3-wavelet analysis in volcanology the case of phlegrean · pdf filewavelet analysis in...

Journal of Environmental Science and Engineering A 6 (2017) 300-307 doi:10.17265/2162-5298/2017.06.003

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

D DAVID PUBLISHING

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

calderaactually in quiescenceis 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.


302

(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 X1

and X2, fixing X1, several quantities and all function

of X2 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

X1 and X2. Then, the displacement vector:

s= d ( X 2)− d 0( X 2) (2)

where d0(X2) indicates the displacement vector at

starting time t0 = 0 seconds. Also, the baselength: l=∣d 0( X 2) (3)

and the direction:

d ' ( X 2)=d 0( X 2)

l ( X 2) (4)

Then, the deformational tilt [2]:

ΩD= z× [(s× d 0)

l] (5)

where the circumflex z is the unit vector of z axes of

Cartesian coordinate system in which particles X1 and

X2 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


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 6.25 × 10-2 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 )L

=2(C− S )

L (7)

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


304

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

√gh (8)

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].


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. ω0, 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= s0 2 jδj (9)

where s0 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 =1δj

log2(N δts0

) (10)

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

Wn(s) with index n that goes from 1 to N (this last one

has been defined in Eq. (10)). The square modulus of

Wn(s) gave the so-called local wavelet spectrum. Their

distribution is given from the Eq. (11).

∣W n(s )2∣σ 2 →

12

Pk χ 22

(11)

Eq. (11) means that local wavelet spectrum follows

a chi-square distribution modulated by a factor Pk. The

latter is a red noise Fourier spectrum. Its form is:

Pk =1− α2

1+ α2− 2αcos(2πkN

) (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 Pk

could be considered as a red noise Fourier spectrum.

This parameter is put equal to 0.72. 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


306

Fig. 5 Local wavelet spectrum of tiltmetric data recorded by North Tunnel tiltmeter in Pozzuoli for May 2008.

Fig. 6 Local wavelet spectrum of tidal data recorded by Mareographic station in Pozzuoli for May 2008.

station in Pozzuoli), two examples of these wavelet

local spectra are showed and precisely those ones are

related to May 2008. 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


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 10-4-10-2 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. 2004. “Volcanic

Hazard Assessment at the Restless Campi Flegrei

Caldera.” Bulletin of Volcanolog 66 (6): 514-30.

[2] Agnew, D. C. 1986. “Strainmeters and Tiltmeters.”

Reviews of Geophysics 24 (3): 579-624.

[3] Bilham, R., Romano, P., and Scarpa, R. 2010. “Detecting

the Unrest Episode at Campi Fegrei, Italy, by

Nanosensitivity Instruments.” In EGU General Assembly

Conference Abstracts 12: 3481.

[4] Hutter, K., Chubarenko, I. P., and Yongqi, W. 2014. 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. 2009. “Analysis of Water Level Oscillations by Using Methods of Nonlinear Dynamics.” International Journal of Modern Physics B 23 (28-29): 5530-42.

[6] Torrence, C., and Compo, G. P. 1998. “A Practical Guide to Wavelet Analysis.” Bulletin of the American Meteorological Society 79 (1): 61-78.

[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): 873-80.

[8] Romano, P. 2012. “The Ground Deformations: Tools, Methods and Application to Some Italian Volcanic Regions.” Ph.D. thesis in Physics, X Cycle, University of Salerno, Italy.

3-wavelet analysis in volcanology the case of phlegrean · pdf filewavelet analysis in...

Documents