# Characterization of volcanic regimes and identification of significant transitions using geophysical data: a review

## Abstract

A volcano can be considered as a dynamical system, and each time series recorded at a volcano can be interpreted as one of its observables. It is therefore theoretically possible to extract, even from a single time series, information about the underlying governing system. This is done through a procedure called “embedding” that is based on the intuitive statement that the only time series available carries with it information also about the time evolution of other parameters that we are not able to sample or observe. Carrying out this embedding procedure requires estimates of key parameters such as the optimal delay time and a proper embedding dimension. Other independent but often conceptually similar procedures allow decompositions of the time series into components that may in turn be associated to different source processes. The key to the characterization of volcanic regimes is a process of data reduction, aimed at parsing the amount of data into its most useful components which can then facilitate the interpretation of the system. The approaches presented here can be used to conduct such a data reduction phase, and the reduced data stream can be used not only for characterizing different volcanic regimes but also for determining transitions between them, examining their relationship with external or internal events such as tectonic or volcano-tectonic seismic events, looking for precursors of paroxysmal eruptive phases etc. These results can become additional inputs for physical models in order to understand in detail the physical changes that occurred in the volcanic system and their possible consequences. In this paper, the existing literature on this subject will be reviewed and the prospects of future research will be discussed.

## Keywords

Time series data reduction Dynamical analysis Embedding Precursors Volcanic regimes Pattern recognition## Notes

### Acknowledgments

The author wishes to acknowledge the invaluable help resulted from discussions with his coauthors and former students of the last couple of decades. The methods described here were studied and/or developed also during several research periods spent by the author in foreign institutions, including the following:

-Instituto de Geofísica, Universidad Nacional Autónoma de México (UNAM), México D.F., México

-Earthquake Research Institute, The University of Tokyo, Tokyo, Japan

-ITMO University, St. Petersburg, Russia

-Centro de Investigaciones en Ciencias de la Tierra (CICTERRA)—Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Córdoba, Córdoba, Argentina

Figures are based on original drawings by my former students Fausto Barazza and Luca Barbui.

The paper was improved substantially by the thoughtful comments of the reviewers, Art Jolly and Servando De la Cruz Reyna, and of the editor Steve Self; their help is warmly acknowledged.

## References

- Acernese F, Ciaramella A, De Martino S, Falanga M, Tagliaferri R (2000) Neural networks for blind sources separation of Stromboli explosion quakes, in
*ICA2000, international workshop on independent component analysis and blind signal separation*, 19–22 June 2000, Helsinki, FinlandGoogle Scholar - Acernese F, Ciaramella A, De Martino S, Falanga M e, Tagliaferri R (2003) Neural networks for blind sources separation of Stomboli explosion quakes. IEEE Trans Neural Netw 14:1Google Scholar
- Acernese F, Ciaramella A, De Martino S, Falanga M, Godano C, Tagliaferri R (2004) Polarisation analysis of the independent components of low frequency events at Stromboli volcano (Aeolian Islands, Italy). J Volcanol Geotherm Res 137:153–168Google Scholar
- Aldrich C, Barkhuizen M (2003) Process system identification strategies based on the use of singular spectrum analysis. Mineral Eng 16:815–826Google Scholar
- Alligood KT, Sauer TD, Yorke JA (2000) Chaos: an introduction to dynamical systems, Springer, 3. ed., 603 ppGoogle Scholar
- Arámbula-Mendoza R, Lesage P, Valdés-González C, Varley NR, Reyes-Dávila G, Navarro C (2011) Seismic activity that accompanied the effusive and explosive eruptions during the 2004–2005 period at Volcán de Colima, Mexico. J Volcanol Geotherm Res 205(1–2):30–46Google Scholar
- Araujo AFR and Rego RLME (2013) Self-organizing maps with a time-varying structure.
*ACM Comput Surv*46, 1, Art. 7, 38 pp. DOI: http://dx.doi.org/ 10.1145/2522968.2522975 - Aspinall WP, Woo G, Voight B, Baxter PJ (2003) Evidence based volcanology: application to eruption crises. J Volcanol Geotherm Res 128(1–3):273–285Google Scholar
- Aspinall W, Carniel R, Jaquet O, Woo G, Hincks T (2006) Using hidden multi-state Markov models with multi-parameter volcanic data to provide empirical evidence for alert level decision-support. J Volcanol Geotherm Res 153(1–2):112–124. doi: 10.1016/j.jvolgeores.2005.08.010 Google Scholar
- Bebbington MS (2007) Identifying volcanic regimes using hidden Markov models. Geophys J Int 171(2):921–942. doi: 10.1111/j.1365-246X.2007.03559.x Google Scholar
- Bebbington MS (2013) Assessing probabilistic forecasts of volcanic eruption onsets. Bull Volcanol 75(12):1–13Google Scholar
- Bell AF, Naylor M, Heap MJ, Main IG (2011) Forecasting volcanic eruptions and other material failure phenomena: an evaluation of the failure forecast method. Geophys Res Lett 38, L15304. doi: 10.1029/2011GL048155 Google Scholar
- Bell AF, Naylor M, Main IG (2013) The limits of predictability of volcanic eruptions from accelerating rates of earthquakes. Geophys J Int 194(3):1541–1553Google Scholar
- Beyreuther M, Wassermann J (2011) Hidden semi-Markov model based earthquake classification system using weighted finite-state transducers. Nonlinear Process Geophys 18(1):81–89Google Scholar
- Beyreuther M, Carniel R, Wassermann J (2008) Continuous hidden Markov models: application to automatic earthquake detection and classification at Las Canãdas caldera, Tenerife. J Volcanol Geotherm Res 176(4):513–518. doi: 10.1016/j.jvolgeores.2008.04.021 Google Scholar
- Beyreuther M, Hammer C, Wassermann J, Ohrnberger M, Megies T (2012) Constructing a hidden Markov model based earthquake detector: application to induced seismicity. Geophys J Int 189(1):602–610Google Scholar
- Bicego M, Acosta-Munoz C, Orozco-Alzate M (2013) Classification of seismic volcanic signals using hidden-Markov-model-based generative embeddings. IEEE Trans Geosci Remote Sens 51(6):3400–3409Google Scholar
- Bishop C (1995) Neural
*networks for pattern recognition*, Oxford University Press. 500 ppGoogle Scholar - Bonaccorso A, Bonforte A, Calvari S, Del Negro C, Di Grazia G, Ganci G, Neri M, Vicari A, Boschi E (2011) The initial phases of the 2008–2009 Mount Etna eruption: a multidisciplinary approach for hazard assessment. J Geophys Res B Solid Earth 116(3), B03203Google Scholar
- Bonadonna C, Folch A, Loughlin S, Puempel H (2012) Future developments in modelling and monitoring of volcanic ash clouds: outcomes from the first IAVCEI-WMO workshop on Ash Dispersal Forecast and Civil Aviation. Bull Volcanol 74(1):1–10Google Scholar
- Bottiglieri M, De Martino S, Falanga M, Godano C, Palo M (2005) Statistics of inter-time of Strombolian explosion-quakes. Europhys Lett 72(3):492–498. doi: 10.1209/epl/i2005-10258-0 Google Scholar
- Box G, Jenkins GM, Reinsel G (1994) Time series: forecasting and control, 3rd edn. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
- Bozzo E, Carniel R, Fasino D (2010) Relationship between Singular Spectrum Analysis and Fourier analysis: theory and application to the monitoring of volcanic activity. Comput Math Appl 60(3):812–820, 08Google Scholar
- Broomhead DS, King GP (1986) Extracting qualitative dynamics from experimental data. Phys D 20:217–236Google Scholar
- Cabras G, Carniel R, Wassermann J (2008) Blind source separation: an application to the Mt. Merapi volcano, Indonesia. Fluct Noise Lett 8:3–4, L1-L12Google Scholar
- Cabras G, Carniel R, Wasserman J (2010) Signal enhancement with generalized ICA applied to Mt. Etna Volcano, Italy. Boll Geofis Teor Appl 51(1):57–73Google Scholar
- Cabras G, Carniel R, Jones J (2012) Non-negative matrix factorization: an application to Erta’Ale volcano, Ethiopia. Boll Geofis Teor Appl 53(2):231–242. doi: 10.4430/bgta0056 Google Scholar
- Cabras G, Carniel R, Jones J, Takeo M (2014) Reducing wind noise in seismic data using non-negative matrix factorization: an application to Villarrica volcano, Chile. Geofísica Int 53–1:77–85Google Scholar
- Cannata A, Giudice G, Gurrieri S, Montalto P, Alparone S, Di Grazia G, Favara R, Gresta S, Liuzzo M (2010) Relationship between soil CO2 flux and volcanic tremor at Mt. Etna: implications for magma dynamics. Environ Earth Sci 61(3):477–489Google Scholar
- Carbone D, Zuccarello L, Montalto P, Rymer H (2012) New geophysical insight into the dynamics of Stromboli volcano (Italy). Gondwana Res 22(1):290–299Google Scholar
- Cárdenas-Peña D, Orozco-Alzate M, Castellanos-Dominguez G (2013) Selection of time-variant features for earthquake classification at the Nevado-del-Ruiz volcano. Comput Geosci 51:293–304Google Scholar
- Carniel R (2005) Development of a new diagnostic protocol using a neuro-dynamical tool,
*Chaos*. Solitons Fractals 24(1):349–352Google Scholar - Carniel R, Di Cecca M (1999) Dynamical tools for the analysis of long term evolution of volcanic tremor at Stromboli. Ann Geofis 42(3):483–495Google Scholar
- Carniel R, Iacop F (1996) Spectral precursors of paroxysmal phases of Stromboli. Ann Geofis XXXIX(2):327–345Google Scholar
- Carniel R, Tárraga M (2006) Can tectonic events change volcanic tremor at Stromboli? Geophys Res Lett 33(20):L20321Google Scholar
- Carniel R, Casolo S, Iacop F (1996) “Spectral analysis of volcanic tremor associated with the 1993 paroxysmal events at Stromboli”. In: McGuire WJ, Jones AP and Neuberg J (eds),
*Volcano instability on the Earth and other planets*, Geological Society Special Publication n. 110, 373–381Google Scholar - Carniel R, Di Cecca M, Rouland D (2003) Ambrym, Vanuatu (July–August 2000): spectral and dynamical transitions on the hours-to-days timescale. J Volcanol Geotherm Res 128(1–3):1–13Google Scholar
- Carniel R, Ortiz R, Di Cecca M (2006a) Spectral and dynamical hints on the timescale of preparation of the 5 April 2003 explosion at Stromboli volcano. Can J Earth Sci 43:41–55Google Scholar
- Carniel R, Barazza F and Pascolo PB (2006b)
*Improvement of Nakamura technique by singular spectrum analysis, soil dynamics and earthquake engineering*, Elsevier, 26, 1, 55–63Google Scholar - Carniel R, Barazza F, Tárraga M, Ortiz R (2006c) On the singular values decoupling in the singular spectrum analysis of volcanic tremor at Stromboli. Nat Hazards Earth Syst Sci 6:903–909Google Scholar
- Carniel R, Tárraga M, Barazza F, García A (2008a) Possible interaction between tectonic events and seismic noise at Las Cañadas Volcanic Caldera, Tenerife, Spain. Bull Volcanol 70(9):1113–1121. doi: 10.1007/s00445-007-0193-7 Google Scholar
- Carniel R, Jaquet O, Tárraga M (2008b) Perspectives on the application of the geostatistical approach to volcano forecasting at different time scales. Chapter 14, In: Gottsmann J and Marti J (eds.):
*Caldera volcanism: analysis, modelling and response, Developments in Volcanology*, Elsevier, Vol. 10, Pages 471–487, doi: 10.1016/S1871-644X(07)00014-9 - Carniel R, Barbui L, Jolly AD (2013a) Detecting dynamical regimes by Self-Organizing Map (SOM) analysis: an example from the March 2006 phreatic eruption at Raoul Island, New Zealand Kermadic Arc. Boll Geofis Teor Appl 54(1):39–52Google Scholar
- Carniel R, Jolly AD, Barbui L (2013b) Analysis of phreatic events at Ruapehu volcano, New Zealand using a new SOM approach. J Volcanol Geotherm Res 254:69–79Google Scholar
- Ceamanos X, Waske B, Benediktsson JA, Chanussot J, Fauvel M, Sveinsson JR (2010) A classifier ensemble based on fusion of support vector machines for classifying hyperspectral data. Int J Image Data Fusion 1(4):293–307Google Scholar
- Chouet B (2003) Volcano seismology. Pure Appl Geophys 160(3–4):739–788Google Scholar
- Chouet BA, Matoza RS (2013) A multi-decadal view of seismic methods for detecting precursors of magma movement and eruption. J Volcanol Geotherm Res 252:108–175Google Scholar
- Chouet BA, Shaw HR (1991) Fractal properties of tremor and gas-piston events observed at Kilauea Volcano, Hawaii. J Geophys Res 96:10177–10189Google Scholar
- Cichocki A, Amari S (2003) Adaptive blind signal and image processing. John Wiley, Chichester, UKGoogle Scholar
- Cichocki A, Georgiev P (2003) Blind source separation algorithms with matrix constraints,
*IEICE Trans*. Fundam Electron Commun Comput Sci E86-A:513–522Google Scholar - Cichocki A, Zdunek R, Phan T, Amari S (2009) Nonnegative matrix and tensor factorizations: applications to exploratory multy-way data analysis and blind source separation. Wiley, Tokyo, 500 ppGoogle Scholar
- Cleveland RB, Cleveland WS, McRae JE, Terpenning I (1990) STL: a seasonal-trend decomposition procedure based on loess. J Off Stat 6(3–73):1990Google Scholar
- Collier L, Neuberg J (2006) Incorporating seismic observations into 2D conduit flow modelling. J Volcanol Geotherm Res 152(3–4):331–346Google Scholar
- Collinson ASD, Neuberg JW (2012) Gas storage, transport and pressure changes in an evolving permeable volcanic edifice. J Volcanol Geotherm Res 243–244:1–13Google Scholar
- Cornelius RR, Scott PA (1993) A materials failure relation of accelerating creep as empirical description of damage accumulation. Rock Mech Rock Eng 26:233–252Google Scholar
- Currenti G, Del Negro C, Lapenna V, Telesca L (2005) Fluctuation analysis of the hourly time variability of volcano-magnetic signals recorded at Mt. Etna volcano, Sicily (Italy). Chaos Solitons Fractals 23:1921–1929Google Scholar
- Cusano P, Petrosino S, Saccorotti G (2008) Hydrothermal origin for sustained long-period (LP) activity at Campi Flegrei volcanic complex, Italy. J Volcanol Geotherm Res 177(4):1035–1044Google Scholar
- Daubechies I (1990) Wavelet transform, time-frequency localization and signal analysis. IEEE Trans Inf Theory 36(5):961–1005Google Scholar
- Daubechies I (1992) Ten lectures on wavelets, vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM—Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992. ISBN:0-89871-274-2Google Scholar
- D’Auria L, Giudicepietro F, Martini M, Orazi M, Peluso R, Scarpato G (2010) Polarization analysis in the discrete wavelet domain: an application to volcano seismology. Bull Seismol Soc Am 100(2):670–683Google Scholar
- De la Cruz Reyna S, Tilling R (2008) Scientific and public responses to the ongoing volcanic crisis at Popocatépetl volcano, México: importance of an effective hazards warning system. J Volcanol Geotherm Res 170:121–134. doi: 10.1016/j.jvolgeores.2007.09.002 Google Scholar
- De la Cruz Reyna S, Tárraga M, Ortiz R, Martínez Bringas A (2010) Tectonic earthquakes triggering volcanic seismicity and eruptions: case studies at Tungurahua and Popocatépetl volcanoes. J Volcanol Geotherm Res 193:37–48Google Scholar
- De la Cruz-Reyna S, Reyes-Davila G (2001) A model to describe precursory material-failure phenomena: application to short-term forecasting at Colima volcano. Mexico Bull Volcanol 63:297–308Google Scholar
- De Lauro E, De Martino S, Falanga M, Palo M, Scarpa R (2005) Evidence of VLP volcanic tremor in the band [0.2–0.5] Hz at Stromboli volcano, Italy. Geophys Res Lett 32 (17), art. no. L17303, 1–4Google Scholar
- De Lauro E, De Martino S, Falanga M, Palo M (2006) Statistical analysis of Stromboli VLP tremor in the band [0.1–0.5] Hz: some consequences for vibrating structures. Nonlinear Processes Geophys 13:393–400Google Scholar
- De Lauro E, De Martino S, Falanga M, and Palo M (2009a) Modelling the macroscopic behavior of Strombolian explosions at Erebus volcano,
*Physics of the Earth and Planetary Interiors*,176,3–4,174–186Google Scholar - De Lauro E, De Martino S, Falanga M, Palo M (2009b) Decomposition of high-frequency seismic wavefield of the Strombolian-like explosions at Erebus volcano by independent component analysis. Geophys J Int 177(3):1399–1406Google Scholar
- De Lauro E, De Martino S, Falanga M, Palo M (2011) Self-sustained vibrations in volcanic areas extracted by Independent Component Analysis: a review and new results. Nonlinear Process Geophys 18(6):925–940Google Scholar
- De Lauro E, De Martino S, Palo M, Ibañez JM (2012) Self-sustained oscillations at Volcán de Colima (México) inferred by independent component analysis. Bull Volcanol 74(1):279–292Google Scholar
- De Martino S, Falanga M, Scarpa R, Godano C (2005) Very long period volcanic tremor at Stromboli, Italy. Bull Seismol Soc Am 95:1186–1192Google Scholar
- De Martino S, Falanga M, Palo M, Montalto M, Patanè D (2011) Statistical analysis of the seismicity during the Strombolian crisis of 2007, Italy: evidence of a precursor in tidal range. J Geophys Res 116, B09312. doi: 10.1029/2010JB007503 Google Scholar
- Del Negro C, Greco F, Napoli R, Nunnari G (2008) Denoising gravity and geomagnetic signals from Etna volcano (Italy) using multivariate methods. Nonlinear Process Geophys 15(5):735–749Google Scholar
- Del Pin E, Carniel R, Tárraga M (2008) Event recognition by detrended fluctuation analysis: an application to Teide-Pico Viejo volcanic complex, Tenerife, Spain. Chaos Solitons Fractals 36(5):1173–1180. doi: 10.1016/j.chaos.2006.07.044 Google Scholar
- Eckmann JP, Ruelle D (1985) Ergodic theory of chaos and strange attractors. Rev Mod Phys 57:617–656Google Scholar
- Elliot DF, Rao KR (1982) Fast transforms: algorithms, analysis, applications. Academic, New YorkGoogle Scholar
- Endo TE, Murray T (1991) Real-time seismic amplitude measurement (RSAM). A volcano monitoring and prediction tool. Bull Volcanol 53:533–545Google Scholar
- Esposito AM, Giudicepietro F, D’Auria L, Scarpetta S, Martini M, Coltelli M, Marinaro M (2008) Unsupervised neural analysis of very long period events at Stromboli volcano using the self-organizing maps. Bull Seismol Soc Am 98:2449–2459. doi: 10.1785/0120070110 Google Scholar
- Esposito A, D’Auria L, Giudicepietro F, Peluso R, Martini M (2013) Automatic recognition of landslides based on neural network analysis of seismic signals: an application to the monitoring of Stromboli volcano (Southern Italy). Pure Appl Geophys 170:1821–1832Google Scholar
- Esposito A, D’Auria L, Angelillo A, Giudicepietro F, Martini M (2014) Predictive analysis of the seismicity level at Campi Flegrei volcano using a data-driven approach. In “Recent advances of neural network models and applications”,
*Proceedings of the 23rd Workshop of the Italian Neural Networks Society (SIREN)*, May 23–25, Vietri sul Mare, Salerno, Italy. Series “Smart Innovation, Systems and Technologies” Vol. 26, Springer, pp 133–145Google Scholar - Falsaperla S, Graziani S, Nunnari G, Spampinato S (1996) Automatic classification of volcanic earthquakes by using multi-layered neural networks. Nat Hazards 13(3):205–228Google Scholar
- Falsaperla S, Alparone S, Spampinato S (2003) Seismic features of the June 1999 tectonic swarms in the Stromboli volcano region, Italy. J Volcanol Geotherm Res 125(1–2):121–136Google Scholar
- Fattori Speranza F, Carniel R (2008) Structural changes of volcanic tremor at Stromboli volcano. J Volcanol Geotherm Res 171(1–2):103–117Google Scholar
- Flandrin P, Rilling G, Gonçalvés P (2004) Empirical mode decomposition as a filter bank. IEEE Signal Process Lett 11:112–114Google Scholar
- Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33:1134–1140Google Scholar
- Fukuzono T, Terashima H (1985) Experimental study of slope failure in cohesive soils caused by rainfall. In: Int Symp on Erosion, Debris Flow and Disaster Prevention. Tsukaba, JapanGoogle Scholar
- García A, Fernández-Ros A, Berrocoso M, Marrero JM, Prates G, De la Cruz-Reyna S, Ortiz R (2014) Magma displacements under insular volcanic fields, applications to eruption forecasting: El Hierro, Canary Islands, 2011–2013. Geophys J Int 197(1):322–334. doi: 10.1093/gji/ggt505 Google Scholar
- Garcia-Aristizabal A, Selva J, Fujita E (2013) Integration of stochastic models for long-term eruption forecasting into a Bayesian event tree scheme: a basis method to estimate the probability of volcanic unrest. Bull Volcanol 75(2):1–13Google Scholar
- Geirsson H, Rodgers M, LaFemina P, Witter M, Roman D, Muñoz A, Tenorio V, Alvarez J, Jacobo VC, Nilsson D, Galle B, Feineman MD, Furman T, Morales A (2014) Multidisciplinary observations of the 2011 explosive eruption of Telica volcano, Nicaragua: implications for the dynamics of low-explosivity ash eruptions. J Volcanol Geotherm Res 271:55–69Google Scholar
- Giacco F, Esposito AM, Scarpetta S, Giudicepietro F, Marinaro M (2009) Support vector machines and MLP for automatic classification of seismic signals at Stromboli volcano. In: Apolloni B, Bassis S, Morabito FC (Eds.),
*WIRN. Frontiers in Artificial Intelligence and Applications*, vol. 204. IOS Press, pp. 116–123Google Scholar - Godano C, Capuano P (1999) Source characterisation of low frequency events at Stromboli and Vulcano islands (Isole Eolie Italy). J Seismol 3:393–408Google Scholar
- Gottsmann JH, Carniel R, Coppo N, Wooller L, Hautmann S, Rymer H (2007) Oscillations in hydrothermal systems as a source of periodic unrest at caldera volcanoes: multiparameter insights from Nisyros, Greece. Geophys Res Lett 34(L07307):1–5Google Scholar
- Green RM, Bebbington MS, Cronin SJ, Jones G (2013) Geochemical precursors for eruption repose length. Geophys J Int 193(2):855–873Google Scholar
- Gunn LS, Blake S, Jones MC, Rymer H (2014) Forecasting the duration of volcanic eruptions: an empirical probabilistic model. Bull Volcanol 76(1):1–18, in pressGoogle Scholar
- Hammer C, Ohrnberger M (2012) Forecasting seismo-volcanic activity by using the dynamical behavior of volcanic earthquake rates. J Volcanol Geotherm Res 229–230:34–43Google Scholar
- Hammer C, Beyreuther M, Ohrnberger M (2012) Seismic-event spotting system for volcano fast-response systems. Bull Seismol Soc Am 102(3):948–960. doi: 10.1785/0120110167 Google Scholar
- Hammer C, Ohrnberger M, Fah D (2013) Classifying seismic waveforms from scratch: a case study in the alpine environment. Geophys J Int 192:425–439Google Scholar
- Hansen BE (1992) Testing for parameter instability in linear models. J Policy Model 14(4):517–533Google Scholar
- Harris AJL, Carniel R, Jones J (2005) Identification of variable convective regimes at Erta Ale Lava lake. J Volcanol Geotherm Res 142(3–4):207–223Google Scholar
- Hastie T, Tibshirani R, Friedman J (2002) The elements of statistical learning. Springer, Berlin, 533 ppGoogle Scholar
- Hayakawa M, Liu J-Y, Hattori K, and L Telesca (2009) Preface in “
*Electromagnetic phenomena associated with earthquakes and volcanoes*” (Eds. Hayakawa M, Liu JY, Hattori K and Telesca L), Phys Chem Earth 34, 341–342Google Scholar - Hellweg M (2000) Physical models for the source of Lascar’s harmonic tremor. J Volcanol Geotherm Res 101:183–198Google Scholar
- Huang NE, Shen ZS, Long RM, Wu C, Shih H-H, Zheng Q, Yen N-C, Tung C-C, Liu H-H (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc R Soc London Ser A 454:903–995Google Scholar
- Hyvärinen A, Karhunen J and Oja E (2001) Independent component analysis, John WileyGoogle Scholar
- Ichihara M, Takeo M, Yokoo A, Oikawa J, Ohminato T (2012) Monitoring volcanic activity using correlation patterns between infrasound and ground motion. Geophys Res Lett 39, L04304Google Scholar
- Jaquet O, Carniel R (2001) Stochastic modelling at Stromboli: a volcano with remarkable memory. J Volcanol Geotherm Res 105:249–262Google Scholar
- Jaquet O, Carniel R (2003) Multivariate stochastic modelling: towards forecasts of paroxysmal phases at Stromboli. J Volcanol Geotherm Res 128:261–271Google Scholar
- Jaquet O, Sparks RSJ and Carniel R (2006) Magma memory recorded by statistics of volcanic explosions at the Soufrière Hills volcano, Montserrat, in Mader HM, Coles SG, Connor CB and Connor LJ (eds), “
*Statistics in Volcanology*”, IAVCEI Publications n. 1, Geological Society, ISBN 978-1-86239-208-3, 296 ppGoogle Scholar - Jones JP, Carniel R, Malone SD (2012a) Sub-band decomposition and reconstruction of continuous volcanic tremor. J Volcanol Geotherm Res 213–214:98–115Google Scholar
- Jones JP, Carniel R, Malone SD (2012b) Decomposition, location, and persistence of seismic signals recovered from continuous tremor at Erta 'Ale, Ethiopia. J Volcanol Geotherm Res 213–214:116–129Google Scholar
- Julian BR (1994) Volcanic tremor: nonlinear excitation by fluid flow. J Geophys Res 99:11859–11877Google Scholar
- Julian B (2000) Period doubling and other non-linear phenomena in volcanic earthquakes and tremor. J Volcanol Geotherm Res 101:19–26Google Scholar
- Kantz H, Schreiber T (1997) Nonlinear time series analysis. Cambridge University Press, CambridgeGoogle Scholar
- Kawakatsu H, Yamamoto M (2007) Volcano seismology. Treatise Geophys 4:389–420Google Scholar
- Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411Google Scholar
- Kilburn CRJ (2003) Multiscale fracturing as a key to forecasting volcanic eruptions. J Volcanol Geotherm Res 125(3–4):271–289Google Scholar
- Klose CD (2006) Self-organizing maps for geoscientific data analysis: geological interpretation of multidimensional geophysical data. Comput Geosci 10(3):265–277Google Scholar
- Kohonen T (1982) Self-organised formation of topologically correct feature map. Biol Cybern 43:56–69Google Scholar
- Konstantinou KI (2002) Deterministic non-linear source processes of volcanic tremor signals accompanying the 1996 Vatnajökull eruption, Central Iceland. Geophys J Int 148(3):663–675Google Scholar
- Konstantinou KI, Lin CH (2004) Nonlinear time series analysis of volcanic tremor events recorded at Sangay volcano, Ecuador. Pure Appl Geophys 161(1):145–163Google Scholar
- Kuan CM, Hornik K (1995) The generalized fluctuation test: a unifying view. Econom Rev 14(2):135–161Google Scholar
- Langer H, Falsaperla S, Powell T, Thompson G (2006) Automatic classification and a-posteriori analysis of seismic event identification at Soufriere Hills volcano, Montserrat. J Volcanol Geotherm Res 153(1–2):1–10Google Scholar
- Langer H, Falsaperla S, Masotti M, Campanili R, Spampinato S, Messina A (2009) Synopsis of supervised and unsupervised pattern classification techniques applied to volcanic tremor data at Mt. Etna. Italy Geophys J Int 178:1132–1144. doi: 10.1111/j.1365-246X.2009.04179.x Google Scholar
- Langer H, Falsaperla S, Messina A, Spampinato S, Behncke B (2011) Detecting imminent eruptive activity at Mt Etna, Italy, in 2007–2008 through pattern classification of volcanic tremor data. J Volcanol Geotherm Res 200:1–17Google Scholar
- Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401:788–791Google Scholar
- Lee C-W, Lu Z, Kwoun O-I, Won J-S (2008) Deformation of the Augustine Volcano, Alaska, 1992–2005, measured by ERS and ENVISAT SAR interferometry. Earth Planets Space 60(5):447–452Google Scholar
- Leibert W, Pawelzik K, Schuster HG (1991) Optimal embeddings of chaotic attractors from topological considerations. Europhys Lett 14:521–526Google Scholar
- Lesage P (2008) Automatic estimation of optimal autoregressive filters for the analysis of volcanic seismic activity. Nat Hazard Earth Syst Sci 8:369–376Google Scholar
- Lin M-J, Jeng Y (2010) Application of the VLF-EM method with EEMD to the study of a mud volcano in southern Taiwan. Geomorphology 119:97–110Google Scholar
- Lippmann RP (1987) Introduction to computing with neural nets. IEEE ASSP Mag 4(2):4–22Google Scholar
- Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141. doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 Google Scholar
- Lovallo M, Marchese F, Pergola N, Telesca L (2007) Fisher information analysis of volcano-related advanced, very-high-resolution radiometer (AVHRR) thermal products time series. Phys A 384:529–534Google Scholar
- Lovallo M, Marchese F, Pergola N, Telesca L (2009) Fisher information measure of temporal fluctuations in satellite advanced very high resolution radiometer (AVHRR) thermal signals recorded in the volcanic area of Etna (Italy). Commun Nonlinear Anal Numer Simul 14:174–181Google Scholar
- Madonia P, Cusano P, Diliberto IS, Cangemi M (2013) Thermal anomalies in fumaroles at Vulcano island (Italy) and their relationship with seismic activity. Phys Chem Earth 63:160–169Google Scholar
- Mallat S (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Pattern Anal and Mach Intell 11(7):674–693Google Scholar
- Marchese F, Pergola N, Telesca L (2006) Investigating the temporal fluctuations in satellite advanced very high resolution radiometer thermal signals measured in the volcanic area of Etna (Italy). Fluct Noise Lett 6:L305–L316Google Scholar
- Martini F, Tassi F, Vaselli O, Del Potro R, Martinez M, del Laat RV, Fernandez E (2010) Geophysical, geochemical and geodetical signals of reawakening at Turrialba volcano (Costa Rica) after almost 150 years of quiescence. J Volcanol Geotherm Res 198(3–4):416–432Google Scholar
- Marzocchi W, Sandri L, Furlan C (2006) A quantitative model for volcanic hazard assessment,
*Statistics in Volcanology*, edited by Mader HM, Coles SG, Connor CB and Connor LJ, IAVCEI Publications, Geol Soc LondGoogle Scholar - Marzocchi W, Sandri L, Selva J (2010) BET_VH: a probabilistic tool for long-term volcanic hazard assessment. Bull Volcanol 72(6):705–716Google Scholar
- Masotti M, Falsaperla S, Langer H, Spampinato S, Campanini R (2006) Application of support vector machine to the classification of volcanic tremor at Etna, Italy. Geophys Res Lett 33Google Scholar
- Masotti M, Campanini R, Mazzacurati L, Falsaperla S, Langer H, Spampinato S (2008) TREMOrEC: a software utility for automatic classification of volcanic tremor. Geochem Geophys Geosyst 9, Q04007. doi: 10.1029/2007GC001860 Google Scholar
- Matheron G (1962)
*Traité de géostatistique appliquée*. Tome 1, Editions Technip, Paris, 334 ppGoogle Scholar - Mineva A, Popivanov D (1996) Method for single-trial readiness potential identification, based on singular spectrum analysis. J Neurosci Methods 68:91–99Google Scholar
- Nakano M, Kumagai H (2005) Response of a hydrothermal system to magmatic heat inferred from temporal variations in the complex frequencies of long-period events at Kusatsu–Shirane volcano. Jpn J Volcanol Geotherm 147:233–244Google Scholar
- Nakano M, Kumagai H, Kumazawa M, Yamaoka K, Chouet B (1998) The excitation and characteristic frequency of the long-period volcanic event: an approach based on an inhomogeneous autoregressive model of a linear dynamic system. J Geophys Res 103:10 031–10 046Google Scholar
- Newhall CG, Hoblitt RP (2002) Constructing event trees for volcanic crises. Bull Volcanol 64:3–20. doi: 10.1007/s004450100173 Google Scholar
- Ohrnberger M (2001) Continuous automatic classification of seismic signals of volcanic origin at Mt. Merapi, Java, Indonesia. Ph.D. thesis, Institut fuer Geowissenschaften, Universitaet PostdamGoogle Scholar
- Orozco-Alzate M, Acosta-Muñoz C and Makario Londoño-Bonilla J (2012) The automated identification of volcanic earthquakes: concepts, applications and challenges.
*Earthquake Research and Analysis—Seismology, Seismotectonic and Earthquake Geology*, D’Amico S. (Ed.), ISBN: 978-953-307-991-2, InTech, CroatiaGoogle Scholar - Packard NH, Crutchfield JP, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45(9):712–716Google Scholar
- Palo M, Cusano P (2013) Wavefield decomposition and phase space dynamics of the seismic noise at Volcàn de Colima, Mexico: evidence of a two-state source process. Nonlinear Processes Geophys 20:71–84Google Scholar
- Papageorgiou E, Foumelis M, Parcharidis I (2012) Long-and short-term deformation monitoring of Santorini volcano: unrest evidence by DInSAR analysis.
*IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing*, 5 (5), art. no. 6220261, 1531–1537Google Scholar - Pistolesi M, Delle Donne D, Pioli L, Rosi M, Ripepe M (2011) The 15 March 2007 explosive crisis at Stromboli volcano, Italy: assessing physical parameters through a multidisciplinary approach. J Geophys Res Solid Earth 116, B12206Google Scholar
- Procaccia I (1988) Universal properties of dynamically complex systems: the organisation of chaos. Nature 333:618–623Google Scholar
- Pshenichny CA, Nikolenko SI, Carniel R, Vaganov PA, Khrabrykh ZV, Moukhachov VP, Akimova-Shterkhun VL, Rezyapkin AA (2009) The event bush as a semantic-based numerical approach to natural hazard assessment (exemplified by volcanology). Comput Geosci 35(5):1017–1034Google Scholar
- Rilling G, Flandrin P, Gonçalvès P (2002) Empirical
*mode decomposition MATLAB codes*. http://perso.ens-lyon.fr/patrick.flandrin/emd.html - Ripepe M, Harris AJL, Carniel R (2002) Thermal, seismic and infrasonic evidences of variable degassing rates at Stromboli volcano. J Volcanol Geotherm Res 118:285–297Google Scholar
- Rogers JA, Stephens JA (1995) SSAM real time seismic spectral amplitude measurement on PC and its application to volcano monitoring. Bull Seism Soc Am 85:632–639Google Scholar
- Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for the calculating largest Lyapunov exponents from small datasets. Phys D 65:117–134Google Scholar
- Rouwet D, Tassi F, Mora-Amador R, Sandri L, Chiarini V (2014) Past, present and future of volcanic lake monitoring. J Volcanol Geotherm Res, in pressGoogle Scholar
- Samsonov S, van der Kooij M, Tiampo K (2011) A simultaneous inversion for deformation rates and topographic errors of DInSAR data utilizing linear least square inversion technique. Comput Geosci 37(8):1083–1091Google Scholar
- Schick R, Riuscetti M (1973) An analysis of volcanic tremor at South-Italian volcanoes. Zeit Geophysik 39:262–274Google Scholar
- Schmidt MN, Larsen J, Hsiao FT, (2007) Wind noise reduction using non-negative sparse coding, in
*IEEE Workshop on Machine Learning for Signal Processing*, 431–436Google Scholar - Segall P (2013) Volcano deformation and eruption forecasting. Geochem Soc Spec Publ 380(1):85–106Google Scholar
- Shannon CE (1948) “A mathematical theory of communication”, Bell Syst Tech J, 27, 379–423 & 623–656Google Scholar
- Shaw R (1984) The dripping faucet as a model chaotic system. Aerial Press, Santa Cruz, CAGoogle Scholar
- Sparks RSJ (2003) Forecasting volcanic eruptions. Earth Planet Sci Lett 210:1–15Google Scholar
- Sparks RSJ, Biggs J, Neuberg JW (2012) Monitoring volcanoes. Science 335:1310–1311Google Scholar
- Takens F (1981)
*Detecting strange attractors in turbulence, in dynamical systems and turbulence*, lecture notes in mathematics, vol 898. Springer, Berlin, pp 336–381Google Scholar - Tárraga M, Carniel R, Ortiz R, Marrero JM, García A (2006) On the predictability of volcano-tectonic events by low frequency seismic noise analysis at Teide-Pico Viejo volcanic complex, Canary Islands. Nat Hazards Earth Syst Sci 6:365–376Google Scholar
- Tárraga M, Carniel R, Ortiz R, García A (2008a) The failure forecast method. Review and application for the realtime detection of precursory patterns at reawakening volcanoes. Chapter 13 In: Gottsmann, J. and Marti, J (eds.):
*Caldera volcanism: analysis, modelling and response, Developments in Volcanology*, Elsevier, Vol. 10, 447–469, doi: 10.1016/S1871-644X(07)00013-7 - Tárraga M, Carniel R, Ortiz R, García A, Moreno H (2008b) A dynamical analysis of the seismic activity of Villarrica volcano (Chile) during September–October 2000. Chaos, Solitons Fractals 37(5):1292–1299Google Scholar
- Tárraga M, De La Cruz-Reyna S, Mendoza-Rosas AT, Carniel R, Martínez-Bringas A, García A, Ortiz R (2012) Dynamical parameter analysis of continuous seismic signals of Popocatépetl volcano (Central Mexico): a case of tectonic earthquakes influencing volcanic activity. Acta Geophys 60(3):664–681. doi: 10.2478/s11600-012-0020-1 Google Scholar
- Telesca L, Lovallo M, Carniel R (2010) Time-dependent Fisher information measure of volcanic tremor before 5 April 2003 paroxysm at Stromboli volcano, Italy. J Volcanol Geotherm Res 195:78–82Google Scholar
- Tilling RI (1989) Volcanic hazards and their mitigation: progress and problems. Rev Geophys 27(2):237–269. doi: 10.1029/RG027i002p00237 Google Scholar
- Tokarev PI (1963) On a possibility of forecasting of Bezymianny volcano eruptions according to seismic data. Bull Volcanol 26:379–386Google Scholar
- UNDRO (1979)
*Natural disasters and vulnerability analysis. Office of the United Nations Disaster Relief Co-ordinator (UNDRO)*, Report of Expert Group Meeting (9–12 July 1979), UNDRO, GenevaGoogle Scholar - Vapnik V (1998) Statistical learning theory. Wiley and Sons, NewYorkGoogle Scholar
- Vargas-Bracamontes DM, Nava FA, Reyes-Dávila GA (2009) Time-scale wavelet patterns related to the 1998–1999 eruptions of the Colima volcano, and their possible implications for eruption forecasting. J Volc Geotherm Res 184(3–4):271–284Google Scholar
- Vila J, Macià R, Kumar K, Ortiz R, Moreno H, Correig AM (2006) Analysis of the unrest of active volcanoes using variations of the base level noise seismic spectrum. J Volcanol Geotherm Res 153:11–20Google Scholar
- Voight B (1988) A method for prediction of volcanic eruptions. Nature 332(10):125–130Google Scholar
- Walden AT, Contreras Cristan A (1998) The phase-corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events. Proc R Soc A Math Phys Eng Sci 454:2243–2266Google Scholar
- Welch PD (1967) The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoustics AU-15:70–73Google Scholar
- Weston J, Watkins C (1999) Multi-class support vector machines, Proc. ESANN99, ed. Verleysen M, D. Facto Press, BruxellesGoogle Scholar
- Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1:1–41Google Scholar
- Wu C, Zhou R (2006) Application of Hilbert-Huang transform in extracting dynamic properties of seismic signals. J Earthq Eng Eng Vib 26(5):41–46Google Scholar
- Xue Y, Cao J, Tian R (2013) A comparative study on hydrocarbon detection using three EMD-based time–frequency analysis methods. J Appl Geophys 89:108–115Google Scholar
- Zeileis A (2005) A unified approach to structural change tests based on ML scores, F statistics, and OLS residuals. Econ Rev 24(4):445–466Google Scholar
- Zeileis A, Leisch F, Hornik K, Kleiber C (2002) strucchange: an R package for testing for structural change in linear regression models. J Stat Softw 7(2):1–38Google Scholar