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Design and application of an adaptivenonstationary filter for noise reductionin volcanomagnetic monitoring at MtEtnaRosalba Napoli a , Antonio Pistorio a b , Danila Scandura a , GildaCurrenti a , Filippo Greco a & Ciro Del Negro aa Istituto Nazionale di Geofisica e Vulcanologia – Sezione diCatania, Italyb Dipartimento Elettrico, Elettronico e Sistemistico – Universit´degli Studi di Catania, Italy

Available online: 14 Jul 2011

To cite this article: Rosalba Napoli, Antonio Pistorio, Danila Scandura, Gilda Currenti, FilippoGreco & Ciro Del Negro (2011): Design and application of an adaptive nonstationary filter for noisereduction in volcanomagnetic monitoring at Mt Etna, Geomatics, Natural Hazards and Risk, 2:3,291-304

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Design and application of an adaptive nonstationary filter for noise

reduction in volcanomagnetic monitoring at Mt Etna

ROSALBA NAPOLI*{, ANTONIO PISTORIO{,{, DANILA SCANDURA{,GILDA CURRENTI{, FILIPPO GRECO{ and CIRO DEL NEGRO{{Istituto Nazionale di Geofisica e Vulcanologia – Sezione di Catania, Italy

{Dipartimento Elettrico, Elettronico e Sistemistico – Universita degli Studi di Catania,

Italy

(Received 28 September 2010; in final form 23 March 2011)

Volcanomagnetic monitoring is critically dependent on the ability to detect andisolate local magnetic variations related to volcanic activity. Accurate detection of

volcanomagnetic anomalies attributable to the dynamics of volcanoes requiresremoval from measurements of the Earth’s magnetic field, fluctuations of externalorigin which may be up to hundreds of nanotesla during geomagnetic storms. The

commonly used method of taking simple differences of the total intensity withrespect to the simultaneous value at a remote reference is only partially successful.Variations in the difference fields are thought to arise principally from contrastingelectromagnetics of rock properties at magnetometer sites. With the aim of

improving the noise reduction of geomagnetic time series from the magneticnetwork of Mt Etna, we developed an adaptive filtering. Magnetic vector data areincluded as input to the filter, to account for the orientation of the magnetic field.

The filter is able to estimate and adapt the model parameters continuously bymeans of the new observations, so that the estimated signal closely matches theobserved data. Therefore, the filtering accuracy is improved in order to reduce the

residual components. Experimental data collected on Mt Etna during 2010 areanalysed to relate the field variation at a given station to the field at other sites,filtering out undesired noise and enhancing signal-to-noise ratio.

1. Introduction

Over the last few decades, volcanomagnetic monitoring has played an increasing rolein improving the knowledge of the geophysical processes preceding and accompany-ing volcanic unrest (Zlotnicki and Bof 1998, Del Negro and Currenti 2003, Napoliet al. 2008). Volcano monitoring is concerned with the detection of local magneticfield changes attributable to the dynamics of the volcano’s plumbing system andremoval of the geomagnetic field variations with no geophysical significance.

Volcanomagnetic signals are usually very small, within 1*10 nT, and must bedetected in the presence of very much larger time variations, with periods fromminutes to days, produced by natural geomagnetic fluctuations of external origin.These fluctuations make the detection of volcanic source effects more difficult and

*Corresponding author. Email: rosalba.napoli@ct.ingv.it

Geomatics, Natural Hazards and RiskVol. 2, No. 3, September 2011, 291–304

Geomatics, Natural Hazards and RiskISSN 1947-5705 Print/ISSN 1947-5713 Online ª 2011 Taylor & Francis

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may lead to misinterpretation of data. Ionospheric and magnetospheric electriccurrent systems related to solar activity are the main sources for natural geomagneticfluctuations. Time variations of the external current systems produce time-varyingmagnetic fields (external primary transitory field, Bte) that induce electrical currentsinside the Earth by electromagnetic induction. These induced currents in turnproduce time-varying magnetic fields (internal secondary transitory field, Bti).

Although the external primary field Bte may undergo rapid changes both in timeand space, the space variation of time changes is smooth and of long wavelength. Ingeneral, the spatial distribution of the primary field can be considered uniformcompared with the scale of a volcano, and therefore the classical differentialtechnique, based on simultaneous simple differences among the magnetic fieldamplitudes recorded at several sites on a volcano and a reference station, is the mostfrequently used and most reliable method to reduce this effect (Napoli et al. 2008).

Even if data reduction analysis is employed properly, both periodic and non-periodic geomagnetic changes have clearly been observed in the magnetic reducedsignals. Since fluctuations are present even when no volcanic activity is apparentlyaffecting the signal (Zlotnicki et al. 2000), it is evident that external sources areresponsible for these variations. Spatial changes in both magnetic and electro-magnetic properties of the local crustal rocks make the temporal fluctuations, withperiods from minutes to days, of the induced fields Bti different at each station(Parkinson 1983). At different positions, temporal fluctuations appear with differentproperties and characters because of the interaction of Bte with the localenvironment (Zhou and Wei 1998), but they should be interrelated by theirelectromagnetic impedances (Steppe 1979).

Over the last few decades, a variety of methodologies have been proposed toimprove the reduction process of geomagnetic time series aimed at enhancing thedetectability of volcanomagnetic effects (Currenti et al. 2005a, 2005b, Del Negroet al. 2008). In particular, a notable approach, relative to predictive methods basedon classical Wiener filters theory, was devised by Davis et al. (1981). Predictivemethods are flexible enough to allow easy changes in the filter design, varying interms of the number and choice of input channels and complexity of the filters used.However, the predictive filter technique begins with the assumption that theunderlying physical mechanism is dominated by a stationary process. Practicalfindings have shown that assuming the signal to be stationary is restrictive. If weassume the phenomenology of the process to be time-variant, a nonstationaryapproach is required to better filter out the natural geomagnetic fluctuations. In thisregard, we have been testing an approach based on an adaptive filter, and we haveinvestigated its accuracy by applying it to geomagnetic time series acquired on MtEtna by the continuously recording magnetic stations.

The adaptive filter was applied to experimental data collected during 2010 toreduce undesired noise and enhance signal-to-noise ratio. This filtering techniqueshould improve the ability to detect and isolate magnetic changes related to volcanicactivity and consequently to achieve substantial improvements in the evaluation ofthe volcanic processes.

2. Vector models analysis

Improvement in noise reduction in the geomagnetic field can be achieved if thecauses generating the different inductive responses at the different magnetic sites are

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taken into account. The internal transitory field Bti is different at each site because ofthree main effects (Davis et al. 1979): (i) contrasting conductivity; (ii) susceptibilitycontrast; and (iii) nonparallel local total fields.

Although external geomagnetic disturbances induce currents normal to thegeomagnetic variations, the direction of the electric current is deflected by localgeology. Lateral changes in electrical conductivity cause the directional anomaly ofthe electrical currents, from which the internal transient field Bti arises. While thevertical fields usually do not induct significant effects, anomalies of the horizontalcomponent correspond to shallow low-resistivity structures, as they attenuate morerapidly than the vertical anomalous component with increasing distance from thestructure of interest. In other words, the anomalous horizontal fields are morelocalized in comparison with the anomalous vertical fields. Where the electricalconductivity of the crustal rocks of a volcano changes over short distances, timechanges can vary correspondingly. Differences in underground conductivity betweentwo close (order of 10 km apart) sites will make the time variable fields different,even if the primary field from ionospheric and magnetospheric origins is the same(Parkinson 1983).

Part of the internal transitory field Bti is due to induced magnetization attributableto the susceptibility of the static crustal source (Parkinson 1983). Local geologicalstructures with magnetic susceptibility w cause a locally induced modification inresponse to a magnetic disturbance DBte of about wDBte, relying on the geometry ofthe magnetic structures and the position of the station.

Nonparallel local total fields arise principally from the heterogeneity of remanentmagnetization.

Usually the external primary field Bte, the internal secondary transitory field Bti,and local total fields have different directions at each magnetic site. Therefore,external geomagnetic fluctuations induce large disturbances in the total fielddirection which are not removed in the amplitude of total difference field when theclassical differential technique is used. This is why all methods based only on totalfield information are partially successful (Davis et al. 1981). In order to reduce thesevariations, information on the direction of the difference vector is necessary toimprove the reduction of disturbance field, and magnetic vector data should be usedin any geomagnetic data analysis.

3. Adaptive filtering

Over the last few decades the analysis of geomagnetic time series have beendominated by the constraint of stationarity (the assumption that the statistics of aprocess or system do not change with time), an assumption that can be attributed tothe need for simplification of the signal processing algorithm. Usually nonstatio-narity is regarded as an undesirable feature, in as much as it significantly increasesthe complexity of the geomagnetic data analysis; however, it can actually be a usefulfeature to produce superior results in signal processing (Hopgood 2001).

For this reason, we have been testing an approach based on an adaptive filter,where all the variables are considered not to be stationary. The filter tends to reducethe variations that are common to different sites and the output is an estimate of thesignal based on the reference site observations (see figure 1). The method allowsremoving the correlating variations in order to emphasize the local changes at themagnetic sites (Rosenberg et al. 1999).

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The technique of analysis is based on the estimation of a time-varying parametersvector trained on a sliding time window of rectangular type and fixed length in whichparameter estimates are based only on a finite number of past data samples frommagnetic stations (Hattingh 1988, Manolakis et al. 2005). The objective of theadaptive filter is to estimate the filter parameters vector continuously by minimizinga cost function represented by the Mean Squares Error (MSE) between the filteroutput and the observed data (Manolakis et al. 2005). The filter parameters areupdated iteratively using new observations. By means of a weighted linearcombination of mi past samples of p input signals u1(t), . . . , up(t) and from n pastsamples of the sequence to be filtered y(t), it is possible to obtain an estimate of y(t)through time-varying filter parameters aij(t), as follows:

yðtÞ ¼Xni¼1

a0i tð Þy t� ið Þ þXp

i¼1

Xmi

j¼0aij tð Þui t� jð Þ ð1Þ

The residual component (the difference between the observed value y(t) at theparticular site and the estimated value y(t)) contains only the local effects that arerelated to the internal dynamics of the site (Hattingh 1988).The above expression (1)in matrix form becomes:

yðtÞ ¼ uðtÞTaðtÞ ð2Þ

where a (t) is the parameters vector and u(t) the input vector, defined as:

aðtÞ¼½a01ðtÞ ::: a0nðtÞ a10ðtÞ ::: a1m1ðtÞ a20ðtÞ ::: a2m2

ðtÞ ap0ðtÞ ::: apmpðtÞ�T

uðtÞ¼½yðt�1Þ ::: yðt�nÞ u1ðtÞ ::: u1ðt�m1Þ u2ðtÞ ::: u2ðt�m2Þ upðtÞ ::: upðt�mpÞ�T

The values of the aij(t) parameters are determined by minimizing the MSEbetween the observation y(t) and the estimated value y(t) through the model inequation (2). That leads to the solution of a linear inverse problem of a system ofN equations:

yðtÞ ¼ UðtÞaðtÞ

Figure 1. Adaptive filter structure. The objective of the adaptive filter is to estimate andupdate the filter parameters continuously by means of the new observations (Reference signal),so that predictions (Filter Output) closely match the observed data (Signal).

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where y(t) is the vector of observed data to be filtered and U(t) the data matrixdefined as:

U ðtÞ¼

yðt�1Þ . . . yðt�nÞ u1ðtÞ . . . u1ðt�m1Þ . . . upðtÞ . . . upðt�mpÞyðt�2Þ . . . yðt�n�1Þ u1ðt�1Þ . . . u1ðt�m1�1Þ . . . upðt�1Þ . . . upðt�mp�1Þ

.. . . . . .. . . .. . . . . .. . . . . .. . . . .. .yðt�NÞ . . . yðt�n�Nþ1Þ u1ðt�Nþ1Þ . . . u1ðt�m1�Nþ1Þ . . . upðt�Nþ1Þ . . . upðt�mp�Nþ1Þ

2664

3775

The linear inverse problem can be simply solved using the Least Mean Squares(LMS) algorithm, where the parameters vector is found as:

aðtÞ ¼ ½UðtÞTUðtÞ��1UðtÞTyðtÞ ð3Þ

In the case of the nonstationary approach, the LMS algorithm must be runcontinuously and the a(t) parameters vector should be recalculated using newavailable data. The above expressions are recomputed, updating the data matrix withthe new vector of data at time tþ1. The LMS algorithm, after performing theupdates on the data matrix U(t), calculates again the solution, applying equation (3).This procedure is not computationally efficient, because the evaluations of the matrixinverses may require a long computational time and an adaptive algorithm might bepreferable (Kuruoglu 1998).

The classical and simplest adaptive algorithm adjusts the linear filter parameterswith every coming sample by using the gradient descent method (Hattingh 1988). Itavoids the re-computation of the inverse of the data matrix. This method finds aminimum of the MSE (E) at time t between the real vector data y(t) and theestimated values y(t) by estimating the gradient. Using the basic equation for thegradient descent method, the a(t) parameters vector is estimated as:

aðtÞ ¼ aðt� 1Þ � brE ð4Þ

where b is the learning rate, and the differential operator r is calculated with respectto the parameters vector a(t) (Hattingh 1988).

The estimate gradient is given by (Hattingh 1988):

rE ¼ �2½yðtÞ � yðtÞ�uðtÞ ð5Þ

Substituting equation (5) in equation (4), the expression for updating the parametersvector is given by:

aðtÞ ¼ aðt� 1Þ þ 2beðtÞuðtÞ ð6Þ

The values of the parameters at time t depend on: (i) the values of the parameters attime (t–1); (ii) the error between the real value and the estimated value obtained withthe previous parameters; and (iii) the input vector at time t. The learning ratedetermines the speed by which the parameters of adaptive filter are updated. Thisalgorithm has the drawback of being strongly dependent on the b parameter, whichlargely affects the stability and convergence speed of the algorithm. For stablebehaviour of the LMS algorithm, the b parameter must satisfy the followingconstraint (Hattingh 1988, Haykin 1996): 05 b51/lmax, where lmax is the largesteigenvalue of the auto-correlation matrix of U.

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An alternative to LMS is represented by Recursive Least Mean Squares (RLMS)algorithm, which does not suffer from these drawbacks. RLMS may be considered asa stochastic Gauss–Newton optimization algorithm (Kuruoglu 1998). Gauss–Newton algorithms are known to converge onto the minimum of the MSE fromany starting point in one step, with the assumption that the first two orderderivatives of the MSE with respect to the parameters vector are continuous, andtheir values are known at every point. The derivation of the RLMS algorithm isbased on the matrix inversion lemma or Woodbury’s identity (Kuruoglu 1998). Thisalgorithm is performed in a loop and, as new samples are available, a newparameters vector, a(t) is computed as follows:

aðtþ 1Þ ¼ aðtÞ þ kðtþ 1Þ½yðtþ 1Þ � yTðtþ 1ÞaðtÞ� ð7Þ

where a(t) is the previous parameters vector, y(tþ1) is the output value at time tþ1,yT(tþ1)a(t) is the estimated output at time tþ1 obtained with the parameters vectorsestimated at time t, and k(tþ1) is a weight factor defined as:

kðtþ 1Þ ¼ ½Uðtþ 1ÞTUðtþ 1Þ��1yðtþ 1Þ ð8Þ

In this way, the filter coefficients change and adapt recursively. In addition to theadvantage of conceptual and computational simplicity, this technique is suitable forextracting common changes from geomagnetic signals when a correlated referencesignal is available.

4. Noise reduction in Etna volcanomagnetic series

During the last few years, the detection of clear magnetic signals associated with therenewal of the volcanic activity (Del Negro and Currenti 2003, Napoli et al. 2008) ledto an increase in magnetic monitoring of Mt Etna. A permanent magnetic networkequipped with Overhauser effect magnetometers has been set up since the end of1998 (Del Negro et al. 2002). At present, the network consists of five scalarmagnetometers (BVD, BCN, PTL, PDN, DGL) and two magnetic gradiometers(CST, PDG), which simultaneously sample the Earth’s magnetic field at 5 s. Eachmagnetic gradiometer station consists of two sensors (namely CSTsouth, CSTnorth,PDGsouth and PDGnorth) horizontally spaced by about 50 m. Stations are locatedat elevations ranging between 1700 and 3000 m a.s.l. along a north–south profilecrossing the summit craters. The magnetic reference station Cesaro (CSR) is installedfurther west (about 27 km) on the Nebrodi Mountains (see figure 2). During 2009 anew magnetic station (CSRV) equipped with a vectorial magnetometer (resolution0.1 nT) was installed 30 m from the scalar magnetometer of CSR. The vectorialmagnetometer, devised at INGV-Roma 2 Section, guarantees uninterrupted workingunder harsh environmental conditions with a high long-term stability and restrainedthermal drift (Palangio et al. 2004). Magnetic field measurements are usuallydifferentiated with respect to the reference station (CSR) to isolate local magneticfield changes and cancel out common noise from ionospheric and magnetosphericsources.

In figure 3, the 10-min means of total intensity variations from 21 January to 13May 2010 observed at magnetic stations relative to CSR are shown. We ignored theDGL and CST stations which have been running for a shorter time interval.

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Although the magnetic disturbances are reduced by about 95%, significantvariations are observed in the differenced data in correspondence of strong externalactivity (geomagnetic K index values more than 5; see figure 3), when highgeomagnetic components clearly appear. These disturbances can seriously hinder theaccurate detection of volcanomagnetic signals, especially when we expect only asmall volcanomagnetic signal either due to weak volcanic activity or the largedistance between the source zone and the observation sites.

4.1 Nonstationary analysis

To improve the reduction process of geomagnetic time series gathered onMt Etna, weapply the nonstationary filter using the RLMS algorithm by means of the vector fieldcomponents of CSRV and total field from Etna magnetic array as reported below:

yðtÞ ¼Xni¼1

a0i tð Þy t� ið Þ þXm1

i¼0a1i tð ÞX t� ið Þ þ

Xm2

i¼0a2i tð ÞY t� ið Þ þ

Xm3

i¼0a3i tð ÞZ t� ið Þ

þXm4

i¼0a4i tð ÞCSR t� ið Þ ð9Þ

Figure 2. Schematic map of the Etna summit area and locations of magnetic stations. Insetshows the position of the reference stations.

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where y is the station to be filtered, X, Y, Z are the vector components of CSRV,CSR is the total field recorded at reference station. The choice of parameters numbern and mi relies on the estimation of a quality factor using the Akaike InformationCriterion (Akaike 1974). An efficient filter was accomplished when the number offilter coefficients m1¼m2¼ . . . ¼m4 reaches 5. The inclusion of more coefficientsled to no further improvements. Moreover, since our purpose is to estimate thecomponents correlated with the reference station and to evidence the volcano-related

Figure 3. 10-min mean differences of total magnetic intensity with respect to CSR stationfrom 21 January to 13 May 2010. Geomagnetic storms occurred in April and May arehighlighted (top). The local K index values are also shown (bottom).

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signal in the residual components of Etna’s magnetic station, the past samples of thesignal to be filtered were not used as input leading to n¼ 0. The accuracy of the filterwas investigated by applying it to geomagnetic time series recorded from themagnetic network on Mt Etna between 21 January and 13 May 2010 whensignificant geomagnetic storms (see figure 3) due to high solar activity occurred. Sothis period is particularly indicated to assess the performance of filtering techniquefor reducing the geomagnetic disturbances which affect the magnetic fields atstations. The response to external magnetic fields also depend on the latitude of sites.It has been noted that the amplitude of variation in H component at the highestlatitude stations is stronger than that at lower latitudes. Therefore, it is advisable touse data from observatories of geomagnetic latitude close to the monitoringnetwork. A correlation analysis, between total field observed at CSR and thoserecorded from Etna stations, was carried out to verify whether the external primaryfields are sufficiently uniform over the studied area. During the whole period,magnetic signals show significant correlations (see table 1); therefore, it is reasonableto assume that vector field data from CSRV (just few metres from CSR) are alsoconsistent to be used for this processing.

The 10-min average of X, Y, and Z components are analysed (see figure 4). Theresidual components of the signals from Etna magnetic stations are computed (seefigure 5) and their associated standard deviations compared to that obtained fromthe differential method (see table 2).

The results show that the nonstationary filtering process is carried out successfully,especially if we look at the low residual components obtained during the mostdisturbed days. More importantly, no explicit choice of the period of the filterdefinition has to be made to accommodate the nonstationary behaviour of the dataas, due to the adaptive structure, parameters vector is updated continuously on asample-to-sample basis.

The adaptation of the parameters vector allows enhancement of the filteringprocess as their updating is continually addressed to minimize the cost function.Even if the geomagnetic signals change their dynamical behaviours because ofvariations in the geomagnetic activity (see figure 3), the filter is able to adapt itself tothe new conditions. The adaptive approach is found to be superior over the wholeperiod at each station. After filtering the data sets, the residuals have a very lowstandard deviation (STD) in comparison with that obtained by the differentialmethod. At all stations, the STD is reduced to a range from 0.6 to 0.3. The ratio ofthe STD between the residuals from the adaptive filter and from the differential

Table 1. Correlation coefficients between total magnetic field from Mt. Etna array and totalmagnetic field at CSR during 2010.

BCN BVD PDGnorth PDGsouth PDN CSR

BCN 1.000 0.983 0.988 0.982 0.992 0.981BVD 0.983 1.000 0.996 0.995 0.994 0.993PDGnord 0.988 0.996 1.000 0.997 0.996 0.990PDGsud 0.982 0.995 0.997 1.000 0.997 0.995PDN 0.992 0.994 0.996 0.997 1.000 0.996CSR 0.981 0.993 0.990 0.995 0.996 1.000

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method is within 1/3 and 4/5. The improvements with respect to the simpledifferential method are especially gainful during periods of strong magnetic storms.

To evaluate and appreciate the efficiency of filtering procedure, the residuals wereanalysed not only in the time domain, but also in the frequency domain. The analysisof frequency residual components is useful to verify the ability of the filter to capturethe frequency domain characteristics. The power spectra of residuals are shown infigure 6. The residuals calculated by taking differences between stations aredominated by large power at diurnal periods. After adaptive filtering, the largecontribution of the diurnal component is strongly reduced. However, PDGnorth,PDGsouth and PDN stations show increased amplitude at frequencies just below thediurnal peak. It seems that the main contribution of the diurnal component is shiftedto lower frequencies.

Figure 4. Total magnetic field (F) and vector components (X, Y, Z) from CSR and CSRVreference stations.

Table 2. Standard deviations of magnetic stations obtained for differential technique andadaptive filter.

Filtering technique BCN BVD PDGnorth PDGsouth PDN

10-minutes means difference 1.770 0.962 1.128 0.784 0.736Nonstationary analysis 0.605 0.630 0.666 0.621 0.342

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5. Discussion and conclusions

Up until now, the filtering of geomagnetic noise has been a very complex probleminvolving the development of algorithms to reduce transient fields, which could be ofthe same order as the volcanomagnetic signal to be detected.

The reduction of residual components is the first objective in the detection ofmagnetic anomalies because of their small magnitude. If very rapid changes in thefield are indeed characteristic of volcanomagnetic events, then filtering techniques forremoving short-period geomagnetic noise due to the induction effect may be veryhelpful in increasing the detectability of volcano-related magnetic field changes.

In this article, we propose an adaptive algorithm, based on the use of magneticvectorial data, to properly process geomagnetic time series acquired in volcanic area.The algorithm does not require a complex implementation and it is extremely easy todesign. Data from vector component magnetometer permit a better estimate of theground currents induced from the external transitory magnetic field. The magneticvector data acquired at CSRV, which is only 30 km away from the magnetic networkof Etna, were used as input to the filter. This allowed the orientation of thedisturbance field to be accounted for, and therefore guaranteed good performance ofthe filtering process. The adaptive vectorial filtering developed works well bothduring quiet days and strong magnetic storms. The diurnal solar variation, which isthe main component of the transient field, is reduced at almost all stations. Filtered

Figure 5. Residual components (the difference between the observed values and theestimated values) after filtering 10-min means of total magnetic intensity at Etna stations.

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signals of PDGnorth and BCN stations, located on the northern and southern flanksof the volcano, respectively, still have a certain high variation during the magneticstorm in May 2010. This could be explained by considering that the adaptive filteringmay enhance the effects produced by the electromagnetic response of local geologicalstructures. To support this hypothesis, it is worth noting that in the filtered signal ofPDGsouth station, which is only 50 m away from PDGnorth, the main componentof the transient field is better reduced. Local magnetic surveys at the sites of themonitoring network as well as installation of a new vectorial magnetometer in thesummit area could provide new insights about the local site characteristics and betterclarify the internal dynamics of the sites. This information could also be useful toexplain the different behaviours observed in the power spectra of residuals and, inparticular, the shift in the frequency showed by PDN and PDG stations. Bothstations are located on the northern flank of the volcano characterized by structuralcomplexity (dykes, rift, faults, etc.). To date, there have been no geological and/or

Figure 6. Power spectrum of the difference field at magnetic stations (black) and the powerspectrum of their residual components after filtering (red). (Available in colour online).

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geophysical studies describing in detail medium magnetization heterogeneity(Currenti et al. 2011) of this area which, reasonably, could be the main reason forthe different behaviours of geomagnetic signals.

Our findings support that the vectorial nonstationary technique is particularlysuitable in a real-time monitoring system, given the low computational cost. Sincethe filter parameters are updated at each step, as new data are available, it does notrequire a previous data set over which the filter parameters have to be estimated.This method was especially effective in reducing the residuals associated with diurnalvariations, thus advancing the detecting volcanomagnetic events that may also beindicators of ongoing dynamic processes during times of apparent rest.

Acknowledgements

We are indebted to all personel of the Division of Gravity and Magnetism of INGV-Sezione di Catania who ensure the regular working of the permanent magneticnetwork at Mt Etna. We are grateful to the Associated Editor, Luciano Telesca, andtwo anonymous reviewers for their helpful comments.

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