extracted independent signals have been denoised by using a nonlinear technique (Kostelich and Schreiber, 1993). This technique is based on the recognition of the eventual low-dimensional dynamics underlying the temporal series and on the projection of the signal in the opportune embedding space. This denoising technique is an algorithm essentially based on the single value decomposition (Abarbanel, 1995). When we apply ICA to tremor across the full-frequency range ( Hz) we are able to recognize three different components in three objectively separated frequency bands corresponding to the wave field at high frequency (above 0.5 Hz). Note that, at high frequency, tremor and explosions have the same independent components (Acernese et al., 2003; Falanga, 2003; Ciaramella et al., 2004a). By using the entire frequency band ( Hz), however, there is no way to separate the 30- to 42-sec components. This is the first indication that the very-lowfrequency contribution is caused by modes traveling with a different velocity with respect to the phases present at high frequencies. Polarization Analysis We study the polarization state of the wave field by first performing the particle-motion analysis and then applying the standard polarization filter by Kanasewich (1981). This is a well-known technique based on the diagonalization of the covariance matrix of the three components of the records. As a result we find that, investigating the full lowfrequency band ( Hz), tremor shows strong analogies with the explosions, namely the wave field points toward the crater area with a linear and radial polarization. In Figure 4 we show some results coming from polarization analysis. On the map we show the azimuthal distribution of the incoming directions of a volcanic-tremor sample lasting several minutes. It is related to all seismometers and it shows that the wave field in Hz comes from the crater region. Once again, we claim that the radial polarization, supported by a high-rectilinearity coefficient (RL), is strong at the top ring and less evident at the middle ring, and the scattering becomes predominant at the bottom. The stations on this level, in fact, show low RL coefficients and azimuth values spanning a large range of variation because of their low signal-to-noise ratio and for the larger contribution of the oceanic noise. A different interpretation of this result is the presence of a deeper source, already guessed by Chouet et al. (2003) for transient signals observed by the same seismic network. So we may also conclude that this very low mode Figure 3. Denoised components extracted by ICA in the range Hz in the vertical direction. The amplitudes are in nondimensional units.

5 1190 Short Notes Figure 4. Rose plots obtained by polarization analysis superimposed on a map of the seismic station locations. reproduces the same characteristics, in terms of polarization features, of the wide band. Once again, the distribution peak of the incoming waves, for example at T1 station, is in the range of 30 40, centered around 35 with respect to the North; moreover, the RL is higher then 0.7. However, as suggested by Hellweg (2003), polarization results should be carefully inspected for discriminating the wave types because of the complexity of the medium. Finally, we have estimated the apparent velocity of this component using a standard correlation technique. We obtain values of very low velocity on the order of 100 m/sec. This suggests that we are dealing with a subsonic slow wave originating in the crater area, confirming the indications we have deduced from the ICA. Conclusions A detailed study of very long tremor records, in the VLP band (2 50 sec), exhibits, in addition to the phases at the short periods, the presence of components peaked around 30 sec as illustrated in Figure 2b. The ICA-extracted time signals present similar waveforms (Fig. 3). We hypothesize that these three signals arise from a common source effect. The differences among them may be due to pressure fluctuations. For example, if we are looking at the growing of bubbles, the latter cannot always be generated at the same size. The existence of a low-frequency component in the volcanic tremor from a shallow source has been observed only in a few cases worldwide, as for example at Aso and Usu volcanoes in Japan (Kawakatsu et al., 2000; Yamamoto et al., 2002). The accurate analysis in the time space and frequency domain, performed by using linear and nonlinear techniques, does not show that these components are related to meteorological causes, as reported by Seidl et al. (1996) for the Kilauea volcano. These components seem to have the same properties as explosions in the VLP band, peaked at about 0.1 Hz. The recorded signals are characterized by a radial polarization with a high RL coefficient at top sensors near the active vents. Scattering becomes predominant toward bottom stations. From signal-attenuation and particle-motion analyses we can infer that the source is located at a shallow depth beneath the crater region, and it can be associated with a portion of the shallow plumbing system, indistinguishable from the source of the VLP transient signals associated with the explosions modeled by Chouet et al. (2003). The appearance of a slow wave having a subsonic apparent velocity suggests that we are dealing with a sort of a tube wave, such as the crack wave investigated by Ferrazzini and Aki (1987). However, this interpretation is open to discussion. In fact, the waves modeled by Ferrazzini and Aki are trapped at the surface of a thin, water-filled crack and they are not observable from the ground surface. We have planned to install a few borehole seismometers and strain meters to answer that problem and to improve the present monitoring system. For these waves, the Q of the resonator, corresponding to the spectral peak, is f Q 1, (6) Df indicating a low-impedance contrast and a higher viscosity of the gas fluid mixture. This evidence may exclude that these waves are trapped body waves bounded by a strongimpedance contrast as suggested by Aster et al. (2003) for transient VLP signals observed at Erebus volcano. In particular, we may suppose that this mode is a signature of the characteristics of superficial two-phase systems, may be a geometric feature (it might be related to a curvature of the source), and/or a local pressure variation produced by fluids inside the shallow plumbing system. The frequency distribution of higher modes also indicates a nonlinear source process. Possible sources of these oscillations have been postulated by Julian (1994) and Ida (1996). In particular, Ida (1996) suggested a model with a constant supply rate of fluids inside a cylinder conduit for a variety of almost periodic signals observed on volcanoes, based on tilt and volumetric strain changes. The evidence of a significant component of the volcanic tremor in this low-frequency range, where a nonnegligible part of the seismic energy is emitted, is a relevant observation made in this study. This observation is not trivial for understanding and modeling the source process associated with volcanic tremor. Our observations are, however, limited

6 Short Notes 1191 by the frequency band of the broadband seismometers and their constitutive principles which make tilt components from the horizontal movements unresolvable at very long periods (Wielandt and Forbriger, 1999). Our result further confirms the necessity of using high-sensitivity and widefrequency-band instruments to monitor and model eruptive phenomena. Acknowledgments We thank an anonymous referee and Charlotte Rowe for comments and suggestions. We thank Bernard Chouet, Marcello Martini, and Giuliano Milana for providing the high-quality data used in this work. References Abarbanel, H. D. I. (1995). Analysis of Observed Chaotic Data, Springer- Verlag, New York. Acernese, F., A. Ciaramella, S. De Martino, R. De Rosa, M. Falanga, and R. Tagliaferri (2003). Neural networks for blind-source separation of Stromboli explosion quakes, IEEE Trans. Neural Networks 14, no. 1, Arciniega-Ceballos, A., B. A. Chouet, and P. Dawson (1999). 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A preliminary survey of the broadband seismic wavefield at Puu Oo, the active vent of Kilauea volcano, Hawaii, Ann. Geofis. 39, Yamamoto, M., H. Kawakatsu, K. Yomogida, and J. Koyama (2002). Long period (12 sec) volcanic tremor observed at Usu 2000 eruption: seismological detection of a deep magma plumbing system, Geophys. Res. Lett. 29, no. 9, 1329, doi /2001GL Wielandt, E., and T. Forbriger (1999). Near-field seismic displacement and tilt associated with the explosive activity of Stromboli, Ann. Geofis. 42, Dipartimento di Fisica Università di Salerno Via S. Allende, Baronissi (SA), Italy demartino@sa.infn.it rosfal@sa.infn.it roberto.scarpa@sa.infn.it (S.D., M.F., R.S.)

7 1192 Short Notes INFM, sezione di Salerno Baronissi (SA), Italy (S.D., M.F., R.S.) Dipartimento di Scienze Ambientali II Università di Napoli Naples, Italy (C.G.) INFM, sezione di Napoli, gruppo coordinato II Università di Napoli Naples, Italy (C.G.) INFN, sezione di Napoli gruppo coordinato di Salerno Baronissi (SA), Italy (S.D., M.F.) Manuscript received 8 April 2004.