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Bulletin of the Seismological Society of America, Vol. 97, No. 1B, pp. 184–197, February 2007, doi: 10.1785/0120050252

Attenuation and Source Parameters of Shallow Microearthquakes

at Mt. Etna Volcano, Italy

by Elisabetta Giampiccolo, Salvatore D’Amico, Domenico Patane, and Stefano Gresta

Abstract We estimated the attenuation laws of high-frequency seismic waves inthe shallow crust (depth �5 km) and earthquake source parameters by using a se-lected data set of 320 shallow events (2.6 � MD � 4.2), recorded at Mt. Etna volcanoduring the last two flank eruptions occurring in 2001 and 2002–2003. The qualityfactor (Q) was estimated from spectra of P and S waves for 24 stations of the localpermanent network by applying a spectral ratio technique. The results show varia-tions in both QP and QS as a function of frequency, according to the power lawQ � Q0 f n, with n ranging between 0.3 and 1.3 for P waves and between 0.2 and0.9 for S waves. As typical of volcanic environments, strong azimuthal variations ofQP were also found, suggesting the presence of local strong lateral heterogeneitiesand/or of fluid-filled cracked volumes. After correction for attenuation, we estimatedthe source parameters (seismic moment, source radius, and stress drop) of a subsetof 66 shallow events, under the assumption of a circular dislocation. The estimatedseismic moments M0 range from 1013 to 1015 N m. The source radii (r) are confinedbetween 100 and 1000 m and stress drop (Dr) ranges between 0.2 MPa and about4 MPa. Combining the source parameters obtained in this study with those calculatedby Patane et al. (1997) for an old data set of smaller microearthquakes (109 � M0 �1014 N m) recorded in the same area, we re-evaluated the scaling relationship betweenseismic moment (M0) and corner frequency ( fc) for the earthquakes with M0 rangingbetween 1013 and 1015 N m. We confirm that microearthquakes at Mt. Etna seem notto obey a scaling relationship, as generally observed for moderate to large�3M � f0 c

earthquakes, as the slope of the scale dependence is about 4.3 or higher. Assumingthat this dependence is real, within the uncertainty in the results, a departure fromthe self-similarity exists for the volcanotectonic earthquakes at Mt. Etna.

Introduction

The resolution of source parameters with decreasingmagnitudes is of fundamental interest in the derivation ofearthquake-scaling relationships and the determination ofthe stress drop of local earthquakes. This is of particularimportance in complex volcanic environments, such asMt. Etna volcano, where foreshock-mainshock-aftershock se-quences are rarely observed and the seismicity is character-ized by microearthquakes that seldom exceed magnitude 4.0.Also the evaluation of seismic attenuation represents a maingoal for the quantitative estimate of the parameters whichcontrol the propagation of elastic waves and the source pro-cesses acting inside volcanoes. The shallower crustal materialmay undergo significant spatial and temporal changes inphysical properties affecting the attenuation structure. Infact, pressure, temperature, saturation state of the rocks, frac-tures, and lithologic variations are all factors known to affectthe quality factor (Q) of the medium, which is inverselyproportional to the attenuation (e.g., Spencer, 1981). In vol-

canic areas, low Q-values are usually associated with frac-tured fluid-filled systems (Zucca et al., 1994) or to partialmelting and/or magma chambers (e.g., de Lorenzo et al.,2001; Tusa et al., 2004; De Gori et al., 2005; Martınez-Arevalo et al., 2005).

Both path attenuation and site effects are crucial inseismic-source studies. In fact, they may strongly influencethe appearance of seismograms and their spectral shape, af-fecting the low-frequency level and hindering the calculationof the corner frequency. This problem is at its worst in thestudy of microearthquakes because the higher frequenciesneeded to define the smaller sources are strongly affected byattenuation along the path and by near-surface site effects(Abercrombie, 1995). Therefore, a proper knowledge ofthese mechanisms is required for the appropriate determi-nation of source dimensions. Some previous studies haveexamined the crustal Q-structure at Mt. Etna volcano. In-vestigations on attenuation of seismic waves were performed

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 185

Figure 1. Map showing the Mt. Etna seismic net-work (triangles) and the location of the selected earth-quakes. Labels refer to the stations used in this study.Gray and white circles represent the earthquakes re-corded before and during the 2001 and 2002–2003eruptions, respectively. East–west and north–southcross sections are also reported.

by using both coda waves (Del Pezzo et al., 1987; Del Pezzoand Patane, 1992; Ibanez et al., 1993) and direct P and Swaves (Patane et al., 1994, 1997). These studies showed thatthe effect of attenuation on seismic radiation at Mt. Etna isconsiderable. Patane et al. (1994) reported significant vari-ations of Q from P waves (QP) as a function of depth. Inparticular, a drop in QP-values for earthquakes located atdepths less than 5 km was observed (Patane et al., 1997),supporting the idea that the upper part of the crust and theshallow volcanic layers are characterized by low Q. How-ever, detailed analyses were limited only to few earthquakesrecorded at a few stations; the poor data set of events re-corded at depth less than 5 km available at that time did notallow the authors to infer reliable and definitive attenuationlaws for shallower depths. Since January 2001, the improve-ment of the permanent seismic network on Mt. Etna volcanoand the high rate of shallow seismic activity, which precededand accompanied the last eruptions, have generated muchnew data at shallow depths. Thus, more accurate analysesare now possible. Recently, a P-wave attenuation tomogra-phy study was carried out, down to 15 km depth, using high-quality data recorded between 1994 and 2001 (De Gori etal., 2005). Results from this first tomography have been re-fined in the shallow layers (at about 2 km) of the volcanicedifice by Martınez-Arevalo et al. (2005), further confirmingsignificant variations of QP as a function of depth and azi-muth. As commonly adopted, to image the attenuation struc-ture with local earthquakes (Scherbaum, 1990; Lees andLindley, 1994; Haberland and Rietbrock, 2001; Rietbrock,2001; Eberhart-Phillips and Chadwick, 2002), a frequency-independent Q was assumed in both studies. However, manyprevious studies carried out in the area (e.g., Del Pezzo et al.,1987; Del Pezzo and Patane, 1992; Ibanez et al., 1993; Pataneet al., 1994, 1997) showed a dependence of Q on frequency,according to the power law Q � Q0 f n, at least in the 2- to10-Hz frequency band (Patane et al., 1994).

In the present article, we use a data set of about 300shallow (depth �5 km) microearthquakes, selected amongmore than 3000 events recorded during two intense seismicswarms that preceded and accompanied the 2001 and 2002–2003 flank eruptions. The quality factor Q is estimated byusing seismic spectra of P and S waves for 24 stations byapplying a spectral ratio technique (Tsujura, 1966). Varia-tions of QP and QS as a function of frequency are investigatedin detail, and an estimate of the source parameters (seismicmoment, source radius, and stress drop) and the scaling re-lations for a subset of earthquakes is also attempted.

Instruments and Data

Data from 24 stations (labeled in Fig. 1) of the Mt. Etnapermanent seismic network, run by Istituto Nazionale diGeofisica e Vulcanologia of Catania (INGV-CT), were ana-lyzed. Eight of the stations considered in this analysis wereequipped with three-component velocity sensors, whereas the16 remaining stations were equipped with one-component

short-period (1 sec) velocity sensors; all stations were lo-cated on volcanic products. Although other stations wereoperating during the two seismic sequences analyzed, dataat these stations exhibited either poor signal-to-noise ratio,no sufficient time delay between P and S phases, or saturatedP waves, making them poor candidates for accurate seismic-attenuation analysis. Signals from remote stations weretransmitted in real time/near-real time to Catania (by radio,local area network, or cable), where they were continuouslyrecorded on drums and digitized at a sampling rate of 160 Hz(analog stations) and 125 Hz (digital stations). The antialias-ing filter was set at 35 Hz.

Earthquakes have been located by using the HYPO-ELLIPSE code (Lahr, 1989), which takes into account thedifference in altitude of the seismic stations with a seven-layer, one-dimensional velocity model (Hirn et al., 1991). Theselected data set (Fig. 1) consists of 320 well-located events(erh �1 km, erz �1 km, gap �100�, and rms �0.20 sec),with duration magnitude (MD) ranging between 2.6 and 4.2,and focal depth less than 5 km. All earthquakes used in thisstudy have tectonic-earthquake-type waveforms, consistentwith double-couple source mechanisms, with high-frequencycontent, sharp first arrivals, and clear S phases (see Patane andGiampiccolo, 2003). Their spectra are characterized by a rela-tively flat low-frequency response below the corner frequencyand rapid fall-off above the corner frequency.

Attenuation Analysis: QP and QS Estimate

QP and QS in the upper 5 km of the crust were estimatedby using a spectral ratio method known as the single-station

186 E. Giampiccolo, S. D’Amico, D. Patane, and S. Gresta

method (Tsujura, 1966). Following this technique, the ob-served amplitude A( f ) of body waves at a frequency f canbe expressed by the relationship:

�pft/QA ( f )R( f )e0A( f ) � , (1)r

where A0( f ) is the spectral amplitude at the source, R( f ) isthe site-response function, r is the source-to-receiver dis-tance, and e�pft/Q is the attenuation term with t being thetravel time and Q the quality factor. Having assigned twofrequencies f1 and f2, the natural logarithm of the ratio of thecorresponding amplitudes is:

A( f ) A ( f ) R( f ) p( f � f )t1 0 1 1 1 2ln � ln � ln � . (2)A( f ) A ( f ) R( f ) Q2 0 2 2

If A0(f1)/A0(f2) and R(f1)/R(f2) are constant and independentof travel time, the function ln[A(f1)/A(f2)] plotted versus t,will display the slope �p(f1 � f2)/Q (e.g., Patane et al.,1994; Tselentis, 1998).

The preceding relationships are based on the assump-tions that Q is constant over the frequency band studied andthat the source spectrum is similar for all the earthquakesanalyzed. The latter assumption may hold when microearth-quakes lying within a small magnitude range are used. Forthis analysis we selected a subset of 270 events with MD

ranging between 2.6 and 3.0.To perform the spectral analysis of body waves for the

selected earthquakes, we used 1-sec windows for P wavesrecorded on the vertical component to avoid contaminationfrom S waves; 2-sec windows were chosen for S waves,recorded on the horizontal components. Therefore, only theeight three-component stations were considered for QS es-timation. We applied a cosine taper window to both ends ofthe signal for a width of 25% of the full-time length, anddisplacement spectra were computed by fast Fourier trans-form (FFT). Figure 2 shows an example of a seismogramrecorded at a three-component station (ESPC) and relatedP-and S-wave displacement spectra, not corrected for instru-mental response.

To evaluate Q, equation (2) was applied to spectral data,appropriately smoothed by a three-point moving-averagewindow to increase the stability of the results. The naturallogarithm of the ratio [A( f1)/A( f2)] was plotted versus t, whichwas then fitted by least-square linear regression (Fig. 3).Spectral amplitudes were calculated over 2.5-Hz-wide fre-quency bands centered at f1 and f2. We set f2 � 2.5 Hz andf1 at 5, 7.5, 10, 12.5, 15, and 17.5 Hz for both P and S waves.In general, scatter in data points around the regression lineis small for all the frequency bands. The obtained QP- andQS-values estimated at reference frequencies located in themiddle of each considered bandwidth are reported in Tables1 and 2, respectively, together with the 1r standard devia-tion. In general, the standard deviation does not exceed 30%.

The stations listed in Tables 1 and 2 are arranged in descend-ing order of the number of data used. The results show var-iations of both QP and QS as a function of frequency, accord-ing to the power law Q � Q0 f n, with the frequencydependence coefficient n ranging between 0.3 and 1.3 for Pwaves and between 0.2 and 0.9 for S waves (Tables 3 and 4).By averaging the Q-values obtained at all stations we cal-culated the average attenuation laws QP � 16 � 1.2f 0.8�0.1

and QS � 32 � 1.1f 0.5�0.03, for P and S waves, respectively.If we look at the Q-values obtained at each station and fre-quency, we observe that the stations located in the centraland western sectors generally give lower values of QP thanthe stations located on the eastern sector, at least at low fre-quencies (Fig. 4a). Similar observations come from the esti-mates of QS (Fig. 4b). In fact, we observe lower values of QS

at stations ECPN and ETFI, located in the central area nearthe summit craters, and at station EMGR. Finally, the QS /QP

ratio is, for most of the stations, greater than 1 (Table 5),whereas at stations ECPN and EMGR and at lower frequen-cies at station ETFI QS /QP is less than 1 (�0.6).

Source Parameters from Spectral Modeling

The study of earthquake-source parameters and faultingprocesses of small earthquakes is important for clarifyingthe scaling of earthquake sizes and stress drops. Althoughkinematic earthquake-source models are not satisfactory interms of rupture dynamics, they provide reliable results interms of stress drop and coseismic slip distribution. Source-parameter studies of microearthquakes are usually per-formed in the frequency domain and the spectra of the eventsare largely interpreted by using simple models (e.g., Aki,1967; Brune, 1970; Madariaga, 1976; Boatwright, 1978,1980).

To calculate the source parameters of the microearth-quakes shown in Figure 1, we selected from the whole dataset only the earthquakes shared by the largest number ofstations (ECCS, ECVS, EMFO, EMGR, EMPL, ENCS, EPET,ERSA, ESVO, EVNA, ESPC, EMVT), for a total of 116 events.The P-wave spectrum at each station was computed on a128-sample window (corresponding to 0.8 sec, at a samplingrate of 160 Hz) starting from the P onset, appropriately se-lected to avoid contamination from the S phase, and multi-plied by a Hanning window to avoid affecting the onset.Then, spectra were corrected for instrumental response andfor geometrical spreading by normalizing them to stationEMFO (chosen as the one displaying the most complete dataset). Although most of the selected stations are located onbasement hard rocks exposed at the surface, spectral ratioscomputed with respect to station EMFO show, at some sta-tions (e.g. EVNA, ECCS, ECVS, EPET), a sharp departurefrom a flat response. Such effects disappear when spectra arecorrected for the attenuation term by using the�pft/Q ( f )

PeQP(f) factor previously calculated for each station. This sug-gests that the station site effects and path attenuation arestrongly coupled in affecting the observed ground motion.

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 187

Figure 2. Example of seismograms recorded at station ESPC (left) and of P- andS-wave displacement spectra, uncorrected for the instrumental response (right).

In Figure 5 examples of earthquake spectra, correctedfor instrumental response, attenuation, and normalized toEMFO station, are shown together with the average spec-trum. Looking at the spectral shapes (Fig. 5), we observethat the performed corrections are satisfactory and that theaverage spectrum represents the behavior of the individualspectra well.

The average spectrum was inverted using the simplifiedfunctional form of the source spectrum with a single cornerfrequency, described by the Boatwright (1978, 1980)equation:

2c 1/2S( f) � X /[1 � ( f/ f ) ] (3)0 c

In equation (3), the spectral parameters X0, fc, and c repre-sent the low-frequency amplitude level, the corner fre-quency, and the high-frequency spectral fall-off beyond the

corner frequency, respectively. This simplified functionalform of the spectrum well matches the spectral shapes ofmicroearthquakes at Mt. Etna (e.g., Patane et al., 1994,1997). The following conditions were met to obtain spectralparameters by the asymptotic fit of log-log displacementspectra: number of spectra used to compute the averagespectrum �4 (about 65% of the whole subset of 116 events)and correlation coefficient between the average spectrumand theoretical model �0.8 (about 90% of the whole subsetof 116 events).

The high-frequency decay rate c ranges between 2 and3 and corner frequencies range from 1.8 to 5.5 Hz (Table 6).In Figure 6 the P-wave average spectra of some of the earth-quakes shown in Figure 5 are reported together with the besttheoretical fit and the spectrum of the background noise.

Source parameters (seismic moment, stress drop, andsource radius) were then calculated for a total of 66 events

188 E. Giampiccolo, S. D’Amico, D. Patane, and S. Gresta

Figure 3. Example of least-squares estimate of the frequency-dependent qualityfactor QP at station ERSA, with f2 � 2.5 Hz and f1 ranging between 5 and 17.5 Hz.

(Table 6). The seismic moment (M0) was estimated by thefollowing relationship (e.g., Keilis-Borok, 1959):

X03M � 4pqm R (4)0 P FUh,�

where q is the density of the medium (2700 kg/m3), R is thehypocentral distance (here assumed as the source-EMFO sta-tion distance), mP is the P-wave velocity computed as a func-tion of depth, F is the free surface factor (assumed as 2), andUh,� is the mean radiation pattern (0.4) (e.g. Patane et al.,1997). The estimated seismic moments (M0) range between1013 and 1015 N m (Table 6).

The source radius (r) and the stress drop (Dr) were cal-culated following Madariaga (1976):

VPr � 0.32 (5)fc

7M0Dr � . (6)316r

Source radii range from about 100 to about 1000 m, whereasstress drops are confined between 0.2 MPa and about 4 MPa(Table 6). To extend the earthquake moment range our re-sults were combined with those obtained by Patane et al.(1997), who calculated the source parameters of a small dataset of microerthquakes (about 50 events), with local mag-nitude 0.8 � ML � 3.5 and depth between 1 and 25 km(40% of the events were located at depth less than 5 km).Since they estimated seismic moments ranging between 109

and 1014 N m, a total data set of events with seismic mo-ments ranging between 109 and 1015 N m was available forscaling law derivation in the present study. In Figure 7a wereport the relationship between seismic moment and sourceradius, together with the lines of constant stress drop. A cleardependence of the seismic moment on source dimension andstress drop can be observed. Moreover, the trend of seismic

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 189

Table 1QP Values and Relative Errors (1r) at Different Seismic Stations and Central Frequencies, Obtained by Spectral Ratios

with f2 � 2.5 Hz and f1 Ranging between 5 and 17.5 Hz

QP � 1r

StationName

No. ofData 3.75 Hz 5 Hz 6.25 Hz 7.5 Hz 8.75 Hz 10 Hz

EMFO 195 46 � 12 44 � 9 55 � 12 69 � 14 59 � 9 61 � 9EMGR 183 73 � 16 59 � 9 68 � 10 86 � 13 88 � 12 93 � 13ECVS 176 57 � 11 79 � 15 84 � 14 96 � 17 96 � 15 99 � 14ERSA 157 51 � 11 57 � 12 60 � 11 75 � 14 90 � 16 101 � 18EPET 151 51 � 11 69 � 15 81 � 16 81 � 14 82 � 12 87 � 12ENCS 148 40 � 8 39 � 6 55 � 9 52 � 7 61 � 9 83 � 12EPIS 139 55 � 8 66 � 9 71 � 8 93 � 11 111 � 15 143 � 22ETAR 134 49 � 11 46 � 8 55 � 9 58 � 9 85 � 17 87 � 17ECCS 133 53 � 13 79 � 21 75 � 17 86 � 20 88 � 19 96 � 20EVNA 133 78 � 22 100 � 25 125 � 35 159 � 45 207 � 60 257 � 80EMPL 111 21 � 4 53 � 14 76 � 23 58 � 15 68 � 18 90 � 27ECDV 93 45 � 14 52 � 13 76 � 21 86 � 24 94 � 23 116 � 27EZPO 73 118 � 39 151 � 50 140 � 39 177 � 45 228 � 77 326 � 116ETFI 56 60 � 18 35 � 10 28 � 7 42 � 11 37 � 8 44 � 10ESPC 50 47 � 10 58 � 13 67 � 14 67 � 11 65 � 10 70 � 10EVNR 46 24 � 6 29 � 7 35 � 8 47 � 11 62 � 17 88 � 25EMVT 42 21 � 5 36 � 8 51 � 14 59 � 15 73 � 19 76 � 18ESVO 41 17 � 4 32 � 9 36 � 8 42 � 13 90 � 38 124 � 48EMDV 39 29 � 11 52 � 22 39 � 10 72 � 25 57 � 16 50 � 12EPMN 37 114 � 44 179 � 72 126 � 36 175 � 63 213 � 84 384 � 145ECIS 37 25 � 9 43 � 15 43 � 13 36 � 8 64 � 21 76 � 26ECTS 34 50 � 19 61 � 21 69 � 23 123 � 49 159 � 63 150 � 51ECPN 30 22 � 11 24 � 9 34 � 12 45 � 18 43 � 16 —ECBD 21 61 � 26 69 � 24 108 � 45 75 � 22 80 � 18 105 � 29

Table 2QS Values and Relative Errors (1r) at Different Seismic Stations and Central Frequencies, Obtained by Spectral Ratios

with f2 � 2.5 Hz and f1 Ranging between 5 and 17.5 Hz

StationName

No. ofData

QS � 1r

3.75 Hz 5 Hz 6.25 Hz 7.5 Hz 8.75 Hz 10 Hz

ECCS 85 86 � 18 112 � 22 119 � 20 111 � 16 115 � 16 121 � 16EMPL 78 76 � 18 85 � 18 95 � 20 108 � 23 116 � 24 128 � 27ESPC 32 68 � 14 87 � 15 86 � 12 88 � 11 93 � 11 93 � 10ECPN 23 17 � 7 20 � 6 21 � 5 24 � 6 29 � 8 31 � 8ETFI 22 27 � 7 30 � 6 40 � 7 49 � 9 53 � 9 58 � 10EMVT 21 95 � 40 94 � 33 80 � 21 85 � 23 82 � 21 90 � 21ESVO 19 72 � 33 95 � 44 99 � 44 136 � 63 153 � 71 180 � 93EMGR 17 32 � 8 43 � 9 49 � 9 54 � 9 58 � 9 62 � 10

moment versus corner frequency shown in Figure 7b seemsto display a steplike pattern consisting of the following twosegments: earthquakes with seismic moment 1012 � M0 �1015 N m follow a scaling law, the corresponding�4.3M � f0 c

source dimensions range between 200 and 1000 m and stress-drop values range between 0.1 MPa and about 10 MPa; forearthquakes having lower seismic moments (109 � M0 � 1012

N m), a slope greater than seven is observed ,�7.3(M � f )0 c

the corresponding source dimensions are confined between70 and 400 m and the stress-drop values are very low (from0.01 to 0.1 MPa).

The obtained seismic moments were used to estimate

the moment magnitude (MW) by using Kanamori (1977) re-lationship:

M � (log M /1.5) � 10.73 (7)W 0

Hanks and Kanamori (1979) showed that moment magni-tude MW is equivalent to the local magnitude (ML). There-fore, we considered the ML estimates recently obtained byD’Amico and Maiolino (2005) for the seismic swarm oc-curring at Mt. Etna on 27 October 2002, and compared bothMW and ML magnitude estimates. We derived the followingempirical relation for Etnean earthquakes:

190 E. Giampiccolo, S. D’Amico, D. Patane, and S. Gresta

Table 3Estimates of QP at 1 Hz (Q0) and n by Using the Relationship

Q � Q0 f n (the 1r Standard Deviation Is Also Reported)

Station Name Q0 � 1r n � 1r

EMFO 28 � 4 0.3 � 0.09EMGR 23 � 4 0.6 � 0.09ECVS 31 � 5 0.5 � 0.09ERSA 18 � 4 0.7 � 0.1EPET 29 � 5 0.5 � 0.11ENCS 17 � 5 0.6 � 0.14EPIS 15 � 4 0.9 � 0.12ETAR 21 � 6 0.6 � 0.16ECCS 29 � 6 0.5 � 0.11EVNA 15 � 3 1.2 � 0.09EMPL 5 � 3 0.7 � 0.3ECDV 12 � 2 0.9 � 0.08EZPO 41 � 15 0.8 � 0.19ETFI 7 � 6 0.8 � 0.4ESPC 34 � 5 0.3 � 0.07EVNR 4 � 1 1.3 � 0.17EMVT 6 � 1 1.1 � 0.09ESVO 4 � 1 1.3 � 0.3EMDV 12 � 4 0.6 � 0.15EPMN 45 � 8 0.7 � 0.1ECIS 7 � 2 1 � 0.14ECTS 8 � 3 1.3 � 0.2ECPN 6 � 2 0.9 � 0.17ECBD 37 � 8 0.4 � 0.11

Table 4Estimates of QS at 1 Hz (Q0) and n by Using the Relationship

Q � Q0 f n (the 1r Standard Deviation Is Also Reported)

Station Name Q0 � 1r n � 1r

ECCS 66 � 13 0.3 � 0.1EMPL 37 � 2 0.5 � 0.03ESPC 51 � 7 0.3 � 0.07ECPN 7 � 1 0.6 � 0.07ETFI 8 � 1 0.8 � 0.07EMVT 56 � 12 0.2 � 0.11ESVO 21 � 4 0.9 � 0.09EMGR 14 � 2 0.7 � 0.06

Figure 4. Distribution of QP (a) and QS (b) valuescomputed at each station at 1, 5, and 10 Hz. Red linescontour areas characterized by low QP values, as re-vealed by De Gori et al. (2005).

Table 5QS/QP Ratio Calculated at Each Station for the

Different Central Frequencies

StationName

QS /QP

3.75 Hz 5 Hz 6.25 Hz 7.5 Hz 8.75 Hz 10 Hz

ECCS 0.6 0.7 0.6 0.8 0.8 0.8EMPL 0.3 0.6 0.8 0.5 0.6 0.7ESPC 0.7 0.7 0.8 0.8 0.7 0.8ESVO 0.2 0.3 0.4 0.3 0.6 0.7ETFI 2.2 1.2 0.7 0.9 0.7 0.6ECPN 1.3 1.2 1.6 1.9 1.5 —EMGR 2.3 1.4 1.4 1.6 1.5 1.5EMVT 0.2 0.4 0.6 0.7 0.9 0.8

Log(M ) � (17.60 � 0.37) � (1.12 � 0.10)M (8)0 L

with coefficient of variation of the regression R2 � 0.8.Using equation (8), we computed the ML for all the

66 events (Table 6). ML values can be considered consistentwith MW, within 0.3 magnitude units, in 80% of the cases.For the events of 27 October 2002, strong differences be-tween ML and MD can be observed (Table 6), due to thesuperposition of earthquake signals and the high tremor am-plitude, typical of pre-eruptive and eruptive stages, that oftendo not allow a reliable estimate of the duration of earth-quakes. In fact, from a rough comparison of the MD valueswith ML estimated in this study, we observe that for themajority of the events (about 80%) MD can be consideredconsistent with ML within 0.4 magnitude units. In general,the highest discrepancies are observed for events with esti-

mated MD �3.0. Note that a good agreement is also observedbetween the M0 � ML relationship here estimated and theempirical M0 � MD relation

Log(M ) � (17.8 � 1.9) � (0.9 � 0.1)M (9)0 D

previously calculated at Mt. Etna by Patane et al. (1993),considering local earthquakes that occurred during a non-eruptive period.

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 191

Figure 5. Examples of earthquake spectra, corrected for instrumental response,attenuation, and normalized to EMFO station distance. The average spectrum (thick line)is also shown.

Discussion and Conclusions

The present study examines the estimate of thefrequency-dependent characteristics of seismic-wave atten-uation in the shallower crust at Mt. Etna volcano and thecomputation of source parameters of microearthquakes(depth �5 km) recorded in the area. We selected 320 shal-low microearthquakes recorded before and during 2001 and2002. The high quality of both one- and three-componentrecords permits a reliable estimate of QP and QS in the

whole-frequency range investigated (2–18 Hz). As reportedin previous studies on attenuation of seismic waves per-formed at Mt. Etna (e.g., Del Pezzo et al., 1987; Del Pezzoand Patane, 1992; Ibanez et al., 1993; Patane et al., 1994,1997), it was found that QP and QS are clearly frequency-dependent according to the power law Q � Q0 f n, with nranging between 0.3 and 1.3 for P waves, and between 0.2and 0.9 for S waves. This result is in agreement with whatis commonly observed in volcanic and tectonic regions char-

192 E. Giampiccolo, S. D’Amico, D. Patane, and S. Gresta

Table 6Hypocentral and Source Parameters Calculated for a Selected Subset of Events (See Text for Details)

Date (dd/mm/yy) andOrigin Time (hh:mm:ss)

Lat.(� N)

Lon.(� E)

Depth(km) MD ML MW

X0

(m sec) fc c

M0

(N m)r

(m)Dr

(MPa)

12/07/01 23:06:55 37.719 15.024 0.81 2.7 2.6* 2.9 1.79E�06 5.3 2.0 2.70E�13 237 0.888512/07/01 23:09:35 37.711 15.022 2.12 2.6 2.6* 2.9 8.55E�07 4.8 2.0 2.72E�13 320 0.363813/07/01 00:11:08 37.741 15.006 1.41 2.6 3.0* 3.2 5.48E�06 3.5 2.5 9.02E�13 343 0.978313/07/01 00:31:55 37.741 15.010 0.94 2.6 3.2* 3.4 8.68E�06 4.0 2.3 1.47E�14 310 2.145713/07/01 00:42:04 37.714 15.041 �0.16 2.6 2.3* 2.7 2.48E�06 4.4 2.0 1.33E�13 221 0.543613/07/01 00:42:31 37.740 15.005 0.60 2.6 3.3* 3.5 1.09E�05 4.5 2.5 2.06E�14 283 3.994913/07/01 01:30:52 37.707 15.044 1.31 2.8 3.0* 3.2 6.29E�06 4.0 2.5 7.89E�13 302 1.249213/07/01 01:36:45 37.711 15.042 1.42 2.9 2.7* 3.0 3.00E�06 4.0 2.5 3.59E�13 300 0.582313/07/01 01:39:02 37.712 15.017 1.26 2.8 3.1* 3.3 7.52E�06 4.2 2.5 1.21E�14 292 2.116513/07/01 02:34:09 37.705 15.044 1.20 2.6 2.4* 2.8 1.46E�06 4.0 2.4 1.92E�13 304 0.299313/07/01 02:37:49 37.716 15.013 1.20 2.6 3.0* 3.2 5.28E�06 5.0 2.3 8.76E�13 244 2.647313/07/01 03:26:11 37.715 15.013 0.71 2.8 3.4* 3.5 1.37E�05 4.0 2.5 2.48E�14 315 3.453113/07/01 03:29:45 37.723 15.009 0.66 2.7 3.0* 3.2 4.50E�06 5.0 2.5 8.30E�13 251 2.301613/07/01 03:34:57 37.724 15.010 0.40 2.6 2.9* 3.2 8.00E�06 4.2 2.5 6.97E�13 239 2.226513/07/01 03:58:06 37.725 15.042 0.66 2.8 2.5* 2.9 2.11E�06 5.0 2.5 2.37E�13 253 0.6413/07/01 04:01:02 37.729 14.999 0.36 2.6 3.2* 3.4 1.55E�05 4.0 2.7 1.59E�14 253 4.28413/07/01 05:49:31 37.701 15.046 1.06 2.9 2.9* 3.2 5.14E�06 4.6 2.5 7.00E�13 269 1.57413/07/01 07:49:13 37.698 15.064 2.44 2.6 2.9* 3.2 2.83E�06 4.6 2.3 7.09E�13 320 0.94613/07/01 08:38:41 37.710 15.041 1.18 2.8 3.1* 3.3 9.50E�06 4.5 2.4 1.21E�14 274 2.589513/07/01 09:15:52 37.695 14.968 �0.09 2.6 2.8* 3.1 3.86E�06 4.7 2.5 4.97E�13 204 2.556913/07/01 10:41:53 37.715 15.018 1.88 2.6 2.7* 3.0 2.96E�06 4.5 2.2 4.16E�13 256 1.084413/07/01 11:55:25 37.716 15.016 2.85 3.0 3.6* 3.6 1.30E�05 3.5 2.0 3.69E�14 408 2.381913/07/01 12:35:57 37.721 15.039 2.06 2.7 3.1* 3.3 4.49E�06 4.7 2.3 1.13E�14 325 1.434613/07/01 13:43:15 37.715 15.019 2.56 2.6 2.7* 3.0 1.47E�06 4.4 2.0 4.30E�13 330 0.523713/07/01 18:53:02 37.739 15.082 5.36 2.5 3.1* 3.3 2.99E�06 4.6 2.3 1.06E�14 355 1.038313/07/01 19:50:43 37.716 15.017 2.88 2.6 2.4* 2.8 6.40E�07 4.4 2.5 1.80E�13 327 0.225513/07/01 21:59:04 37.709 15.041 1.53 3.0 3.3* 3.4 1.37E�05 4.0 2.2 1.70E�14 294 2.920413/07/01 22:32:00 37.711 15.021 1.77 2.6 2.3* 2.7 9.40E�07 5.5 2.3 1.35E�13 213 0.614813/07/01 23:46:26 37.699 15.016 1.71 2.6 2.7* 3.0 2.13E�06 4.2 2.3 3.54E�13 279 0.715214/07/01 00:06:05 37.724 14.947 �1.59 2.7 2.5* 2.9 1.88E�06 4.7 2.7 2.61E�13 204 1.341314/07/01 01:20:10 37.727 15.010 1.33 3.0 3.2* 3.4 9.22E�06 3.7 2.3 1.48E�14 328 1.829627/10/02 00:16:45 37.758 15.005 1.11 2.7 2.8 3.1 3.09E�06 4.0 2.7 5.56E�13 307 0.843827/10/02 00:35:03 37.727 14.996 0.01 3.0 3.6 3.6 2.39E�05 3.3 2.7 3.61E�14 347 3.778627/10/02 00:41:49 37.731 15.006 0.42 3.2 3.1 3.3 1.16E�05 2.8 2.7 1.01E�14 354 1.002627/10/02 01:07:46 37.754 15.090 3.05 2.4 3.3 3.5 6.94E�06 3.5 2.7 1.97E�14 400 1.345327/10/02 01:11:25 37.751 15.004 4.09 3.0 4.0 3.9 1.61E�05 2.8 2.5 1.04E�15 635 1.775727/10/02 01:13:32 37.760 14.991 1.90 3.3 3.9 3.9 5.22E�05 2.0 2.7 9.46E�14 579 2.133827/10/02 01:26:24 37.755 15.012 3.31 3.0 3.2 3.3 4.88E�06 3.5 2.7 1.29E�14 391 0.943527/10/02 01:28:17 37.808 15.051 �1.56 3.5 2.8 3.1 6.08E�06 3.0 2.3 5.79E�13 320 0.772527/10/02 01:37:11 37.759 15.018 3.33 2.6 3.0 3.3 3.80E�06 3.5 2.7 9.58E�13 390 0.705627/10/02 01:42:21 37.770 15.023 1.18 2.7 3.0 3.2 5.49E�06 3.4 2.9 8.79E�13 357 0.848727/10/02 01:53:01 37.778 15.030 �1.59 2.5 2.8 3.1 7.48E�06 3.4 2.7 5.50E�13 285 1.035327/10/02 02:15:17 37.767 15.011 2.03 2.5 3.5 3.6 8.26E�06 3.0 2.7 2.99E�14 511 0.981427/10/02 02:18:29 37.763 15.008 3.68 3.2 4.1 4.1 6.04E�05 1.8 3.0 1.56E�15 734 1.728527/10/02 02:29:28 37.763 15.015 3.14 3.5 3.9 3.9 2.76E�05 2.1 2.9 7.55E�14 649 1.20727/10/02 02:39:10 37.763 15.014 2.25 3.3 3.9 3.9 2.77E�05 2.2 2.9 9.16E�14 691 1.213927/10/02 02:42:11 37.813 15.097 2.12 3.4 3.9 3.9 1.92E�05 2.4 2.7 7.97E�14 634 1.370627/10/02 02:50:25 37.771 15.026 3.16 4.2 3.4 3.5 8.55E�06 2.5 2.7 2.25E�14 555 0.57727/10/02 03:28:55 37.770 15.010 1.20 2.8 3.5 3.6 1.66E�05 2.5 3.0 3.02E�14 489 1.126227/10/02 03:53:26 37.759 15.005 2.83 2.5 3.5 3.6 1.00E�05 3.0 2.7 3.11E�14 477 1.258627/10/02 04:17:07 37.762 15.024 2.55 2.9 3.9 3.9 3.34E�05 2.3 2.7 9.47E�14 637 1.601527/10/02 05:02:04 37.761 15.015 2.95 2.5 3.3 3.4 6.06E�06 3.2 3.0 1.70E�14 446 0.84227/10/02 05:20:57 37.778 15.026 3.47 2.6 3.3 3.4 6.76E�06 3.0 2.3 1.74E�14 449 0.840327/10/02 05:31:11 37.772 15.030 4.47 3.3 4.2 4.1 3.58E�05 2.0 2.7 1.97E�15 865 1.331127/10/02 05:46:45 37.776 15.022 2.95 3.4 4.1 4.0 4.59E�05 1.8 2.5 1.35E�15 786 1.214727/10/02 06:06:55 37.778 15.022 3.10 3.4 3.8 3.8 2.30E�05 3.3 3.0 6.63E�14 423 3.836427/10/02 06:26:13 37.763 15.013 0.95 2.8 3.1 3.3 6.55E�06 3.0 2.7 1.15E�14 414 0.71227/10/02 06:28:14 37.774 15.023 5.27 2.9 4.1 4.0 2.45E�05 2.1 2.7 1.27E�15 762 1.255127/10/02 06:49:32 37.775 15.026 3.40 2.9 3.8 3.8 2.47E�05 2.1 2.7 6.39E�14 633 1.104

(continued)

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 193

Table 6Continued

Date (dd/mm/yy) andOrigin Time (hh:mm:ss)

Lat.(� N)

Lon.(� E)

Depth(km) MD ML MW

X0

(m sec) fc c

M0

(N m)r

(m)Dr

(MPa)

27/10/02 07:32:06 37.782 15.021 4.30 3.2 4.2 4.1 3.05E�05 1.8 2.5 1.98E�15 973 0.941227/10/02 08:04:32 37.772 15.019 �1.12 2.8 3.0 3.2 1.00E�05 3.0 2.5 7.79E�13 320 1.039627/10/02 11:03:01 37.784 15.033 0.02 2.6 2.9 3.1 4.97E�06 3.0 2.3 6.60E�13 380 0.524527/10/02 12:09:58 37.786 15.036 0.03 2.7 2.9 3.1 4.67E�06 4.0 2.7 6.13E�13 284 1.166927/10/02 14:42:44 37.792 15.035 0.02 2.5 3.0 3.2 6.19E�06 3.0 2.7 8.79E�13 380 0.698927/10/02 14:56:29 37.792 15.042 2.32 2.7 3.4 3.5 7.00E�06 2.8 2.7 2.36E�14 534 0.679627/10/02 15:51:07 37.827 15.066 2.38 3.0 3.9 3.9 1.85E�05 2.2 2.7 8.35E�14 689 1.1143

Stars indicate the ML values estimated from equation (8).

Figure 6. P-wave average spectra (black solid line) of some of the earthquakesshown in Figure 5, along with the best theoretical fit (black dashed line) and the spec-trum of the background noise (gray solid line).

acterized by a high degree of heterogeneity (e.g., Del Pezzoet al., 1983; Patane et al., 1997; Giampiccolo et al., 2003,2006). In some cases, however, we observe a lower fre-quency dependence of Q for P and/or S waves (e.g., ESPC,EMFO, ECCS, and EMVT stations). Because the intrinsic at-tenuation is frequency independent, while Q due to scatter-ing increases with increasing frequency (Aki, 1980; Dainty,1981), we suggest that upcoming rays intersect volumes

characterized by the presence of magma bodies and partialmelting of rocks. This might result in a dominance of intrin-sic absorption over scattering attenuation. On the other hand,we would expect scattering attenuation to be significant forlonger path lengths because of the highly heterogeneousstructure of the volcano and its surroundings. When the scalelength of the heterogeneity is comparable to the wavelengthof the seismic waves interacting with it, the effect of scat-

194 E. Giampiccolo, S. D’Amico, D. Patane, and S. Gresta

Figure 7. (a) Relationship between seismic mo-ment and source radius for the new data set (graycircles) and that (open circles) from Patane et al.(1997). The lines of constant stress drop are also re-ported. (b) Scaling relation between seismic momentand corner frequency for the entire data set.

tering is expected to be maximum (Aki and Richards, 1980;Menke et al., 1985). Another interesting result is that thestations located in the central and western areas, in general,show lower values of QP at 1 Hz (Q0) than the stations lo-cated on the eastern sector. Usually a high degree of crackingand/or the presence of melt and fluids in the fractures lowerboth QP and QS (Bourbie et al., 1987; Sato et al., 1989).

In some cases we observe differences among closelylocated stations, suggesting the existence of azimuthal vari-ation of QP due to the presence of strong lateral heteroge-neities, as commonly observed in volcanic settings. Ourresults are consistent with the results obtained by De Goriet al. (2005) and Martınez-Arevalo et al. (2005) whoperformed QP-tomography studies at Mt. Etna assuming afrequency-independent attenuation mechanism. In Figure 4,red contours border the low QP volumes revealed in the shal-lowest layers (above 6 km) by De Gori et al. (2005). There

is a good agreement with the low QP-values obtained at somestations in our study with the De Gori et al. (2005) findings,at least at low frequencies. Finally, what we observed for QP

seems to also hold for QS, but the limited amount of dataavailable at the three-component stations prevents any reliableconclusion in terms of spatial variation of QS. The QS/QP

ratio is, for most of the stations, greater than 1 (Table 5),as already observed at Mt. Etna (e.g., Patane et al., 1994)and in other volcanic areas with any kind of tectonic regimefor the upper crust (e.g., Bianco et al., 1999; Hough et al.,1999; Prejean and Ellsworth, 2001). Laboratory measure-ments constrain the QS/QP ratio to be less than unity in fluid-saturated rock matrices and larger than unity in dry rocks(e.g., Winkler and Nur, 1982). Therefore, QS/QP valuesmuch less than unity, in general, agree with a significantdeparture from perfect elasticity because of the decreasedrigidity of the medium. In our case, only at stations ECPNand EMGR and at lower frequencies at station ETFI isQS/QP less than 1 (�0.6). Considering that ETFI and ECPNare located near the summit crater, the presence of partialmelt in the central feeding system may produce a strongerattenuation for S waves than for P waves at these stations.On the other hand, at station EMGR local higher fracturingof the rocks could be responsible for the decrease of theQS/QP ratio.

Based on the preceding results, we may conclude thatQ-measurements are an important key for the study of sourceparameters of small to moderate earthquakes at Mt. Etna.Undercorrection for attenuation could make the corner fre-quencies of small earthquakes appear inordinately low, lead-ing to anomalously low stress-drop estimates (Hanks, 1982;Anderson and Hough, 1984; Anderson, 1986). In fact, it iswell known that severe attenuation of high-frequency waves,often correlated with near-surface geology, occurs at shallowdepth beneath the receiver sites, producing apparent cornerfrequencies unrelated to the source dimension of the earth-quake (e.g., Frankel, 1982; Hanks, 1982; Malin and Waller,1985; Frankel and Wennerberg, 1989; Hough, 1997). Thisevidence suggests that the apparent scaling breakdown atlow magnitudes may reflect an attenuation effect. To in-crease the reliability of source-parameter estimates, it is bet-ter to determine a frequency-dependent Q-model over a widefrequency band and estimate the source parameters of largernumbers of earthquakes. Previous studies on source param-eters of microerthquakes at Mt. Etna have been performedon small data sets (Patane et al., 1994, 1995, 1997; Centa-more et al., 1997). However, a proper attenuation model forthe local upper crust (depth �5 km) was less constrained atthat time. In the present study a larger data set was analyzedusing detailed and robust information on seismic attenuationat depths less than 5 km. Therefore, once we developed asuitable model for attenuation in the shallow crust at Mt.Etna, we proceeded to compute the source parameters of asubset of 66 shallow events, after appropriate corrections forinstrumental response, attenuation, and geometrical spread-ing were made. In general, we observed that the spectra of

Attenuation and Source Parameters of Shallow Microearthquakes at Mt. Etna Volcano, Italy 195

the same earthquake at different stations share a similarshape (Fig. 5), indicating that directivity and/or azimuthaleffects are of second order with respect to, for instance,seismic noise, which primarily affects the spectral shape.Combining our results with those of Patane et al. (1997)we estimated the scaling relations for microearthquakeswith M0 ranging between 109 and 1015 N m. We found thatearthquakes with seismic moment ranging between 1012 and1015 N m, follow a relationship. Because we�4.3M � f0 c

appropriately corrected the spectra for attenuation, we mayconclude that the breakdown of the relationship ,�3M � f0 c

generally accepted for large earthquakes, is not an artifactof attenuation, but is real for microearthquakes at Mt. Etna.On the other hand, for smaller earthquakes (109 � M0 �1012 N m), the relation between M0 and fc shows a steeperslope . It is worth stressing that the change in�7.3(M � f )0 c

slope from �4.3 to 7.3 basically occurs for the shallowevents of Patane et al. (1997) data set. Unfortunately, we donot have data with M0 �1012 N m to verify this latter trend.Therefore, such a dramatic slope could be related to a prop-agation effect, since a careful estimate of shallow attenuationwas not available at that time, even though a source effectwhich could characterize ultra or microearthquakes cannotbe excluded.

The source dimensions of the analyzed earthquakes (in-cluding the data set of Patane et al., 1997) vary from about100 to 1000 m and stress-drop values range between 0.01and about 10 MPa. The estimated source dimensions are ofthe same order of the values generally obtained for micro-earthquakes in other tectonic and volcanic settings (e.g., Ab-ercrombie, 1995; de Lorenzo et al., 2001; Prejean and Ells-worth, 2001; Hough and Kanamori, 2002). Moreover, theyoutline a characteristic of the region, being consistent withthe faulting mechanisms observed at Mt. Etna, which gen-erally occur in small areas with maximum dimension of sev-eral hundreds of meters. Surface evidence of these faultingepisodes is well exposed in the eastern flank of the edificewhere the major fault zones consist of fault segments ableto generate only low-magnitude earthquakes (e.g., Pataneand Giampiccolo, 2003). Similarly, the low stress-drop val-ues obtained can be attributed to the low strength of crustalmaterials in the area, where great stress accumulation is hin-dered. All these considerations are consistent with a greatheterogeneity of the crust related to faults, dikes, and intru-sions, which does not allow great stress accumulation orlong-rupture propagation.

The obtained seismic moment–radius relation showsthat the seismic moment increases with increasing sourcedimension. Moreover, looking at Figure 7, a strong vari-ability of stress-drop estimates is clearly evident. Both find-ings are consistent with a breakdown of similarity for micro-earthquakes at Mt. Etna. It is currently debated whetherearthquakes are truly self-similar over their entire size rangeor if the departure from self-similarity often observed is true.Several articles (e.g. Abercrombie, 1995; Bindi et al., 2001;Ide and Beroza, 2001; Hiramatsu et al., 2002) have shown

that there is no breakdown in the self-similarity (constantstress-drop relationship). The results of this study stronglysuggest that the cause in the increasing stress drop can beattributed to a source effect and it is, consequently, a clearviolation of the self-similarity law. This supports the hy-pothesis of differences between the rupture processes ofsmall and large earthquakes, as proposed for microearth-quakes recorded in both tectonic (e.g., Archuleta et al., 1982;Archuleta, 1986; Iio, 1986; Guo et al., 1992; de Lorenzoet al., 2004; Garcıa-Garcıa et al., 2004; Tusa et al., 2006a)and volcanic environments (e.g., Tusa et al., 2006b). Theproblem is far from being resolved, however, and precisedeterminations of source dimension and radiated energy arerequired to resolve it (Kanamori, 2002). In addition, the res-olution of this issue is complicated by the difficulty in ac-curately accounting for and determining the seismic energyradiated by earthquakes over a wide range of event sizes ina consistent manner (Walter et al., 2002).

Acknowledgments

Samantha Hansen and two anonymous referees are gratefully ac-knowledged for useful comments and suggestions. Giuseppina Tusa is alsoacknowledged for useful discussions. This work was supported by GrantsEU-VOLUME FP6-2004-Global-3 and INGV-DPC 2005-V3_6.

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Istituto Nazionale di Geofisica e Vulcanologia95123 Catania, Italygiampiccolo@ct.ingv.it

(E.G., S.D., D.P.)

Dipartimento di Scienze GeologicheUniversita di Catania95126 Catania, Italy

(S.G.)

Manuscript received 12 December 2005.