PAGEOPH, Vot. 123 (1985)

0033-4553/85/050683-1451.50 + 0.20/0 @ 1985 Birkh/iuser Verlag, Basel

Qc of Three Component Seismograms of Volcanic Microearthquakes at Campi Flegrei Volcanic Area - - Southern Italy E. DEL PEZZO, G. DE NATALE, G. SCARCELLAand A. ZOLLO

Abstract - - Digital recordings of three component microearthquake codas from shallow seismic events in the volcanic region of Campi Flegrei - - Southern Italy - - were used with an automatic technique to calculate the attenuation factor Qc (coda Q) in the hypothesis of single S to S backscattering. Results show the same value of Q for each of the three components. This result is interpreted as due to isotropic S wave radiation pattern. A check of the coda method was performed using a single station method based on simple assumptions on the direct SH wave spectrum. Single station Q was averaged over the stations and over the earthquakes. Results show that the two methods lead to comparable results. A frequency dependence quite different from that evaluated in active tectonic regions was found for coda attenuation, comparable to other volcanic areas throughout the world. This is interpreted as due to the presence of magma that affects anelasticity and scattering.

Key words: Q, code waves, volcanic earthquakes.

Introduction

Attenuation is an important property of the medium from which useful information on the earth's structure can be inferred. Moreover its evaluation is the first step in eliminating path effects from spectra made from field data in order to have a correct source spectral shape. The evaluation of the so called quality factor Q(Q = 2rcE/AE), where AE is the fraction of energy lost in a wave cycle, is very important in the volcanic areas where the presence of magma presumably influences the properties of the seismic wave propagation. Another peculiar feature of volcanic areas and, in general, of all active tectonic zones is the strong heterogeneity in the geological structures as compared to the tectonically stable zones. This nonuniformity does not allow the use of deterministic models to explain high frequency seismograms because too many parameters are required. To overcome this difficulty we use scattered waves that are generated in the zone in which primary waves encounter strong variations in elastic properties, for example Osservatorio Vesuviano, 1-80056 Ercolano, Italy

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a small fault or crack, or a local and sudden variation of the density of the rocks. The scattered waves in the short period range (1-30 Hz) compose the part of seismogram that follows the S wave train, the so called coda of the earthquake. There is a recent, and growing, interest in the study of coda waves for the evaluation of the quality factor Qc utilizing the method proposed by AI(I and CHOUET (1975) and revised by AI(I (1980). This single station method furnishes an estimate of Q averaged over the area; it is relatively simple to apply and does not require the knowledge of the response curve of the instruments. Moreover it is possible to experimentally calculate the frequency dependence of Qc without any assumption on its functional form. Results in many areas of the world show that the coda envelope can adequately be described by scattering phenomena in a random medium (AKxand CHOUET, 1975; CHOUET, 1976; CHOUET et al., 1978; RAUTIAN and KHALTURIN, 1978; SINGH and HERMANN, 1983). SATO (1984), KOPNICHEV(1977a, b), and more recently GAO et al. (1983a, b) studied the problems of multiple scattering in two and three dimensional media. They showed that the contribution of multiple scattering is important for high values of travel time evaluated along the coda. For short values of travel times the single scattering hypothesis is acceptable. In this paper we assume the single scattering hypothesis to estimate the seismic coda Q~in the active volcanic area of Campi Flegrei, the observed coda lengths being in the range of acceptance for this hypothesis, as will be shown later. Moreover, we accept the hypothesis of full S to S conversion in the scattering phenomena and check the results obtained with coda waves using a direct method based on the analysis of the SH wave spectrum.

M e t h o d on coda Q evaluation

The adopted technique to evaluate Qc is based on the common hypothesis that coda waves are single S to S scattered waves from randomly distributed heterogeneities. This hypothesis is strictly valid if the mean free paths of the waves between the scatterers are greater than the observed travel distances from the scatterers to the receiver. GAO et al. (1983a) point out that for travel time tc < 0.8 (nay)-1, where a is the scattering cross section, v is the wave velocity, and n is the number of the scatterers per unit volume, the single scattering hypothesis can correctly explain the coda power. In the case of Campi Flegrei a preliminary interpretation of data gives a mean free path of the order of 50 km (CASTELLANOet al., 1984). This means that we can strictly apply the single scattering assumption for travel times tc < 20 s. This is in agreement with our available data that show codas lasting less than 30 seconds. The relationship that expresses the amplitude density spectrum of coda waves as a function of the time is A ( f ] t) = A o ( f ) t - 1 exp ( - nft/Qc)

(1)

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where A(f] t) is the Fourier spectrum of coda amplitude evaluated at time t in the coda. The most commonly applied method to find A(flt) is based on filtering the seismogram in several frequency bands: the envelopes of the filtered traces are proportional to the quantity at the left hand side of rel. 1 (AKI and CNOUET, 1975). This method of filtering has mostly been applied to data obtained with analog recording devices that produce filtered seismograms in several frequency bands centered at frequencies that are spread one octave apart (see TSUJtrRA, 1978; CI4Ob'ET, 1976; CHOUET et al., 1978; CHOUET, 1979; RAUTIAN and KHALTURIN, 1978). When dealing with analog data and analog filters, it is faster to estimate A(fl t) in the way indicated by AKI and CHOUET(1975) without passing through digital conversion. Digital data offer a means of evaluating A (fl t) directly through Fourier Transform (F.T.) techniques. In the last approach, a moving window of time length T slides along the data set of a quantity At (see for example LEE et al., 1985). At every step direct F.T. is evaluated on the data enclosed in cosine tapered time window T containing T/dt samples, where l/dt is the sampling frequency. Denoting by to the time corresponding to the center point of the sliding window, we obtain an evaluation of the Fourier Amplitude of coda as a function the time given by

A(flto) = Ao(f)to" exp (-- rcfto/Qc) where m denotes the coefficient of geometrical spreading (m = 1 for body waves and m = 0.5 for surface waves (AIci and CnOUET, 1975). It must be pointed out that A(f[ to) is a smoothed quantity because of the use of the cosine taper function mentioned above. The Fourier spectrum is averaged for each to over six frequency bands with center frequencies similar to those used by other workers centered at 1.7, 3.0, 6.0, 12.0, and 16 Hz. This allows easier comparison with other results obtained by analog methods. For each frequency band and for each component of the ground velocity, we obtain an envelope of the Fourier amplitude as a function of time. This envelope is smoothed over the variable to because each Fourier spectrum is calculated in a time window that contains 50 percent of the data from the previous one. This procedure is repeated over the entire seismogram. Figure 1 shows an example of application of this technique for an earthquake of the Campi Flegrei area. The envelope of the logarithm of A(f[t) premultiplied by to is plotted for each frequency band. The factor to represent the correction for geometrical spreading assumes a body wave scattering process. This is expressed by the following relationship In (A(f[to).to) = In A o - lrfto/Qc

(2)

which represents a straight line with the slope 7rf/Q~. The slope is easily evaluated by least squares fitting of the envelope over the coda duration. The onset of the coda is generally chosen as the time where the envelope begins to decay regularly, while the end is chosen at the point in which the amplitude of the coda falls below the noise level (e.g. CHOLrET, 1976; AKI, 1980). Another method to pick the coda section

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is based on the shape of the envelope for the quantity In ( A ( f l t ) . to) which generally shows a maximum, a regular decay, and a slow increase (see Figure 1). The increase of the level after the minimum point is due to the noise whose spectrum multiplied by to must increase with time. We evaluate the quantity A(flt) for the entire seismogram and consider the maximum of the envelope as the beginning, and the minimum as the end of the coda. Generally the maximum of the envelope corresponds to a time that is roughly equal to, or more than twice than the shear waves arrival time, see Figure 1 where arrows indicate the beginning and end of codas for the different frequency bands; S - P intervals and P time minus origin time intervals are centered around 1 sec for the most of the earthquakes used in this study. This way of choosing the beginning and end of the coda allows for a completely automatic procedure. In some cases the noise superimposed on the signal produces a very rough envelope and the resulting estimates of the slope and quality factor are poor. A straightforward method to eliminate noisy data is to calculate the correlation coefficient on the linear relation (2). The bad estimates for which the correlation is smaller than a threshold, which is chosen on the basis of data quality, can be automatically rejected. The final Qc is obtained by averaging over the earthquakes. This volume average is accurate if the hypocenters are closely spaced and located very near the station (see e.g. AKI, 1980 for details). The result is an estimate of Qc depending on frequency and averaged over the volume encompassed by the scattered

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waves. The standard error on the average value of Qc is the minimum error on the estimate of Qc for each frequency band.

Data The data used in the present paper were collected with portable digital stations in an experiment carried out by University of Wisconsin, U.S.A., at Campi Flegrei, Italy. Campi Flegrei is a volcanic area in which ground uplift (averaging 3 ram/day; Berrino et al., 1984) associated with considerable microearthquake activity, with maximum local magnitude of 4.0, has recently been observed (Vesuvius observatory technical report n. 1/84). A large part of the microearthquakes (about 90 percent) are located in the northern part of Solfatara crater (Figure 2). A maximum of 12 seismic stations, equipped with three component 1 Hz digital instruments were contemporarily operated during the experiment. The location of the stations is shown in Figure 2. Data are recorded in a time window lasting 60 sec after the triggering time and sampled at a rate of 100 Hz. The triggering is set up by a comparison of the long term and short term averages of the signal. The overall response curve of the instruments is shown in Figure 3. The data are generally very noisy because the network is located near a

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densely inhabited area. Shear waves are generally readable on the horizontal components and could be picked with an accuracy of 0.5 sec or less. Two stations were selected on the basis of the best signal-to-noise ratio, the first one located near the crater of Astroni and the second in the northern-western part of the Campi Flegrei (Figure 2). On a family of about 500 earthquakes, 128 events were selected on the criterion of the best signal-to-noise ratio. Distances were evaluated from S-P time delays. The selected earthquakes are located inside the cluster of epicenters shown in Figure 2, at depths ranging from 2 to 5 km. Coda Q~ was evaluated for 42 earthquakes using three component data recorded in the summer of 1983 at the station located in the crater of Astroni. Vertical components were analyzed for the data of both stations, during the time interval covering January and February 1984.

Result from the investigation of Qc Only slopes of the quantity on the left hand side of relation (2) with correlation coefficient greater than 0.85 were considered for coda Q calculations. A Qc averaged over the earthquakes was obtained for each frequency band and for each component (see Table 1). Generally the coda durations are in the range of 15 to 40 seconds, so the maximum travel distance of the backscattered waves is of the order of 15 to 40 km assuming a velocity of 2.9 km/sec, since the hypocentral distance is less than 4 km, we can neglect the hypocentral distance when compared to the maximum

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Table 1 Qc at station W1 for each of the three components

Station Wl. Minimum correlation coefficient= 0.85 August-September 1983 Q~

Standard deviation on Qc

Standard error on Qc

Average duration of coda

Standard deviation on dur.

Frequency (hz)

Vertical Component 97. 47. 156. 67. 299. 102. 288. 68. 299. 106.

16. 22. 24 14. 15.

27. 31. 33. 18. 5.

19. 19. 10. 6. 18.0

1.7 3.0 6.0 12.0

N-S Component 90. 47. 144. 65. 285. 69. 317. 148. 284. 55.

16. 21. 16. 29. 11.

18. 29. 29. 17. 14.

17. 20. 12. 6. 4.

1.7 3.0 6.0 12.0 18.0

E-WComponent 105. 46. 157. 73. 293. 76. 280. 61. 270. 44.

19. 30. 18. 15. 9.

25. 32. 31. 18. 13.

15. 19. 15. 5. 3.

1.7 3~ 6.0 12.0 18.0

distance to the scatterers that produce a useful signal. According to this hypothesis the volume under investigation has the shape of a hemisphere with a radius of about 20 km. So we have information about the attenuation in the crust beneath the volcanic area of Campi Flegrei. The results are shown in Table 1. They show that the values of the quality factor for the three components of ground motion are similar within the range of uncertainty. This single scattering theory predicts that the directional partition of the energy in the S coda is strongly affected by the focal mechanism of a point shear dislocation at a large lapse time (SATO, 1984). In that case the theory predicts a marked difference in the shape of the coda envelope between the three components of the ground velocity. In the three component records obtained at Campi Flegrei a major excitation of coda energy on one of the two components is quite evident (see Figure 5). These differences do not substantially affect the evaluation of Q because the earthquakes used in this study probably have a wide range of orientation of nodal planes. This makes the values of Q averaged over the earthquakes insensitive to the component of the ground movement. Coda Q range from about 100 at 1.7 Hz to about 300 at 16 Hz, and its frequency dependence is quite irregular as compared to other Q patterns (see Figure 4). In fact in the last three bands shows an almost constant Qc.

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SH wave Q from spectra There is growing evidence that the coda Qc represents Q for shear waves (At
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Table 2

Qs estimates for the listed stations Station

Qs

Standard error

# events

W03 W20 W21 W04 W15 W05 Wl0 W14

143 76 134 172 94 158 216 61

86 34 87 124 79 75 98 11

11 25 6 20 29 6 4 6

Total Average (Qs) = 110 (+50). List of events used for Q~ evaluation. TIME LAT LONG [yr,mo,day,h,min] [degrees,min.] 8401150331 40 49.92 14 8.46 8401161900 40 49.78 14 8.52 8401162351 40 49.42 14 7.59 8401170258 40 49.89 14 8.53 8401170448 40 50.26 14 8.04 8401180206 40 49.79 14 8.65 8401190453 40 49.17 14 8.86 8401211339 40 49.85 14 8.25 8401221345 40 49.98 14 8.84 8401230543 40 49.72 14 8.77 8401240424 40 49.48 14 8.14 8401242250 40 49.70 14 7.79 8401262021 40 49.59 14 8.25 8401272343 40 49.91 14 8.68 8401272353 40 49.77 14 8.57 8401282106 40 49.32 14 8.76 8401290422 40 49.42 14 7.85 8401300022 40 49.57 14 8.05 8401300040 40 49.32 14 7.96 8401300044 40 49.30 14 7.97 8401300601 40 49.55 14 8.52 8401310036 40 49.79 14 8.08 8401310220 40 49.85 14 8.24 8402100548 40 49.86 14 8.22 8402101116 40 49.53 14 8.25 8402110359 40 50.51 14 8.19 8402150159 40 49.67 14 6.59 8402162205 40 49.39 14 7.54 8402172041 40 49.63 14 7.54 8402180402 40 48.75 14 9.40 8402190039 40 50.51 14 8.16 8402200111 40 50.36 14 8.39

DEPTH [Km] .7 2.8 2.1 1.5 3.3 2.6 2.4 1.2 2.0 2.6 .9 2.3 1.9 1.2 2.4 2.5 2.2 1.7 2.3 2.1 .7 2.6 2.3 2.5 2.4 1.8 2.9 2.3 2.5 2.3 2.3 2.9

ERR.H I-Km] .2 .2 .2 .2 .4 .3 .3 .9 .3 .3 .4 .2 .6 .5 .3 .8 .2 .4 .2 .2 .3 .4 .7 .2 .2 .2 .2 .1 .2 .3 .2 .3

ERR.Z [Km] .1 .1 .4 .2 .5 .1 .1 1.8 .4 .1 .2 .2 .4 .8 .2 .4 .1 .5 .1 .1 .2 .2 .4 .1 .1 .2 .1 .1 .1 .1 .1 .1

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wo~

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of the spectrum. In doing so we neglected many negative values of Q that have no physical meaning but a good statistical significance. For this reason we believe that the resulting average Q = 110 (_+50) is representative of the lower limit of the Q estimate. It is worth noting that this limit is almost coincident with the Q of coda waves obtained at the lowest frequency.

Discussion and conclusions

The method used to calculate the coda Q is completely automatic in the sense that it is not necessary to visualize any step of the procedure. The step in which the onset and end of the coda envelope are evaluated is based on the signal to noise ratio estimated in each frequency band. There is a different coda interval in which the straight line is fitted. Generally the last two bands have shorter intervals than the others, but this does not affect the results. In this sense, a verification was carried out on the whole set of available data, fixing not only the threshold on the correlation coefficient, but the duration on each frequency band as well. Results were the same within the limits of uncertainty. No obvious frequency dependence of the quality factor was found for coda Q at Campi Flegrei. For comparison we plot in Figure 4 the log of Qc as a function of the frequency for three volcanic areas, Aeolian Islands (North of the Sicily, DEL PEZZO et al., 1983; Campi Flegrei (this paper) and Hawaii (CHouET, 1976); and two tectonic zones of central and Northern Apennines (DEL P~zzo and ZOLLO, 1984). It is quite clear from these plots that tectonic zones show a more linear pattern than the zones in which volcanoes are present. This may be due to the fact that Qc is a combination of intrinsic Q, Qi, and scattering Q,Q~ = co/gv where 9 is called 'turbidity' and is the reciprocal of the mean free path (DAINTY, 1981). The relationship that connects these quantities is 1/Qt = 1/Qi + gv/co

Fitting this model for the areas that show a linear pattern of log (1/Q~) as a function of the log of the frequency we find a good fit with high values of intrinsic Q and relatively high turbidities (see following table) Fit of Dainty model to Qc patterns Area

Qi

g

Friuli Norcia

> 2000 803

0.02 0.05

No good fits were found for the reported volcanic areas whose patterns show a flattening of Q pattern at higher frequencies for the two Italian areas and almost no frequency dependence for Hawaii. It seems that active faulting processes can create scattering environments that produce pattern of Q~ as a function of the frequency

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that are quite in agreement with constant Qi and g. In these areas Qi and g seem to be controlled by crust thickness (RoECKER et al., 1982). Substantial differences are found for volcanic areas where presumably a further element, magma, influences the scattering environment.

Acknowledgments The authors are grateful to Harue Sato for helpful discussions on the scattering models. One of the two referees is acknowledged for his comments and for English improving of the manuscript. This paper was partly presented in the poster session of the IASPEI meeting held in Tokio in August 1985.

REFERENCES AK1, K. and CHOUET,]]. (1975), Origin of coda waves: source, attenuation and scattering effects. J. Geophys. Res. 80, 3322-3342. AKI, K. (1980), Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res. 85, 6496-6504. BERRINO, G., CORRADO, G., LUONGO, G., TORO, B. (1984), Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. Bull. Volcanol. 47, 2, 187-200. CASTELLANO,M., DEE PEZZO,E. DE NATALE,G. and ZOLLO,A. (1984),Seismic coda Q and Turbidity coefficient at Campi Flegrei Volcanic area-preliminary results. Bull. Volcanol. 47, 2, 219-224. CHOUET, B. (1976), Source, scattering and attenuation effects on high frequency seismic waves. Mass. Inst. Technology, Ph.D. Thesis. CHOUET, B., AKI K. and TSUJURA,M. (1978), Regional variation of the scaling law of earthquake source spectra. B.S.S.A. 68, 49-79. CHOUET, B. (1979), Temporal variation in the attenuation of the earthquake coda near Stone Canyon, California. Geophys. Res. Lett. 6, 143-146. DAINTY, A. M. (1981), A scattering model to explain seismic Q observations in the lithosphere between 1 and 30 Hz. Geophys. Res. Lett. 8, 1126-1128. DEL PEZZO, E., FERULANO,F., GIARRUSSO,A. and MARTINI, M. (1983), Seismic coda Q and scaling law of the source spectra in the Aeolian lslands, Southern Italy. Bull. Seism. Soc. Am. 73, 97 108. DEL PEZZO, E., ROVELLI,A. and ZONNO,G. (1985), Seismic Q and site effects on seismograms of local earthquakes in the Aucona region (central Italy). Annales Geophysicae 3, 5, 629-636. DEL PEZZO, E. and SCARCELLA,G. (1985), Three component coda Q in the Abruzzi-Molise region. Central Apennines. Annales Geophysicae (in press). DEL PEZZO, E. and ZOLLO, A. (1984), Attenuation of coda waves and turbidity coefficient in Central Italy. Bull. Seism. Soc. Am. 74, 6, 2655-2659. DE NATALE,G., ZOLLO, A., DEL GAUDIO,C., RICCIARDI,G. P. and MARTINI, M. (1984), Error analysis in hypocemral locations at Phlegrean Fields. Bull. Volcanol. 47, 2, 209-218. ELLSWORTH,W. L. and KOYANAGI,R. Y. (1977), Three dimensional crust and upper mantle structure of Kilauea Volcano, Hawaii. J. Geophys. Res. 82, 33, 5379-5394. GAg, L. S., LEE, L. C., BISWAS,N. N. and AKI, K. (1983a), Comparison of the effects between single and multiple scattering on coda waves for local earthquakes. Bull. Seism. Soc. Am. 73, 337-389. GAO, L. S., LEE, L. C., BISWAS,N. N. and AKI, K. (1983b), Effects on multiple scattering on coda waves in three dimensional medium. Pageoph, 121, 1.

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KOPNICHEV, Y. F. (1977a), Models for the formation of the coda of the longitudinal wave (Engl. Trans.) Dokl. Akad. Nauk, SSSR, 234, 13-15. KOPNICHEV,Y. F. (1977b). The role of Multiple scattering in theformation of a seismogram's tail (Engl. Trans.) Izv. Akad. Nauk, SSSR Fiz. Zemli, 13, 394-398. LEE, W. H. K., AKI, K., CHOUET,B., JOHNSON,P., MARKS, S., NEWBERRY,J. J., RYALL,A. S., 'STEWART, S. W. and TOTTINGI-IAM,D. M. A preliminary study of coda Q in California and Nevada. Geophys. Res. Lett. (in press). ROECKI~R,S. W., TUCKER, B., KING, J. and HATZFELD,D. (1982), Estimates of Q in central Asia as a function of frequency and depth using the coda of locally recorded earthquakes. Bull. Seism. Soc. Am. 72, 129-149. ROVELLI,A. (1982), On the frequency dependence of Q in Friuli from short period digital records. Bull. Seism. Soc. Am. 72, 2369-2372. RAUTIAN,T. G. and KHALTURIN,V. I. (1978), The use of coda for determination of the earthquake spectrum. Bull. Seism. Soc. Am. 68, 923-948. SATO,H. (1978), Mean free path of S waves under the Kanto district, Japan. J. Phys. Earth 26, 185--198. SATO, H. (1984), Attenuation and envelope formation of three component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J. Geophys. Res. 89, b2, 1221-1241. SINGH,S. K. and HERMANN,R. B. (1983), Regionalization of crustal coda Q in the continental United States. J. Geophys. Res. 88, 527-538. TSUJURA,M. (1978), Spectral analysis of coda waves from local earthquakes. Bull. Earth. Res. Inst. Tokio Univ. 53, 1-48. (Received 9th October 1985, revised 23rd January 1986, accepted 23rd January 1986)