### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[1] We propose a novel approach to analyze continuous seismic signal and separate the sources from background noise. A specific application to the seismicity recorded at Campi Flegrei Caldera during the 2006 ground uplift is presented. The fundamental objective is to improve the standard procedures of picking the emergent onset arrivals of the seismic signals, often buried in the high-level ambient noise, in order to obtain an appropriate catalogue for monitoring the activity of this densely populated volcanic area. This is particularly useful in order to estimate the release of the seismic energy and to put constraints on the source dynamics. An Independent Component Analysis based approach for the Blind Source Separation of convolutive mixtures is adopted to obtain a clear separation of Long Period events from the ambient noise. The approach presents good performance and it is suitable for real time implementation in seismic monitoring. Its application to the continuous seismic signal recorded at Campi Flegrei has allowed the extraction of high-quality waveforms, considerably improving the detection of low-energy events.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[2] A fundamental task in volcano seismology is the detection of the Long-Period (LP) signals and their discrimination from the ambient background noise. Indeed, the dynamical state of a volcano can be defined in terms of energetic release that is strictly related to the number of the recorded events. Moreover, the extraction of enhanced LP signals from the background noise can improve all those studies based on the waveform analysis (i.e., signal classification, location, polarization and cross-correlation). Finally, other interesting information could arise from the analysis of the seismic noise itself that sometimes hides volcanic tremor, a continuous and persistent signal generated by the volcanic source, considered a precursor of eruptions [*Konstantinou and Schlindwein*, 2002].

[3] It is of great relevance, at this point, to adopt an approach that permits a good separation between LPs, volcanic tremor and ambient noise, thus allowing the analysis of all these signals produced by different sources.

[4] In the recent years, many techniques have been proposed for the automatic detection of earthquakes, LP events and volcanic tremor, such as STA/LTA based algorithms [*Evans and Pitt*, 1995], Component Energy Comparison Method (CECM) [*Rouland et al.*, 2009], or analysis of waveform characteristics [*Kao et al.*, 2007] and cross-correlation [*Wech and Creager*, 2008] combined with envelope functions and spectral features used to design neural network for automatic signal classification [*Scarpetta et al.*, 2005].

[5] In seismological framework, seismic signals are thought as the convolution of a source function with path, site and the instrument response. Path effects depend on the medium properties between hypocenters and seismometers, while site effects are related to the local surface geology. Topography and reverberation from geological structures (such as the rim of a caldera or shallow faults) also affect the seismic recordings [*Lay and Wallace*, 1995]. Then primary goal is to perform an appropriate deconvolution of seismic traces to discriminate the signals generated by the volcanic/tectonic source mechanisms from other contributions.

[6] Blind Source Separation (BSS) consists of recovering signals from the observations recorded by several sensors, taking advantage from the statistical properties of the original sources, i.e., coherence, correlation/decorrelation, statistical independence.

[7] Independent Component Analysis (ICA) approaches have been proposed to achieve BSS in case the source signals are mutually statistically independent and mixed instantaneously with an unknown matrix [*Hyvärinen et al.*, 2001]. It has been fruitfully applied to many research fields such as volcanology [see, e.g., *Acernese et al.*, 2003; *Cabras et al.*, 2008; *De Lauro et al.*, 2008], oceanography [*Capuano et al.*, 2011]), acoustics and mechanical vibrations (for the application to musical instruments, see, e.g., *De Lauro et al.* [2007]).

[9] In this paper, we apply for the first time a specific ICA-based approach for the BSS of convolutive mixtures in frequency domain (CICA in the following) [*Ciaramella et al.*, 2006] to detect LP events of very low energy that are buried in background noise, without requiring a dense local network.

[10] This methodology is successfully applied to seismic signal continuously recorded during the entire month of October 2006 at Campi Flegrei (Italy), when a high rate of seismicity in uplift regime occurred. In particular, we focus on the climax (from 26 to 28), when the close occurrence of many LPs, clustered in time, make their detection very hard.

### 2. Blind Source Separation and ICA

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[11] In various real world applications we observe that the source signals have different time delays due to the finite propagation speed in the medium. In addition, time-delayed versions of the same source exist, due to multipath propagation typically caused by reverberations from some obstacles.

[12] In the convolutive mixture model, each element of the mixing matrix **A** in the model **x**(*t*) = **As**(*t*) is a *filter* instead of a scalar. For each convolutive mixture the data model is given by

Equation (1) is a FIR filter model, where each FIR filter is defined by the coefficients *a*_{ikj}. To invert the convolutive mixtures *x*_{i}(*t*), a set of similar FIR filters is typically used:

The output signals *y*_{1}(*t*), …, *y*_{n}(*t*) of the separating system are the estimates of the source signals *s*_{1}(*t*), …, *s*_{n}(*t*) at discrete time *t*. The *w*_{ikj}'s are the coefficients of the FIR filters of the separating system.

[13] In this paper, we propose to solve the problem cast in equation (1) relative to convolutive mixtures of seismic sources, by using the ICA-based approach [*Ciaramella and Tagliaferri*, 2003; *Ciaramella et al.*, 2006]. The main idea of that approach is moving to the frequency domain in order to transform the convolution into multiplication and to apply ICA methods, in complex domain, for instantaneous mixtures. In the frequency domain the data model of equation (1) becomes

where *X*_{i}(*ω*), *S*_{j}(*ω*) and *A*_{ij}(*ω*) are the Fourier transforms of *x*_{i}(*t*), *s*_{j}(*t*) and *a*_{ij}(*t*), respectively. Comparing equation (1) with equation (3), we note that the convolutive mixture problem is transformed into subproblems of instantaneous BSS/ICA models at each frequency.

[14] The transformation in the frequency domain is usually the Short Time Fourier Transform (STFT). Here, the observed mixtures can be broken up into frames (which usually overlap each other, to reduce artifacts at the boundary) and each frame is Fourier transformed. The complex result is added to a matrix of frequency bins and then each point (*X*_{i}(*ω*, *t*)) can be observed both in time and frequency. For each frequency bin, we have, therefore, *n* observations, to which apply the ICA models in complex domain.

[15] However, one of the problems with the Fourier-based approaches is the indeterminacy of scaling and permutation [*Hyvärinen et al.*, 2001]. Scaling indeterminacy means that the scaling in each frequency band can be different and this leads to spectral modifications of the original sources [*Murata et al.*, 2001]. Permutation indeterminacy is a more difficult problem. It is essential to keep the same permutation to avoid that the signal sources have mixed frequency content. To solve the permutation indeterminacy, *Ciaramella et al.* [2006] suggested to match similar estimations with an Assignment Problem (AP) (e.g., Hungarian algorithm) and by using a Kullback-Leibler (KL) divergence. The KL divergence is defined between two discrete *n*-dimensional probability density functions **p** = [*p*_{1} … *p*_{n}] and **q** = [*q*_{1} … *q*_{n}] as

[16] This divergence can be considered as a kind of distance between two probability densities, because it is always nonnegative, and zero if and only if the two distributions are equal. Good performance is obtained considering, as density, the normalized Power Spectrum Densities (PSD) of each signal. The same authors demonstrated that this approach presents good performances on synthetic and benchmark data also considering a global information to obtain the matching (i.e. Dynamic Programming algorithm).

[17] The computational complexity of the method is mainly based on the use of the STFT, on the solution of the ICA problem in complex domain and on the specific approach used for the permutation indeterminacy (for the details, please, refer to *Ciaramella et al.* [2006]). Briefly, STFT can be quickly accomplished by means of a Fast Fourier Transform; the adopted FastICA algorithm is based on a fixed-point algorithm that has a convergence at least quadratic, much faster than other approaches based on the linear convergence obtained by gradient methods. Finally, the permutation indeterminacy is solved by using the Hungarian approach that has a complexity of O(*n*^{3}). All these characteristics make CICA method computationally efficient.

### 3. Campi Flegrei Seismic Activity and Dataset

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[18] Campi Flegrei volcanic complex, located in a densely populated area in the West of Naples (Southern Italy) is a caldera originated by two large collapses occurred during the Campanian Ignimbrite (39 ka) and the Neapolitan Yellow Tuff (NYT; 15 ka) eruptions. The area is affected by a continuous, slow subsidence (bradyseism) interspersed with fast ground uplifts accompanied by seismicity [*Orsi et al.*, 1999]. The last uplift episode occurred in 2004–2006 and was characterized by the largest release of seismic energy ever observed since 1985 [*Saccorotti et al.*, 2007]. Particularly relevant was the observation of LP events in October 2006, that at the present constitute the most remarkable LP swarm ever recorded in the area. These signals are generated by fluid-rock interaction and, although they commonly occur in active volcanic/hydrothermal areas, they have never been observed at Campi Flegrei before July 2000 [*Bianco et al.*, 2004], therefore they attracted a great interest by the scientific community.

[19] The LP activity occurred for about 1 week and climaxed on days 26, 27 and 28, when about 300 events were counted in the seismic catalogue of *Saccorotti et al.* [2007], who applied a trigger coincidence criterion to data recorded at two seismic stations with the best signal-to-noise ratio (SNR). The catalogue is reported as distribution in Figure 1b. LP signals have emergent onsets and appear like spindle-shaped monochromatic oscillations; their spectra exhibit a main peak at frequency around 0.8 Hz attributed to a source effect [*Cusano et al.*, 2008].

[20] Data used for the present analysis were collected by four broadband three-component seismic stations (ASB2, AMS2, TAGG, BGNG; see Figure 1a) of the Campi Flegrei seismic monitoring network, managed by the “Istituto Nazionale di Geofisica e Vulcanologia-Osservatorio Vesuviano (INGV-OV)” (see for details *Saccorotti et al.* [2007]). Specifically, we analyze the seismic signal, continuously recorded for the entire month of October focusing the attention on the climax. The analyzed time series are the recordings of ground velocity (seismograms) along the three directions of motion (North–South, East–West and Vertical) for each station. An example of raw data is shown in Figures 1c–1e.

### 4. Results

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[21] CICA method tested on the seismic signal continuously recorded for the entire month of October has shown that the number of extracted LPs drastically reduces moving away the climax and no LP signals are detected about 1 week before it. Therefore, we show the results relative to the climax which is particularly interesting for the intense LP activity.

[22] We applied CICA considering separately 4 recordings (corresponding to 4 seismic stations) for each direction of ground motion. In Figure 2, we show the comparison between the standard ICA by means of FastICA algorithm [*Hyvärinen et al.*, 2001] and CICA. We can observe that in Figures 2a and 2b the separation of the sources from noise is not clearly obtained as confirmed by their PSDs that show overlapped frequency distributions (Figure 2c). In Figures 2d and 2e, we instead observe that the CICA approach permits to obtain a better result both in the time and frequency domains (Figure 2f). Indeed, from the frequency analysis we can discriminate two fundamental frequency bands, one associated with the LP seismic signals, typically peaked around 0.8 Hz, and another with a broader spectral content associated to the ambient noise [*Peterson*, 1993]. In particular, we can recognize the contribution of both the meteo-marine component (peak below 1 Hz) and the anthropogenic activity (peak at 1.5 Hz).

[23] The results demonstrate that the CICA technique returns two well separated time series thus allowing both reliable picking of the onset arrivals of LP events and further analysis of the remaining noise components.

[24] To obtain a catalogue of the LP events occurred during the three days of climax, we applied an automatic picking based on the comparison of short-term average amplitude (STA) and long-term average (LTA) along the signal to the enhanced time series extracted by the CICA. Reasonable values for LTA and STA are chosen equal to 80s and 0.8 s taking into account the typical frequency content of LPs. Whenever this ratio is greater than a fixed threshold a LP is identified. In Figure 3a a picking estimation example is shown.

[25] The results of the automatic picking procedure are shown in the histogram of Figure 3b. A total of 865 (±5% associated to false pickings, as confirmed by a visual random check of waveforms and spectra) LPs were detected in the time series obtained by CICA. This is a larger number compared to that of the seismic catalogue compiled by *Saccorotti et al.* [2007], who detected in the same period about 300 events. However, as shown by M. Falanga and S. Petrosino (Inferences on the source of long-period seismicity at Campi Flegrei from polarization analysis and reconstruction of the asymptotic dynamics, submitted to *Bulletin of Volcanology*, 2011), the results of a detailed polarization analysis indicate that during the climax of the LP swarm, in addition to the detected LPs classified by *Saccorotti et al.* [2007], a sustained activity consisting of very low-energy volcanic signals occurred too. These low-energetic signals have been enhanced by CICA thus likely increasing the number of picked events.

### 5. Conclusions and Future Remarks

- Top of page
- Abstract
- 1. Introduction
- 2. Blind Source Separation and ICA
- 3. Campi Flegrei Seismic Activity and Dataset
- 4. Results
- 5. Conclusions and Future Remarks
- Acknowledgments
- References

[26] In this paper, we propose a novel approach based on CICA algorithm to analyze continuous seismic signal. The present application regards the extraction of LP events at Campi Flegrei Caldera during the 2006 ground uplift episode.

[27] We perform several experiments comparing the CICA technique with other known in literature (standard and convolutive mixtures) and we observe that CICA permits to obtain optimal performances on the seismic data.

[28] One of the advantages is that the technique combines the data recorded at several seismic stations, thus enhancing the input signals, and correctly separates the different components. This feature is particularly important for the extraction of low-energy LPs that can be hardly discriminated in the background noise.

[29] Fine detection of LP events allows to compile a complete seismic catalogue and to better quantify the seismic energy release. Moreover, the extraction of the waveforms with improved SNR, obtained avoiding expensive installation of borehole seismometers, can be useful also for further studies such as precise locations, polarization analysis or waveform cross-correlation. Indeed, the extraction of cleaner waveforms via CICA allows a more accurate phase picking, thus reducing the uncertainties on the arrival times and consequently improving the source location. Moreover, in the case of swarms of Campi Flegrei in 2006, the cleaner waveforms permit to better identify clusters of similar events, whose stacking at each station further improve the location.

[30] Finally, CICA does not need a specific spacing configuration of the stations and the minimum number required is connected with the number of the source signals. In principle, for Campi Flegrei the extraction of a LP from noise requires only two stations. Obviously, a greater number of mixtures (hence, stations) improves the performance of CICA, so constraining the Blind Source Separation problem. The ability of CICA in deconvolving the different components in a seismic signal, makes it suitable not only for the detection of transients, but also for the study of the seismic noise itself and eventually for its separation into meteo-marine, anthropogenic and volcanic (tremor) sources.

[31] Promising results could arise from the real time implementation of CICA in seismic monitoring networks reducing routine and repetitive work performed by the analysts, and allowing a prompt detection of volcanic signals such as LPs and tremor that often represent indicators of renewing activity.

[32] Moreover, being this method independent of the particular nature of the analyzed seismic events, it is suitable for a broad range of other applications. For instance it would be helpful in fast and precise counting of tectonic earthquakes of huge seismic swarms, when the very close temporal occurrence makes difficult a fine detection.