Wavelet Analysis in Volcanology: The Case of Phlegrean Fields

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1 Journal of Environmental Science and Engineering A 6 (2017) doi: / / D DAVID PUBLISHING Wavelet Analysis in Volcanology: The Case of Phlegrean Fields Giuseppe Pucciarelli Department of Physics E. R. Caianiello, University of Salerno, Fisciano 84084, Italy Abstract: The Phlegrean Fields are an area in the west of Naples (Italy), with a huge interest in geophysical community being a volcanic caldera among the most dangerous in the world. Various techniques of monitoring exist. Among all, the control of ground deformations and variations in sea level has considerable importance. Time series of ground deformation and tidal data in this area have been analysed to highlight these important geophysical features and these results are compared with those obtained from similar data in other time periods. With regard to first mentioned, tiltmetric data have been analysed. These ones come from the tiltmeter network sited in Pozzuoli. Instead, the tidal data come from the tide gauge in Pozzuoli. Data have been analysed by means of a wavelet approach, using a Continuos Wavelet Transform and using, as so-called Wavelet Mother, a Gabor-Morlet wavelet. For each time series, the principal harmonic constituents result: lunar semidiurnal (M2), solar semidiurnal (S2) and lunar diurnal (K1). Other harmonic constituents, having frequencies higher than 1/hour, are present. These last ones could be interpreted as seiches and they could be linked up with generation of discrete plumes of rising magma. Frequencies at which there is the occurrence of these seiches are in agreement with previous studies. Key words: Phlegrean Fields, wavelet analysis, tiltmeter, tides, seiches. 1. Introduction The Phlegrean Fields are an area in the west of Naples (Italy), with a huge interest in geophysical community being a volcanic caldera among the most dangerous in the world. Reason of this is high exposure of people who live in that area (550,000 inhabitants ca.). Various techniques of monitoring exist. Among all, the control of ground deformations and variations in sea level has considerable importance. The first one is used to verify the presence of possible traces related to a magma resurgence which could precede an eventual eruption, while the second one comes in handy to check the phenomenon of the bradyseism, which afflicts in a particular way in this volcanic area. Time series of ground deformation and tidal data in this area have been analysed to highlight these important geophysical features and these results are Corresponding author: Giuseppe Pucciarelli, Ph.D., research fields: geophysics, volcanology and numerical simulation. compared with those obtained from similar data in other time periods. With regard to first mentioned, tiltmetric data have been analysed. These ones come from the tiltmeter network sited in Pozzuoli (that is, Pozzuoli North Tunnel and Pozzuoli South Tunnel). The second typology of data, namely tidal data, comes from the tide gauge in Pozzuoli. These data are not stationary, so it is clear that a conventional Fourier Analysis is not adequate for having a complete picture of frequencies which are present in authors signals. Then, another goal to reach is maintenance of time information, which is impossible to obtain with Fourier Analysis. Therefore, in order to realize an advance analysis of these experimental data, a wavelet approach has been used. Choice of this kind of analysis has been preferred because it allows to have information not only on frequencies but even on time. Then, it is an efficient method to obtain all the frequencies which have present in signal with a good resolution. This factor is relevant in choice of a wavelet approach. For

2 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields 301 example, the Short Time Fourier Transform is time-frequency localized, but the introduction of the window function to cover signals brings with its resolution problems. So, spectral analysis has been obtained by a wavelet approach: results are a local spectrum, for each scale in which signal has been decomposed, and a global one achieved by average on each period of local spectrum. At this proposal, the Continuos Wavelet Transform has been used opting, as so-called Wavelet Mother, for Gabor-Morlet wavelet. This choice has been made because Gabor-Morlet wavelet is a complex function modulated by a Gaussian window: this characteristic makes it extremely suitable for the geophysical applications. For each time series, the principal harmonic constituents appear precisely: lunar semidiurnal (M2), solar semidiurnal (S2) and lunar diurnal (K1). Besides, time series show peaks for some frequencies higher than 1 hour. These peaks highlight the presence of seiches, which are standing waves occuring in total or partial enclosed body water, as Gulf of Naples. Studies about occurrence of these seiches are very important in volcanic areas, because these oscillations could be linked up with generation of discrete plumes of rising magma. Frequencies at which there is the occurrence of these seiches are in agreement with previous studies. 2. A Description of Phlegrean Fields The Phlegrean Fields are an ample volcanic area placed north-west of Naples, Italy, with a diameter between 12 and 15 kilometers. This volcanic caldera actually in quiescence is composed of craters, tiny volcanic cones and locations of secondary volcanism (bradyseism, hot springs and fumarole). A morphologic map of this area is showed in Fig. 1. History of Phlegrean Fields can be splitted into three periods as [1]: Fig. 1 Morphologic map of Phlegrean Fields.

3 302 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields (1) First Phlegrean Period, from 60,000 years ago to 37,000 years ago, when there was the I gnimbrite Campana eruption; (2) Second Phlegrean Period, from 37,000 years ago to 12,000 years ago, when there was the Tufo Giallo Napoletano eruption; (3) Third Phlegrean Period, from 12,000 years ago to September 1,538 ac, when there was the last Phlegrean eruption, which provoked the formation of Mt. Nuovo hill. Actually, the Phlegrean Fields are considered by science community the volcanic area which has the most significant volcanic hazard in the world. Explanation of this concept is very simple. This area has a large population density, therefore, an eventual eruption could cause catastrophic effects. For this reason, the Phlegrean Fields are constantly monitored. Monitoring takes place by means of various instruments networks which produce geophysical and geochemical signals. The first one is used to study ground deformations, sea oscillations, seismic activity and variations of gravitational field [1]. Instead, through the second one, chemical composition of gases given off by fumarole and/or by ground could be analysed. These signals, both geophysical and geochemical ones, are studied through numerical techniques. A study of some signals derived from tiltmetric and mareographic instruments used for Phlegrean Fields monitoring and analysed by means of a wavelet approach is proposed in this paper. 3. Tilt: A Description of the Physical Quantity and Used Instruments Considering two particles in a generic continuous medium whose position vectors are respectively X 1 and X 2, fixing X 1, several quantities and all function of X 2 can be defined. First of all, the baseline: d = r( X 2 ) r ( X 1 ) (1) where r is the position vector respectively computed in X 1 and X 2. Then, the displacement vector: s= d ( X 2 ) d 0 ( X 2 ) (2) where d 0 (X 2 ) indicates the displacement vector at starting time t 0 = 0 seconds. Also, the baselength: l= d 0 ( X 2 ) (3) and the direction: d'( X 2 )= d 0 ( X 2 ) l ( X 2 ) Then, the deformational tilt [2]: (4) Ω D = ẑ [ (s d ) 0 ] (5) l where the circumflex z is the unit vector of z axes of Cartesian coordinate system in which particles X 1 and X 2 are moving. This definition is valid considering the approximation s/l << 1. The operational definition of tilt depends on specific tiltmeter construction. The instruments, from which data have been gathered, are Michelson pot and tube tiltmeters. The instrument shows the following structure. It consists of a sealed rigid pipe half-full of water, which has at its extremities two sensors. And its representation is showed in Fig. 2. Considering the approximation of isothermal conditions, water could be treated as an equipotential surface. Therefore, ground tilt causes one end to fall and the other to raise an equal amount. According to these evidences, the first operational definition of tilt can be produced: Tilt= N S L (6) where N and S are respectively the quantity of water measured in North sensor and in South sensor, while L is the pipe length [3]. Units of measure are radians. If a Michelson tiltmeter is installed close to a magmatic chamber, an ination or an emptying of this one causes an increasing or a decreasing of measured tilt. Sensors are made up of four 5-cm-diameter, chromium-plated, copper balls supporting a central ferromagnetic core whose vertical position is monitored to a precision of 0.1 micron by an LVDT (Linear Variable Displacement Transducer) fastened to

4 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields 303 Fig. 2 Schematic representation of a Michelson pot-and-tube tiltmeter. Fig. 3 Schematic representation of Pozzuoli North and South Tunnels [3]. Table 1 Description of principal characteristics of pot-and-tube tiltmeters in Pozzuoli. Properties Value Stability 0.1 microradian Weekly accuracy 1 nanoradian Tilt resolution at one minute intervals 0.1 nanoradian Sensors sensitivity to change of water levels 0.1 micron Sampling frequency Hz Time of computing data average 90 seconds Time of transmission data to Iridium satellite 120 seconds a stable pillar 20 m underground. For protecting indipendence of measured tilt from local temperature variations, which can add noise to measured tilt signals, Michelson tiltmeter has been completed by a third sensor, called Center sensor, collocated exactly at the half of pipe. This sensor is put to verify signal integrity. Therefore, the second (and conclusive) operational definition of tilt can be obtained: Tilt= N S L = 2(N C ) = 2(C S ) (7) L L Michelson tiltmeters which have been used are situated in Pozzuoli, a town placed near Naples. Tiltmeters are collocated in two tunnels, named North Tunnel and South Tunnel. A map of them is showed in Fig. 3. In the first citated tunnel, there are three tiltmeters which operate in three azimuts, while in South Tunnel three pipes measure two azimuths. Table 1 explains principal characteristics of tiltmeters. Sensors detect a combination of body tide, load tide and volcano inflation. An increasing of tilt could represent a probable volcano ination. Sensors are constituted by four 5-cm-diameter chromium-plated copper balls supporting a central ferromagnetic core whose vertical position is monitored to a precision of 0.1 micron by an LVDT fastened to a stable pillar 20 m underground. Signals detected by sensors are accurate to within 1 percent. 4. Tides, Seiches and Mareographic Network of Phlegrean Fields Tides are periodic oscillations of sea levels provoked a combined effect of gravitational and centripetal forces. A particular type of tides is the seiches. Seiches are free oscillations which occur in natural and/or artificial lagoons as gulfs, lakes and pools. They have a determined period and their occurence depends on single lagoon s form. This kind of oscillations was discovered by Swiss hydrologist

5 304 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields François-Alphonse Forel who, in last years of XXIX century, studied the effects of these oscillations in Lake Geneva, Switzerland [4]. More precisely, seiches are standing waves. When a disequilibrium (provoked by meteorological and/or tectonical reasons) occurs in a lagoon, gravity restores hydrostatical equilibrium by means of a pulse which courses along the lagoon and its velocity is strictly connected with lagoon profondity. The bottom of lagoon reflects this pulse, provoking an interference. Multiple reflections of these pulses produce special standing waves, which are the seiches. Seiches occurence depends on specific characteristics of a determined lagoon. They are: the largeness, the profondity, its contour and the water temperature. The natural period is the period of fundamental resonance s occurrence. Eq. (8) which inscribes the natural period is the so-called Merian s formula: T = 2L (8) gh where T is the longest natural period, L is the lagoon length, h is the average depth of the body of water and g is the acceleration of gravity. Observation of higher harmonics is possible. The n-th harmonic will be observed at 1/n period. In the Section 5, the relevance of the study of seiches in Gulf of Pozzuoli will be explained. The task of monitoring tidal signals in Gulf of Pozzuoli is entrusted to Osservatorio Vesuviano through a mareographic network. Mareographic network of Phlegrean Fields is composed by six main mareographic stations: Naples, Torre del Greco, Pozzuoli, Castellammare di Stabia, Nisida and Miseno. In addition to these ones, there are other three secondary mareographic stations: Pozzuoli Molo Sud Cantieri, Forio d Ischia and Agropoli [5]. The network is showed in Fig. 4. Each main mareographic station is equipped by a mechanic tide gauge constitued by a float and a paper papyrus for data registration and by a digital tide gauge. For each station, sampling time is 5 minutes and sampled data are transmitted by means of GSM (Global System Mobile Communications). Each station which composes the secondary mareographic network of Phlegrean Fields plays a precise role. Pozzuoli Molo Sud Cantieri produces important data for a more detailed study of Phlegrean Bradyseism. Forio d Ischia serves as link with other monitoring Fig. 4 Mareographic network of Phlegrean Fields [5].

6 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields 305 networks of Campania Volcanoes (Ischia and Vesuvio). Finally, Agropoli is a landmark which allows to obtain a comparison between Gulf of Naples tidal signals and southern Tyrrenhian ones. Main goal to obtain by means of analysis of tidal signals is obviously the study of ground deformations, a study realised through comparison of measures obtained by other monitoring instruments. Furthermore, tidal signals are also studied for revealing the potential presence of so-called basin effects. These ones can be showed by means of a spectral analysis of tidal signals. They are very important because possible different basin effects in Gulf of Naples and in Gulf of Pozzuoli could influence exact reconstruction of signals concerning ground deformations, since Naples is the reference mareographic station of the network. 5. Wavelet Analysis of Signals A wavelet analysis of signals derived from tiltmetric and mareographic network of Phlegrean Fields, monitoring for period from May 2008 to July 2008, is proposed. This particular typology of analysis has been chosen for two reasons: (1) It allows the conservation of temporal information about the occurence of frequencies which are present into signals; (2) Because of its particular way to break down the signal (by through shifted and scaled versions of a particular wavelet, named Wavelet Mother), wavelet analysis allows to identify possible non-stationary characteristics of signals. The strategy of this wavelet analysis has followed these steps [6]: (1) Choice of Mother Wavelet. A Gabor-Morlet Wavelet has chosen as Mother Wavelet because it is the most commonly used wavelet for time series analysis and it is suitable for computation in an easy way. ω 0, that is the modulation factor present in Gabor-Morlet Wavelet, is put equal to 6; (2) Choice of a set of scales. Scales have been selected by means of Eq. (9). s j = s 0 2 jδj (9) where s 0 is the smallest resolvable scale and it is equal to sampling time times two. δj is a resolution paramater about chosen scale and j is an index which identifies a determinated scale. It goes from 0 to J. The latter is the larget scale and it is given by Eq. (10). J = 1 δj log ( N δt 2 ) s (10) 0 where N is the number of data and δt is the sampling time. The process of performing wavelet transform has been obtained by means of a software written in Matlab language by Torrence, C. and Compo, G. P. [6]. This software works in the following way: for each scale, software computes the wavelet transform W n (s) with index n that goes from 1 to N (this last one has been defined in Eq. (10)). The square modulus of W n (s) gave the so-called local wavelet spectrum. Their distribution is given from the Eq. (11). W n (s) 2 1 σ 2 2 P χ 2 k 2 (11) Eq. (11) means that local wavelet spectrum follows a chi-square distribution modulated by a factor P k. The latter is a red noise Fourier spectrum. Its form is: 1 α 2 P k = 1+ α 2 2αcos( 2πk N ) (12) where α is the lag-1 autocorrelation and k is the frequency index, which goes from 0 to N/2, where N is number of data which constitute the analysed time series. The choice of α is crucial and is order that P k could be considered as a red noise Fourier spectrum. This parameter is put equal to After the implementation of this choice, Eq. (12) could be interpreted as a sort of background spectrum. That is, if a peak of the considered wavelet local spectrum is above the background spectrum, it is true with a 95% confidence. Wavelet local spectra have been obtained by means of opportune Matlab codes. In Fig. 5 (related to North Tunnel tiltmetric data) and in Fig. 6 (related to tidal data registered by mareographic

7 306 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields Fig. 5 Local wavelet spectrum of tiltmetric data recorded by North Tunnel tiltmeter in Pozzuoli for May Fig. 6 Local wavelet spectrum of tidal data recorded by Mareographic station in Pozzuoli for May station in Pozzuoli), two examples of these wavelet local spectra are showed and precisely those ones are related to May Results highlight a variation in variance included between 8 and 16 hours for each time series. This corresponds to classical harmonics as M2 (lunar semidiurnal), S2 (solar semidiurnal) and K1 (luni-solar diurnal). On the contrary, depending on various time series, local spectra highlight other variations in variance. They are: 3 c/d (this symbol stands for cycles for day), 4 c/d, 6 c/d, 0.7 (approximately 85 minutes), 0.9 (approximately 67 minutes), 1.1 (approximately 55 minutes), 2.3

8 Wavelet Analysis in Volcanology: The Case of Phlegrean Fields 307 (approximately 26 minutes), 2.7 (approximately 22 minutes) and 2.8 (approximately 20 minutes). These two kinds of variations underline the presence of principal harmonic constituents and of seiches, respectively. These seiches (or better part of them) could be interpreted as load tides due to injection of magma plumes in Phlegrean Fields magma chamber. This kind of interpretation is justified by results of data recorded by broadband instruments on volcanic areas similar to Phlegrean Fields as Soufriére Hills and Santiaguito Volcano. These data show the occurence of so-called Ultra-Long Period pressure oscillations. These latter could provoke sea ground deformations in the range of m [7]. Then, the occurence of these seiches is in agreement with previous studies about relation between tiltmetric data of Phlegrean Fields and load tides in Pozzuoli Bay [8]. 6. Conclusions A wavelet analysis of Phlegrean Fields tiltmetric and tidal data for periods from May 2008 to July 2008 has been performed. This typology of analysis has been chosen because wavelet analysis is a powerful instrument to obtain a complete picture of all frequencies (or almost, the majority) present into signals and not to lose time information about their occurence. Wavelet analysis has emphasised both classical harmonics (M2, S2 and K1) and other frequencies. These represent the occurence of seiches. These latter could be associated to these seiches to load tides due to injection of magma plumes in Phlegrean Fields magma chamber. For the future, the effective reliability of this typology of analysis will be tested by means of the use of other tiltmetric and tidal data relative to Phlegrean Fields and recordered by the same instruments in other periods of time. References [1] Orsi, G., Di Vito, M. A., and Isaia, R Volcanic Hazard Assessment at the Restless Campi Flegrei Caldera. Bulletin of Volcanolog 66 (6): [2] Agnew, D. C Strainmeters and Tiltmeters. Reviews of Geophysics 24 (3): [3] Bilham, R., Romano, P., and Scarpa, R Detecting the Unrest Episode at Campi Fegrei, Italy, by Nanosensitivity Instruments. In EGU General Assembly Conference Abstracts 12: [4] Hutter, K., Chubarenko, I. P., and Yongqi, W Physics of Lakes: Volume 3: Methods of Understanding Lakes as Components of the Geophysical Environment. Springer Science & Business Media. [5] Capuano, P., De Lauro, E., De Martino, S., and Falanga, M Analysis of Water Level Oscillations by Using Methods of Nonlinear Dynamics. International Journal of Modern Physics B 23 (28-29): [6] Torrence, C., and Compo, G. P A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79 (1): [7] Papale, P., Papale, P., Vassalli, M., Saccorotti, G., Montagna, C. P., Cassioli, A., et al. 2012, Magma Convection and Mixing Dynamics as a Source of Ultra-Long-Period Oscillations. Bulletin of Volcanology 74 (4): [8] Romano, P The Ground Deformations: Tools, Methods and Application to Some Italian Volcanic Regions. Ph.D. thesis in Physics, X Cycle, University of Salerno, Italy.