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Frequency relationship for seismic Qβ of central southern Italy from accelerograms for the Irpinia earthquake (1980)
Physics of the Earth and Planetary Interiors, 32 (1983) 209—2 17 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands
Frequency relationship for seismic
209
of central southern Italy
from accelerograms for the Irpinia earthquake (1980) Antonio Rovelli Isuituto Nazionale di Geofisica, Osservatorio Geofisico Centrale, Monte Porzio Catone, Rome (Italy) (Received September 27, 1982; revision accepted December 14, 1982)
Rovelli, A., 1983. Frequency relationship for seismic of central southern Italy from accelerograms for the Irpinia earthquake (1980). Phys. Earth Planet. Inter., 32: 209—217. The frequency dependence of for seismic waves in a distance range with a maximum of 150 km from the epicentre of the Irpinia earthquake of November 23, 1980 has been sought using displacement spectral ratios computed from strong-motion accelerograms recorded in the region. The method has been applied to calculate the behaviour of Q~ as a function of frequency in the band 0.1—25 Hz, and to investigate whether azimuthal variations appear in seismic Q~for the lithosphere in central southern Italy. The same result is obtained using data from stations in western south Italy as using data from eastern south Italy, namely,
Q~(f)
40f(Hz)
The linear relationship suggests that apparent Q~depends more on the scale of heterogeneity of the lithosphere, affecting reflection and scattering mechanisms, than on intrinsic energy losses related to the anelasticity of the materials through which the seismic waves propagate. The existence of a peak in Qj~has been investigated in the low-frequency band (0.1—2.5 Hz) using a higher resolution power. A stable result in this low-Qp zone is not possible on the basis of the available data: only in SiX Q~(f) profiles does an evident minimum exist, between 0.2 and 1 Hz, while in nine cases the curves are monotonically increasing from the lowest observable frequencies; a further nine cases appear of uncertain interpretation.
1. Introduction Following the seismic crisis in Friuli (May and September 1976), Console and Rovelli (1981) and Rovelli (1982) observed in this region a strong, practically linear dependence of apparent Q1~on frequency over the range 0.1—10 Hz, both by means of spectral ratios from strong-motion accelerograms at different epicentral distances recorded after the stronger shocks (see Console and Rovelli, 1981), and by analysing waves using of the digital codas of low-magnitude eventsshear processed bandpass filters (see Rovelli, 1982) with numerical methods derived from the analogue techniques 003l-9201/83/$03.00
© 1983 Elsevier Science Publishers B.V.
introduced by Aki and Chouet (1975) and Tsujiura (1978) for coda-wave analysis. Inreviewing a series of previous works (Aki, 1980a; Hermann, 1980; Nuttli, 1980), Aki has demonstrated exhaustively that the dependence of apparent Q~on frequency is general and is stronger the higher the current tectonic activity in the zone in which is measured. Aki (l980a,b; 1981) pointed out that in Japan differences have been found between vanous regions with differing tectonic (in a 08,situations while in other zone inofthe ~fcxf°~).The results zones theKanto same district districtQ,9 Q~ of Fedotov and Boldyrev (1969) for the Kurili Islands and of Rautian and Khalturin (1978) for
210
Garm (Central Asia) revealed an apparent Q dependence on frequency of the type Q~ ~ ffl (with n equal to 0.6 and 0.5, respectively). Using Rayleigh waves, Mitchell (1980, 1981) also found an undeniable, although less marked (proportional to f’1 with 0.2 < n <0.5), dependence of the quality factor on frequency in the upper m:ntle. Also, ~ifln th~
~
13
l4~
l5~
•S.SEVER 41
~0RR~EI~.~*
17
VIESTE
EPICENTER
different regions analysed in the United States. in eastern regions, apparent quality-factor values at the same frequency two or three times higher than in western regions were found; similar results for intrinsic Q for the upper mantle under the United States have been made evident by Der et al. (1982). The recent earthquake in Irpinia (November 23, 1980) and the large number of strong-motion accelerometric stations situated in the epicentral region made it possible to study apparent Q~as a function of seismic-wave frequency in central southern Italy over a range of distances no greater than 150 km from the epicentre in the frequency band 0.1—25 Hz.
16~
~
ERCA,~
IN VIIIIRE
H
1 S.SEV. ‘TRICARICO,~~ ~IAOHOLIP~IA ~
(
TYI~RHENIAN SEA _____
ACCELEROMEIRIC STATIONS
tRIGGERED BY THE IRPINIA EARTHQUAKE OF 23rd NOV. 1980
________________________________________ Fig. 1. Locations of accelerometric stations of the ENEL network that were triggered by the Irpinia earthquake of November 23, 1980.
2. Acquisition and processing of accelerometric data Many of the SMA- 1 accelerometers in central southern Italy in the network set up by Ente Nazionale per l’Energia Elettrica (ENEL) were triggered by the strong Irpinia earthquake of November 23, 1980. Figure 1 shows the locations of the stations used in the present work. Table I shows the site characteristics for each accelerometer. For further information concerning the characteristics of the stations, the instrumentation and the record processing, readers are referred to publications of the Commissione CNEN—ENEL per lo Studio Congiunto dei Problemi Sismici connessi con la Realizzazione di Impianti Nucleari (see for example, Berardi et al., 1981). Accelerometric data were kindly supplied by the Comitato Nazionale per l’Energia Nucleare (CNEN) already digitized on magnetic tape. The first 40.96 s (the equivalent of 4096 samples) of the N—S and E—W components for each of the stations considered were processed using standard Fourier techniques. For those stations with a record duration of less than 40.96 s, i.e., comprising fewer than 4096 samples,
zeros were added to bring the set up to the desired length. From the values of the Fourier spectra (one every 1/40.96 Hz) thus obtained, mean values were calculated for contiguous bands 0.25 Hz wide. The frequency range 0—25 Hz was analysed. A hundred or so spectral-amplitude values were thus obtained as a function of frequency for the two horizontal components for all the stations considered. The spectra were then smoothed drastically using a low-pass filter, i.e., liftering with a roll-off quefrency of 0.05 s and a cut-off quefrency of 0.2 s (for the use of liftering techniques, see for example, Cohen (1970)); instability and sharp peaks were thus removed from the spectra so that smooth, regular curves were obtamed. The smoothed spectra were then corrected for instrumental effects by means of the frequency-response curves H(f) of the accelerometers, which differed slightly from one accelerometer to another, of the general form —
2
H(f)
{(f~/f2
—
1)
—
+ 4h2f02/12J
1/2
211 TABLE I Accelerometric station coordinates and geological characteristics (from Berardi et al., 1981) Accelerometer location
Coordinates
Geological site characteristics
Latitude
Longitude
Arienzo
4I00l~43~r
14°28’OO”
Cinerites and pyroclastites mixed with conoid material (5 m) and grey tuff (5 m), overlying compact limestones of the Campania—Lucania platform
Auletta
4O033~37~~
15°33’30”
Polygenic conglomerates of delta and lacustrine origin, and sand—clay cement (l4~lm)
Bagnoli Irpino
40°49’l5”
15°04’lO”
Limestones, dolomitic limestones, and whitish limestones of the Campania—Lucania platform
Bisaccia
41 ~
150 32’33”
Clays and slates, usually flaky with intercalations of marly limestone, calcarenite and nummulitic rubble (variegated clays)
Bovino
41°l5’02”
15°30’35”
Pliocene sand and sandstone with levels of polygenic puddingstone and sandy clays (25 m) overlying polygenic puddingstone
Brienza
4Oo28~27~~ 15°38’06”
Irregularly stratified polygenic conglomerates with sands, probably of fluviolacustrine origin (25 m), overimposed on flyshoid materials
Calitri
40°55’Ol”
15°26’l9”
Mainly sandstone and grey, yellowish and reddish sands (30 m), resting on marls and grey—blue silty clay
Garigliano
410
l5’32”
l3°49’36”
Thinly stratified limestone and white marly limestone with flint sheets and nodules
Mercato S. Sevenno
40°47’29”
l4°45’5l”
Recent alluvials consisting mainly of sands, gravel and swamp clays (70 m), on lithoid tuff
Rionero in Vulture
40°55’46”
15°40’lO”
Dark, normally stratified subaerial tuff, ranging in colour from grey to dark brown, fairly coherent.
San Severo
4l04l~02~~ 15°23’lO”
Sturno
41001 ‘21”
Torre del Greco
4Oo48~O4~~ 14°23’08”
Leucitic lava ranging from iron-grey to dark, — 25 m thick, overlying lapilli and cinerites from the lower Vesuvius slopes
Tricarico
4Oo37~l5~~
16°09’25”
Calcarenite banks, light yellow or pink in colour, alternating with dark grey marls, with levels of arenaceous silt or sandstone
Vieste
41 o52~43~~
16°09’52”
Thinly stratified limestone and white marly limestone with flint sheets and nodules
Variable-grain, somewhat cemented yellowish sand, with intercalations of conglomerates and clays (Serracapriola sand)
15 oo7~o2~~ Silty clay and dark silty marl, alternating with marly limestone and quartz sandstone
where f is the frequency, h the damping constant (usually between 50 and 70% of critical damping) and f~the normalisation frequency, which varies from 25 to 27 Hz. In order to evaluate the displacement spectra for each of the stations, the vectorial composition of the smoothed and corrected spectra of the two horizontal components was carried out.
3. Seismic-wave attenuation: physical assumptions and observational results Denoting as G~(f) the estimate obtained as outlined above for the amplitude-displacement spectrum for the n th station situated at a distance R~from the epicentre, the energy—frequency distribution of the seismic waves recorded at the nth station may be described by the expression
212
E~(f) JG~(f)12 E0(f)F(R~)e2~~”°~ The seismic-wave energy at the n th station has been assumed to depend on the frequency distribution E 0(f) at the source and on geometric spreading F(R~),which is a function solely of the station’s distance from the focus. The exponential term describes the loss of energy suffered by seismic waves in the medium they are passing through; /3 is the velocity of waves bearing the largest part of the energy recorded (practically speaking, the direct and scattered S waves), and is the term describing the extent to which these waves are attenuated with distance and frequency. This last parameter basically takes two physical mechanisms into account: the conversion of mechanical energy into heat (Aki, l980a), and losses of energy due to scattering of seismic waves caused by crust heterogeneity (Aki, l980b; Dainty and Toksöz, 1981; Dainty, 1981). Assuming that the geometric spreading patterns may vary from spherical propagation, for which F(R~) is inversely proportional to the square of the distance R~(this is the exact case for pure body waves, whose energy propagates along concentric spheres radiating from the focus), to propagation of the surface-wave type, for which F(R~)cr l/R,,, the =
Q~
=
ratio between the energy evaluations made in two stations measuring waves of these types is ohtamed as En(f)/Em(f) ~ (1) where xi 1 for surface waves and xi 2 for body waves. By means of (1), the behaviour of the product f3Q~has been studied as a function of frequency by considering pairs of stations situated more or less on straight lines leaving the epicentre. One constant characteristic observable in this type of analysis is a fairly regular increase of the quantity $Q~with increasing frequency. Since there is no reason to assume that there is any variation in travel time as a function of frequency, /3 has been given a constant value of 3.5 km s~. By varying the stations two at a time, numerous values have been calculated for Q,~as a function of frequency throughout the area analysed, according to =
=
=
Q~(f)=[2irf log e(R~—R~)]//3[log(E~(f)/ Em (I)) xi log( Rm/Rn)] (2) —
As shown in the examples in Fig. 2, plotting of (2) for xi 1 and xi 2 identifies areas providing good estimates for Q~(f). The curves obtained for xi 0 =
=
=
CAUTRI-BISACCIA
v2 v=i
~RN0~SNSEVER00
100 ~ 100
10
BRIENZA—TRICARICO
TORRE
looc
,~c0-GARIGLIANO~20
100 10
-
________
__________
1
_______
10
__________
100
1
_________
10
Hz
Fig. 2. Specimens of ~ computed under the hypothesis of absence of geometrical spreading (v spherical (~ = 2) propagation of seismic waves starting from the focus.
=
100 0), and for surface (v = I) or
213
represent the case in which geometric spreading is neglected and the attenuation of seismic-wave energy is due entirely to the exponential term in (1). An approximately linear increase with frequency can be observed in all cases, independently of xi.
4. Azimuthal
Q~investigations
The large number of accelerometric stations triggered by the strong earthquake of November 23, 1980 and their fairly homogeneous spatial distribution around the epicentre have made it possible to attempt to investigate eventual azimuthal variations of Q~.By selecting pairs of stations
TABLE II List of station pairs used for calculating Q,~and azimuthal estimates of the degree of dependence on frequency Pairs of stations
Azimuth 6
Degree of dependence on frequency (n)
lying approximately in the same direction, two regions with fairly abundant data were found. The first of these, comprising sites mainly on the Tyrrhenian side and stations situated west of the epicentre, is delimited by two straight lines from the epicentre running northwest and southwest, respectively. The second region comprises stations on the Adriatic side and sites east of the epicentre, and is delimited by lines running approximately north-northeast and southeast (see Fig. 1). The Q~( f) profiles obtained by applying (2) for pairs of stations in these two sectors were considered separately. xi 1 was selected as being the value resulting in the greatest stability throughout the frequency range considered. Table II shows the pairs of stations from which data were used. An attempt to effect a fine azimuthal analysis along =
specific straight lines leaving the epicentre failed to give clear results, as many station pairs were unavailable for several specific azimuths: in Table II, 9 is the angle between the straight line connecting the barycentre of the station pair under investigation with the epicentre, and the northwest—southeast directrix crossing the epicentre. ______________
___________
________
aI
Adriatic side Sturno—Bovino Sturno—S. Severo S. Severo—Bovino Bisaccia—5. Severo Calitri—S. Severo Calitri—Bovino Rionero in Vulture—S. Severo Sturno—Vieste Calitri—Bisaccia Calitri—Vieste Rionero in Vulture—Bovino Rionero in Vulture—Vieste Tricarico—Calitri Tricarico—Brienza
410
42° 52° 54° 60° 63° 65° 67° 740
76° 77° 83° 142° 161°
1.0 1.0 0.7 1.1 1.1 1.2 0.9 1.1 0.8 1.4 0.9 0.9 1.0 0.6
10
—
_____________
—
_______________
—
______
—
________________
324° 332° 333° 3370
337° 338° 339~ 347~ 348°
1.4 1.1 1.2 0.9 1.0 1.0 0.9 1.0 1.1
________
_______________
________
________________
________
b) ________________
1~ —
Tyrrhenian side Bagnoli Irpino—Torre del Greco Torre de Greco—Garigliano Garigliano—Mercato S. Severino Bagnoli Irpino—Arienzo Sturno—Torre del Greco Bagnoli Irpino—Garigliano Arienzo—Garigliano Sturno—Garigliano Sturno—Arienzo
______________
_________________
—
______________ ______________
0.1
________
______________
10
I r~uency(Hz)
Fig. 3. Averaged Q~behaviour as a function of frequency, together with standard deviations, calculated separately for (a) the Adriatic and (b) the Tyrrhenian side of central southern Italy.
214
Clear azimuthal variations could not be evidenced:
Q~2,provided that Q~of the medium is
dence for
both east and west of the epicentre. This fact deserves careful consideration. A practically linear relationship between Q~and frequency denotes a constant turbidity g. The turbidity coefficient g was introduced by Nicolaev (1968), and is related to Q~ by the expression
the intrinsic attenuation considered negligible with respect to the last term in (5). This would seem to indicate that the scattering mechanisms for seismic waves in the band 0.1—25 Hz have a greater effect on apparent Q~than do dissipative effects. An effect basically similar from the physical standpoint, although occurring in quite different circumstances, has been reported by Spencer et al. (1982). It was observed that, on analysing seismic data from seismometers situated at various depths along vertical profiles, for small distances between seismometers, Q values calculated using the spectral-ratio method were influenced more by the effects of local stratigraphy than by the actual attenuation undergone by the seismic waves over the distance between the seismometers. Other interesting considerations emerge from a comparison with the isoseismal map for the Irpinia earthquake (Progetto Finalizzato Geodinamica, 1981). By using macroseismic investigations, some strong directional variations in energy attenuation become evident: for example, the approximately horizontal straight line connecting the epicentre with Torre del Greco (or with Garigliano) shows a different degree of attenuation compared to the epicentre—Bovino—S. Severo—vieste straight line. This does not appear in the Q~ (f) plots relating to stations located in these two alignments; a remarkable similarity appears systematically in the behaviour of Q~(f)in these diffferent directions (see for example, Q,~for the pairs Calitri—Bisaccia and Torre del Greco—Garigliano in Fig. 2). In the light of these results, azimuthal variations of the seismic energy seem to depend more on source directivity effects than on spatial variations of the
g
physical attenuation parameters.
when the degree of dependence on frequency (n in the hypothesis that Q ccf”) is plotted with respect to azimuth 9, no correlation of n with 9 is apparent, as can be inferred from the data in Table II. The analysis was thus restricted to the two regions lying respectively to the east and west of the epicentre. Figure 3 shows the mean values and relative standard deviations at each frequency for the two regions. The operation of computing the mean values was performed separately using a suitable calculation code for the data from the east and west sectors and summing all the values (on a logarithmic scale) frequency-by-frequency. Whenever the value for one or more curves at a given frequency deviated from the mean value obtained for all the curves by more than the range identified by the standard deviations, this value was neglected and a fresh calculation made of the mean value and standard deviation at that frequency. The behaviour of Q,3( f) is surprisingly similar in both zones, despite their rather different geological and structural characteristics (see for example, Calcagnile and Panza, 1979). The differences, due more to fluctuations in the evaluation rather than to physical causes, are not appreciable. A realistic fitting of data referring to the 0.1—25 Hz band for the two profiles in Fig. 3 is Q (f’~ 40f(Hz\ (3) —
$‘
=
/
‘
/
2irf,//3Q~
(4)
The result (3) is in good agreement with Dainty’s model (1981) which postulates for body waves that g is practically constant with frequency and depends solely on the number of scattering elements per unit volume, the cross-section of the scattering elements themselves being determined almost solely by their physical size. Dainty’s conclusion, l/Q~(f) = l/Q
+
/lg/2srf
(5)
predicts an approximately linear frequency depen-
5. Detailed analysis for low-Q~zone Theoretical models of Q~for cracked crustal rocks predict a minimum of at frequenciet depending on the width scale of the cracks (see Kikuchi, 1981) or on physical parameters that characterize the degree of interconnection between the cracks, such as viscosity (O’Connell and Budianski, 1977). Aki (1980b, 1981) observed that
215
in tectonically more-active zones, for which at low frequencies (—. 1 Hz) Q~takes values much lower than for tectonically more-stable zones, Q~must have a minimum between — 0.2 and 1 Hz, since the apparent quality factor obtained from surface-wave analysis (e.g., at 0.05 Hz) is extremely high, i.e., between 500 and 1000 (for an exhaustive review of surface-wave attenuation in different situations and for different crust types, see Kovach (1978)). Experimental profiles of apparent Q~versus frequency should, according to Aki, thus display a minimum point for decreasing frequencies, tending to increase again at the lowest frequencies that can be analysed using this method for values corresponding to the characteristic band of surface waves. The means of the spectral amplitude measured every 0.25 Hz, with subsequent drastic smoothing of the spectra, failed to show
resolution frequency spectra were then used for analysis in the 0.05—2.5 Hz band. After low-pass filtering (this time with a roll-off frequency of 0.5 s and a cut-off frequency of 2 s), 24 profiles of high-resolution apparent Q~were obtained as a function of frequency in the 0.05—2.5 Hz band. Not all the Q~( f) curves in the low-frequency range covered displayed a coherent profile. Only six had a clear minimum, between 0.2 and 1 Hz, for both xi I and xi 2. In many cases (nine in fact), the Q~( f) curve is monotonically increasing with frequency. The other nine cases are hard to interpret, as they indicate either an unclear increase in at lower frequencies or else incoherence between the Q~ ( f) behaviour for xi = and that for xi = 2. Typical examples of these different experimental curves are shown in Fig. 4. The low-frequency Q1~’ peak cannot easily be
any detailed apparent Q~ deviations in the low-Q~ zone. The spectral amplitudes calculated every 1/40.96 Hz were thus reconsidered. These high-
displayed with any degree of stability using the local-earthquake spectral-ratio method. This is due partly to the smoothing, which shifts energy into
—
—
CALITRI—SAN SEVERO
=
BItGNOII IRPINO—ARIENZO
:rZ1
-2
=
CALITRI—BISACCIA
______
STURNO-GARIGLIANO io: ~=2
STURNO—TORRE DEL GRECO
CALITRI-TRICARICO
~
RIONERD IN VULTURE—SAN SEVERO ~51!O~52.b2~
RIONERO IN VULTURE-BOVINO ~5~!O,!52O2~
CALITRI—BOVINO ~51~O~:52:O2~
frequency (Hz) Fig. 4. “Zoom” analysis for low-Q~band: left, some Q~(f)plots increasing monotonically; middle, unstable or incoherent trends for v I compared with v = 2; right, Qp(f) behaviour showing a minimum between 0.2 and 1 Hz.
216
neighbouring frequency bands, and partly to the low reliability of the long-period wave spectrum for the inadequate number of cycles in the time interval analysed. Moreover, mainly for the stations closest to the epicentre, source effects of the near field cannot be removed entirely by using the spectral ratios in the longer-wavelength band.
(— 1 Hz), low values of Q~values appear to be two or three times lower than Q~for northern at low frequencies
(<50) are obtained. These
Italy (Friuli) at the same frequency. The curves calculated using high resolution power in the lowQ1~zone display an evident Q~1peak between 0.2 and 1 Hz only in the case of six accelerometric station pairs.
6. Conclusions Acknowledgements As in a previous analysis of Friuli (1976) accelerograms from northern Italy (see Console and Rovelli, 1981), for central southern Italy an approximately linear relationship has been found between apparent Q~for seismic waves and frequency in the 0.1—25 Hz range at distances up to 150 km from the epicentre. These results seem to confirm the model of Dainty (1981) which requires a constant turbidity coefficient for body waves or, equivalently, Q,~proportional to f when the effects of transformation of mechanical energy into heat appear to be negligible. In terms of mean free path, of which g is the inverse, a value of — 20 km is obtained for Irpinia, which is slightly lower than that calculated for other regions (for example, for Friuli l/g 50 km on the basis of both accelerogram spectra and coda-wave analysis). The strong linear dependence of apparent Q,.
3
on frequency shown in central southern Italy using the spectral-ratio method seems to indicate that calculated Q~refers to energy losses due to scattering; a weaker degree of dependence on frequency usually appears for intrinsic Q (see Clements, 1982). On the basis of these considerations it is not surprising that, on a large scale, geological structures differing as greatly as the two areas investigated (i.e., one facing the Tyrrhenian Sea and the other facing the Adriatic Sea) should display approximately the same apparent Q~behaviour, if this parameter is practically dependent only on the scale of heterogeneity of the lithosphere, and on the physical size of the scattering elements. The net increase with frequency found for Q by analysing the Irpinia accelerometric data confirms the correlation observed by Aki (1980b, 1981) between level of tectonic activity and degree of dependence on frequency: also in the present case,
An early version of this work was presented as a Short Communication at the International School of Applied Geophysics (Erice, Italy, 1982). The author thanks the Organizing Committee and in particular Prof. R. Cassinis for this opportunity. Particular gratitude is expressed to Prof. I.P. Kosminskaya for many helpful discussions and for precious Russian material concerning turbidity and seismic-attenuation research. Thanks are due to Prof. E. Boschi for continuous encouragement and support to this research work.
References Aki, K., 1980a. Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys. Earth Planet. Inter., 21: 50—60. Aki, K., 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res., 85: 6496—6504. Aki, K., 1981. Scattering and attenuation of high-frequency body waves (1—25 Hz) in the lithosphere. Phys. Earth Planet. Inter., 26: 241—243. Aki, K. and Chouet, B., 1975. Origin of coda waves: source, attenuation and scattering effects. J. Geophys. Res., 80: 3322—3342. Berardi, R., Berenzi, A. and Capozza, F., 1981. Terremoto Campano—Lucano del 23 Nov. 1980: registrazioni accelerometriche della scossa principale e loro elaborazioni. Annu. Meet., Progetto Finalizzato Geodinamica Udine (Ital 1981 Calcagnile, G. and Panza, G.F., 1979. The lithosphere— asthenosphere system in the Italian area. Proc. 8th Symp. Eur. Geophys. Soc., Vienna, 1979. Clements, J.R., 1982. Intrinsic and its frequency dependence. Phys. Earth Planet. Inter. 27: 286—299. . . Cohen, T.J., 1970. Source-depth determinations spectral, pseudo-autocorrelation and cepstral analysis.using Geophys. J.,
)
Q
R. Astron. Soc., 20: 223—231. Console, R. and Rovelli, A., 1981. Attenuation parameters for
217 Friuli region from strong-motion accelerogram spectra. Bull. Seismol. Soc. Am., 71: 1981—1991. Dainty, AM., 1981. A scattering model to explain seismic observations in the lithosphere between I and 30 Hz. Geophys. Res. Lett., 8: 1126—1128. Dainty, A.M. and Toksoz, M.N., 1981. Seismic codas on the Earth and the Moon: a comparison. Phys. Earth Planet. Inter., 26: 250—260. Der, Z.A., McElfresh, T.W. and O’Donnell, A., 1982. An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the United States in the 0.5—4 Hz band. Geophys. J., R. Astron. Soc., 69: 67—99. Fedotov, S.A. and Boldyrev, S.A., 1969. Frequency dependence of the body-wave absorption in the crust and the upper mantle of the Kurili Island chain. Izv. Akad. Sci. USSR, Phys. Solid Earth, 9: 17—33. Hermann, RB., 1980. estimates using the coda of local earthquakes. Bull. Seismol. Soc. Am., 70: 447—468. Kikuchi, M., 1981. Dispersion and attenuation of elastic waves due to multiple scattering from cracks. Phys. Earth Planet, Inter., 27: 100—105. Kovach, R.L., 1978. Seismic surface waves and crustal and upper mantle structure. Rev. Geophys. Space Phys., 16: I — 13. Mitchell, B.J., 1980. Frequency dependence of shear wave internal friction in the continental crust of eastern North
Q
Q
America. J. Geophys. Res., 85: 5212—5218. Mitchell, B.J., 1981. Regional variation and frequency dependence of Q in the crust of the United States. Bull. Seismol. Soc. Am., 71: 153 1—1538. Nicolaev, A.V., 1968. Seismic properties of weakly heterogeneous media. Izv. Akad. Sci. USSR, Phys. Solid Earth, 8: 83—87. Nuttli, O.W., 1980. The excitation and attenuation of seismic crustal phases in Iran. Bull. Seismol. Soc. Am., 70: 469—485. O’Connell, R.J. and Budianski, B., 1977. Viscoelastic properties of fluid-saturated cracked solids. J. Geophys. Res., 82: 57 19—5735. Progetto Finalizzato Geodinamica, 1981. Il terremoto Campano—Lucano del 23 Nov. 1980: elaborazione preliminare dei dati sismometrici. Consiglio Nazionale delle Ricerche, Rome (Italy). Rautian, T.G. and Khalturin, V.1., 1978. The use of the coda for determination of the earthquake source spectrum. Bull. Seismol. Soc. Am., 68: 923—948. Rovelli, A., 1982. On the frequency dependence of Q in Friuli from short-period digital records. Bull. Seismol. Soc. Am., 72: 2369—2372. Spencer, T.W., Sonnad, J.R. and Butler, T.M., 1982. Seismic stratigraphy or dissipation. Geophysics, 47: 16—24. Tsujiura, M., 1978. Spectral analysis of the coda waves from local earthquakes. Bull. Earth Res. Inst., Tokyo Univ., 53: 1—48.
Q:
Frequency relationship for seismic
209
of central southern Italy
from accelerograms for the Irpinia earthquake (1980) Antonio Rovelli Isuituto Nazionale di Geofisica, Osservatorio Geofisico Centrale, Monte Porzio Catone, Rome (Italy) (Received September 27, 1982; revision accepted December 14, 1982)
Rovelli, A., 1983. Frequency relationship for seismic of central southern Italy from accelerograms for the Irpinia earthquake (1980). Phys. Earth Planet. Inter., 32: 209—217. The frequency dependence of for seismic waves in a distance range with a maximum of 150 km from the epicentre of the Irpinia earthquake of November 23, 1980 has been sought using displacement spectral ratios computed from strong-motion accelerograms recorded in the region. The method has been applied to calculate the behaviour of Q~ as a function of frequency in the band 0.1—25 Hz, and to investigate whether azimuthal variations appear in seismic Q~for the lithosphere in central southern Italy. The same result is obtained using data from stations in western south Italy as using data from eastern south Italy, namely,
Q~(f)
40f(Hz)
The linear relationship suggests that apparent Q~depends more on the scale of heterogeneity of the lithosphere, affecting reflection and scattering mechanisms, than on intrinsic energy losses related to the anelasticity of the materials through which the seismic waves propagate. The existence of a peak in Qj~has been investigated in the low-frequency band (0.1—2.5 Hz) using a higher resolution power. A stable result in this low-Qp zone is not possible on the basis of the available data: only in SiX Q~(f) profiles does an evident minimum exist, between 0.2 and 1 Hz, while in nine cases the curves are monotonically increasing from the lowest observable frequencies; a further nine cases appear of uncertain interpretation.
1. Introduction Following the seismic crisis in Friuli (May and September 1976), Console and Rovelli (1981) and Rovelli (1982) observed in this region a strong, practically linear dependence of apparent Q1~on frequency over the range 0.1—10 Hz, both by means of spectral ratios from strong-motion accelerograms at different epicentral distances recorded after the stronger shocks (see Console and Rovelli, 1981), and by analysing waves using of the digital codas of low-magnitude eventsshear processed bandpass filters (see Rovelli, 1982) with numerical methods derived from the analogue techniques 003l-9201/83/$03.00
© 1983 Elsevier Science Publishers B.V.
introduced by Aki and Chouet (1975) and Tsujiura (1978) for coda-wave analysis. Inreviewing a series of previous works (Aki, 1980a; Hermann, 1980; Nuttli, 1980), Aki has demonstrated exhaustively that the dependence of apparent Q~on frequency is general and is stronger the higher the current tectonic activity in the zone in which is measured. Aki (l980a,b; 1981) pointed out that in Japan differences have been found between vanous regions with differing tectonic (in a 08,situations while in other zone inofthe ~fcxf°~).The results zones theKanto same district districtQ,9 Q~ of Fedotov and Boldyrev (1969) for the Kurili Islands and of Rautian and Khalturin (1978) for
210
Garm (Central Asia) revealed an apparent Q dependence on frequency of the type Q~ ~ ffl (with n equal to 0.6 and 0.5, respectively). Using Rayleigh waves, Mitchell (1980, 1981) also found an undeniable, although less marked (proportional to f’1 with 0.2 < n <0.5), dependence of the quality factor on frequency in the upper m:ntle. Also, ~ifln th~
~
13
l4~
l5~
•S.SEVER 41
~0RR~EI~.~*
17
VIESTE
EPICENTER
different regions analysed in the United States. in eastern regions, apparent quality-factor values at the same frequency two or three times higher than in western regions were found; similar results for intrinsic Q for the upper mantle under the United States have been made evident by Der et al. (1982). The recent earthquake in Irpinia (November 23, 1980) and the large number of strong-motion accelerometric stations situated in the epicentral region made it possible to study apparent Q~as a function of seismic-wave frequency in central southern Italy over a range of distances no greater than 150 km from the epicentre in the frequency band 0.1—25 Hz.
16~
~
ERCA,~
IN VIIIIRE
H
1 S.SEV. ‘TRICARICO,~~ ~IAOHOLIP~IA ~
(
TYI~RHENIAN SEA _____
ACCELEROMEIRIC STATIONS
tRIGGERED BY THE IRPINIA EARTHQUAKE OF 23rd NOV. 1980
________________________________________ Fig. 1. Locations of accelerometric stations of the ENEL network that were triggered by the Irpinia earthquake of November 23, 1980.
2. Acquisition and processing of accelerometric data Many of the SMA- 1 accelerometers in central southern Italy in the network set up by Ente Nazionale per l’Energia Elettrica (ENEL) were triggered by the strong Irpinia earthquake of November 23, 1980. Figure 1 shows the locations of the stations used in the present work. Table I shows the site characteristics for each accelerometer. For further information concerning the characteristics of the stations, the instrumentation and the record processing, readers are referred to publications of the Commissione CNEN—ENEL per lo Studio Congiunto dei Problemi Sismici connessi con la Realizzazione di Impianti Nucleari (see for example, Berardi et al., 1981). Accelerometric data were kindly supplied by the Comitato Nazionale per l’Energia Nucleare (CNEN) already digitized on magnetic tape. The first 40.96 s (the equivalent of 4096 samples) of the N—S and E—W components for each of the stations considered were processed using standard Fourier techniques. For those stations with a record duration of less than 40.96 s, i.e., comprising fewer than 4096 samples,
zeros were added to bring the set up to the desired length. From the values of the Fourier spectra (one every 1/40.96 Hz) thus obtained, mean values were calculated for contiguous bands 0.25 Hz wide. The frequency range 0—25 Hz was analysed. A hundred or so spectral-amplitude values were thus obtained as a function of frequency for the two horizontal components for all the stations considered. The spectra were then smoothed drastically using a low-pass filter, i.e., liftering with a roll-off quefrency of 0.05 s and a cut-off quefrency of 0.2 s (for the use of liftering techniques, see for example, Cohen (1970)); instability and sharp peaks were thus removed from the spectra so that smooth, regular curves were obtamed. The smoothed spectra were then corrected for instrumental effects by means of the frequency-response curves H(f) of the accelerometers, which differed slightly from one accelerometer to another, of the general form —
2
H(f)
{(f~/f2
—
1)
—
+ 4h2f02/12J
1/2
211 TABLE I Accelerometric station coordinates and geological characteristics (from Berardi et al., 1981) Accelerometer location
Coordinates
Geological site characteristics
Latitude
Longitude
Arienzo
4I00l~43~r
14°28’OO”
Cinerites and pyroclastites mixed with conoid material (5 m) and grey tuff (5 m), overlying compact limestones of the Campania—Lucania platform
Auletta
4O033~37~~
15°33’30”
Polygenic conglomerates of delta and lacustrine origin, and sand—clay cement (l4~lm)
Bagnoli Irpino
40°49’l5”
15°04’lO”
Limestones, dolomitic limestones, and whitish limestones of the Campania—Lucania platform
Bisaccia
41 ~
150 32’33”
Clays and slates, usually flaky with intercalations of marly limestone, calcarenite and nummulitic rubble (variegated clays)
Bovino
41°l5’02”
15°30’35”
Pliocene sand and sandstone with levels of polygenic puddingstone and sandy clays (25 m) overlying polygenic puddingstone
Brienza
4Oo28~27~~ 15°38’06”
Irregularly stratified polygenic conglomerates with sands, probably of fluviolacustrine origin (25 m), overimposed on flyshoid materials
Calitri
40°55’Ol”
15°26’l9”
Mainly sandstone and grey, yellowish and reddish sands (30 m), resting on marls and grey—blue silty clay
Garigliano
410
l5’32”
l3°49’36”
Thinly stratified limestone and white marly limestone with flint sheets and nodules
Mercato S. Sevenno
40°47’29”
l4°45’5l”
Recent alluvials consisting mainly of sands, gravel and swamp clays (70 m), on lithoid tuff
Rionero in Vulture
40°55’46”
15°40’lO”
Dark, normally stratified subaerial tuff, ranging in colour from grey to dark brown, fairly coherent.
San Severo
4l04l~02~~ 15°23’lO”
Sturno
41001 ‘21”
Torre del Greco
4Oo48~O4~~ 14°23’08”
Leucitic lava ranging from iron-grey to dark, — 25 m thick, overlying lapilli and cinerites from the lower Vesuvius slopes
Tricarico
4Oo37~l5~~
16°09’25”
Calcarenite banks, light yellow or pink in colour, alternating with dark grey marls, with levels of arenaceous silt or sandstone
Vieste
41 o52~43~~
16°09’52”
Thinly stratified limestone and white marly limestone with flint sheets and nodules
Variable-grain, somewhat cemented yellowish sand, with intercalations of conglomerates and clays (Serracapriola sand)
15 oo7~o2~~ Silty clay and dark silty marl, alternating with marly limestone and quartz sandstone
where f is the frequency, h the damping constant (usually between 50 and 70% of critical damping) and f~the normalisation frequency, which varies from 25 to 27 Hz. In order to evaluate the displacement spectra for each of the stations, the vectorial composition of the smoothed and corrected spectra of the two horizontal components was carried out.
3. Seismic-wave attenuation: physical assumptions and observational results Denoting as G~(f) the estimate obtained as outlined above for the amplitude-displacement spectrum for the n th station situated at a distance R~from the epicentre, the energy—frequency distribution of the seismic waves recorded at the nth station may be described by the expression
212
E~(f) JG~(f)12 E0(f)F(R~)e2~~”°~ The seismic-wave energy at the n th station has been assumed to depend on the frequency distribution E 0(f) at the source and on geometric spreading F(R~),which is a function solely of the station’s distance from the focus. The exponential term describes the loss of energy suffered by seismic waves in the medium they are passing through; /3 is the velocity of waves bearing the largest part of the energy recorded (practically speaking, the direct and scattered S waves), and is the term describing the extent to which these waves are attenuated with distance and frequency. This last parameter basically takes two physical mechanisms into account: the conversion of mechanical energy into heat (Aki, l980a), and losses of energy due to scattering of seismic waves caused by crust heterogeneity (Aki, l980b; Dainty and Toksöz, 1981; Dainty, 1981). Assuming that the geometric spreading patterns may vary from spherical propagation, for which F(R~) is inversely proportional to the square of the distance R~(this is the exact case for pure body waves, whose energy propagates along concentric spheres radiating from the focus), to propagation of the surface-wave type, for which F(R~)cr l/R,,, the =
Q~
=
ratio between the energy evaluations made in two stations measuring waves of these types is ohtamed as En(f)/Em(f) ~ (1) where xi 1 for surface waves and xi 2 for body waves. By means of (1), the behaviour of the product f3Q~has been studied as a function of frequency by considering pairs of stations situated more or less on straight lines leaving the epicentre. One constant characteristic observable in this type of analysis is a fairly regular increase of the quantity $Q~with increasing frequency. Since there is no reason to assume that there is any variation in travel time as a function of frequency, /3 has been given a constant value of 3.5 km s~. By varying the stations two at a time, numerous values have been calculated for Q,~as a function of frequency throughout the area analysed, according to =
=
=
Q~(f)=[2irf log e(R~—R~)]//3[log(E~(f)/ Em (I)) xi log( Rm/Rn)] (2) —
As shown in the examples in Fig. 2, plotting of (2) for xi 1 and xi 2 identifies areas providing good estimates for Q~(f). The curves obtained for xi 0 =
=
=
CAUTRI-BISACCIA
v2 v=i
~RN0~SNSEVER00
100 ~ 100
10
BRIENZA—TRICARICO
TORRE
looc
,~c0-GARIGLIANO~20
100 10
-
________
__________
1
_______
10
__________
100
1
_________
10
Hz
Fig. 2. Specimens of ~ computed under the hypothesis of absence of geometrical spreading (v spherical (~ = 2) propagation of seismic waves starting from the focus.
=
100 0), and for surface (v = I) or
213
represent the case in which geometric spreading is neglected and the attenuation of seismic-wave energy is due entirely to the exponential term in (1). An approximately linear increase with frequency can be observed in all cases, independently of xi.
4. Azimuthal
Q~investigations
The large number of accelerometric stations triggered by the strong earthquake of November 23, 1980 and their fairly homogeneous spatial distribution around the epicentre have made it possible to attempt to investigate eventual azimuthal variations of Q~.By selecting pairs of stations
TABLE II List of station pairs used for calculating Q,~and azimuthal estimates of the degree of dependence on frequency Pairs of stations
Azimuth 6
Degree of dependence on frequency (n)
lying approximately in the same direction, two regions with fairly abundant data were found. The first of these, comprising sites mainly on the Tyrrhenian side and stations situated west of the epicentre, is delimited by two straight lines from the epicentre running northwest and southwest, respectively. The second region comprises stations on the Adriatic side and sites east of the epicentre, and is delimited by lines running approximately north-northeast and southeast (see Fig. 1). The Q~( f) profiles obtained by applying (2) for pairs of stations in these two sectors were considered separately. xi 1 was selected as being the value resulting in the greatest stability throughout the frequency range considered. Table II shows the pairs of stations from which data were used. An attempt to effect a fine azimuthal analysis along =
specific straight lines leaving the epicentre failed to give clear results, as many station pairs were unavailable for several specific azimuths: in Table II, 9 is the angle between the straight line connecting the barycentre of the station pair under investigation with the epicentre, and the northwest—southeast directrix crossing the epicentre. ______________
___________
________
aI
Adriatic side Sturno—Bovino Sturno—S. Severo S. Severo—Bovino Bisaccia—5. Severo Calitri—S. Severo Calitri—Bovino Rionero in Vulture—S. Severo Sturno—Vieste Calitri—Bisaccia Calitri—Vieste Rionero in Vulture—Bovino Rionero in Vulture—Vieste Tricarico—Calitri Tricarico—Brienza
410
42° 52° 54° 60° 63° 65° 67° 740
76° 77° 83° 142° 161°
1.0 1.0 0.7 1.1 1.1 1.2 0.9 1.1 0.8 1.4 0.9 0.9 1.0 0.6
10
—
_____________
—
_______________
—
______
—
________________
324° 332° 333° 3370
337° 338° 339~ 347~ 348°
1.4 1.1 1.2 0.9 1.0 1.0 0.9 1.0 1.1
________
_______________
________
________________
________
b) ________________
1~ —
Tyrrhenian side Bagnoli Irpino—Torre del Greco Torre de Greco—Garigliano Garigliano—Mercato S. Severino Bagnoli Irpino—Arienzo Sturno—Torre del Greco Bagnoli Irpino—Garigliano Arienzo—Garigliano Sturno—Garigliano Sturno—Arienzo
______________
_________________
—
______________ ______________
0.1
________
______________
10
I r~uency(Hz)
Fig. 3. Averaged Q~behaviour as a function of frequency, together with standard deviations, calculated separately for (a) the Adriatic and (b) the Tyrrhenian side of central southern Italy.
214
Clear azimuthal variations could not be evidenced:
Q~2,provided that Q~of the medium is
dence for
both east and west of the epicentre. This fact deserves careful consideration. A practically linear relationship between Q~and frequency denotes a constant turbidity g. The turbidity coefficient g was introduced by Nicolaev (1968), and is related to Q~ by the expression
the intrinsic attenuation considered negligible with respect to the last term in (5). This would seem to indicate that the scattering mechanisms for seismic waves in the band 0.1—25 Hz have a greater effect on apparent Q~than do dissipative effects. An effect basically similar from the physical standpoint, although occurring in quite different circumstances, has been reported by Spencer et al. (1982). It was observed that, on analysing seismic data from seismometers situated at various depths along vertical profiles, for small distances between seismometers, Q values calculated using the spectral-ratio method were influenced more by the effects of local stratigraphy than by the actual attenuation undergone by the seismic waves over the distance between the seismometers. Other interesting considerations emerge from a comparison with the isoseismal map for the Irpinia earthquake (Progetto Finalizzato Geodinamica, 1981). By using macroseismic investigations, some strong directional variations in energy attenuation become evident: for example, the approximately horizontal straight line connecting the epicentre with Torre del Greco (or with Garigliano) shows a different degree of attenuation compared to the epicentre—Bovino—S. Severo—vieste straight line. This does not appear in the Q~ (f) plots relating to stations located in these two alignments; a remarkable similarity appears systematically in the behaviour of Q~(f)in these diffferent directions (see for example, Q,~for the pairs Calitri—Bisaccia and Torre del Greco—Garigliano in Fig. 2). In the light of these results, azimuthal variations of the seismic energy seem to depend more on source directivity effects than on spatial variations of the
g
physical attenuation parameters.
when the degree of dependence on frequency (n in the hypothesis that Q ccf”) is plotted with respect to azimuth 9, no correlation of n with 9 is apparent, as can be inferred from the data in Table II. The analysis was thus restricted to the two regions lying respectively to the east and west of the epicentre. Figure 3 shows the mean values and relative standard deviations at each frequency for the two regions. The operation of computing the mean values was performed separately using a suitable calculation code for the data from the east and west sectors and summing all the values (on a logarithmic scale) frequency-by-frequency. Whenever the value for one or more curves at a given frequency deviated from the mean value obtained for all the curves by more than the range identified by the standard deviations, this value was neglected and a fresh calculation made of the mean value and standard deviation at that frequency. The behaviour of Q,3( f) is surprisingly similar in both zones, despite their rather different geological and structural characteristics (see for example, Calcagnile and Panza, 1979). The differences, due more to fluctuations in the evaluation rather than to physical causes, are not appreciable. A realistic fitting of data referring to the 0.1—25 Hz band for the two profiles in Fig. 3 is Q (f’~ 40f(Hz\ (3) —
$‘
=
/
‘
/
2irf,//3Q~
(4)
The result (3) is in good agreement with Dainty’s model (1981) which postulates for body waves that g is practically constant with frequency and depends solely on the number of scattering elements per unit volume, the cross-section of the scattering elements themselves being determined almost solely by their physical size. Dainty’s conclusion, l/Q~(f) = l/Q
+
/lg/2srf
(5)
predicts an approximately linear frequency depen-
5. Detailed analysis for low-Q~zone Theoretical models of Q~for cracked crustal rocks predict a minimum of at frequenciet depending on the width scale of the cracks (see Kikuchi, 1981) or on physical parameters that characterize the degree of interconnection between the cracks, such as viscosity (O’Connell and Budianski, 1977). Aki (1980b, 1981) observed that
215
in tectonically more-active zones, for which at low frequencies (—. 1 Hz) Q~takes values much lower than for tectonically more-stable zones, Q~must have a minimum between — 0.2 and 1 Hz, since the apparent quality factor obtained from surface-wave analysis (e.g., at 0.05 Hz) is extremely high, i.e., between 500 and 1000 (for an exhaustive review of surface-wave attenuation in different situations and for different crust types, see Kovach (1978)). Experimental profiles of apparent Q~versus frequency should, according to Aki, thus display a minimum point for decreasing frequencies, tending to increase again at the lowest frequencies that can be analysed using this method for values corresponding to the characteristic band of surface waves. The means of the spectral amplitude measured every 0.25 Hz, with subsequent drastic smoothing of the spectra, failed to show
resolution frequency spectra were then used for analysis in the 0.05—2.5 Hz band. After low-pass filtering (this time with a roll-off frequency of 0.5 s and a cut-off frequency of 2 s), 24 profiles of high-resolution apparent Q~were obtained as a function of frequency in the 0.05—2.5 Hz band. Not all the Q~( f) curves in the low-frequency range covered displayed a coherent profile. Only six had a clear minimum, between 0.2 and 1 Hz, for both xi I and xi 2. In many cases (nine in fact), the Q~( f) curve is monotonically increasing with frequency. The other nine cases are hard to interpret, as they indicate either an unclear increase in at lower frequencies or else incoherence between the Q~ ( f) behaviour for xi = and that for xi = 2. Typical examples of these different experimental curves are shown in Fig. 4. The low-frequency Q1~’ peak cannot easily be
any detailed apparent Q~ deviations in the low-Q~ zone. The spectral amplitudes calculated every 1/40.96 Hz were thus reconsidered. These high-
displayed with any degree of stability using the local-earthquake spectral-ratio method. This is due partly to the smoothing, which shifts energy into
—
—
CALITRI—SAN SEVERO
=
BItGNOII IRPINO—ARIENZO
:rZ1
-2
=
CALITRI—BISACCIA
______
STURNO-GARIGLIANO io: ~=2
STURNO—TORRE DEL GRECO
CALITRI-TRICARICO
~
RIONERD IN VULTURE—SAN SEVERO ~51!O~52.b2~
RIONERO IN VULTURE-BOVINO ~5~!O,!52O2~
CALITRI—BOVINO ~51~O~:52:O2~
frequency (Hz) Fig. 4. “Zoom” analysis for low-Q~band: left, some Q~(f)plots increasing monotonically; middle, unstable or incoherent trends for v I compared with v = 2; right, Qp(f) behaviour showing a minimum between 0.2 and 1 Hz.
216
neighbouring frequency bands, and partly to the low reliability of the long-period wave spectrum for the inadequate number of cycles in the time interval analysed. Moreover, mainly for the stations closest to the epicentre, source effects of the near field cannot be removed entirely by using the spectral ratios in the longer-wavelength band.
(— 1 Hz), low values of Q~values appear to be two or three times lower than Q~for northern at low frequencies
(<50) are obtained. These
Italy (Friuli) at the same frequency. The curves calculated using high resolution power in the lowQ1~zone display an evident Q~1peak between 0.2 and 1 Hz only in the case of six accelerometric station pairs.
6. Conclusions Acknowledgements As in a previous analysis of Friuli (1976) accelerograms from northern Italy (see Console and Rovelli, 1981), for central southern Italy an approximately linear relationship has been found between apparent Q~for seismic waves and frequency in the 0.1—25 Hz range at distances up to 150 km from the epicentre. These results seem to confirm the model of Dainty (1981) which requires a constant turbidity coefficient for body waves or, equivalently, Q,~proportional to f when the effects of transformation of mechanical energy into heat appear to be negligible. In terms of mean free path, of which g is the inverse, a value of — 20 km is obtained for Irpinia, which is slightly lower than that calculated for other regions (for example, for Friuli l/g 50 km on the basis of both accelerogram spectra and coda-wave analysis). The strong linear dependence of apparent Q,.
3
on frequency shown in central southern Italy using the spectral-ratio method seems to indicate that calculated Q~refers to energy losses due to scattering; a weaker degree of dependence on frequency usually appears for intrinsic Q (see Clements, 1982). On the basis of these considerations it is not surprising that, on a large scale, geological structures differing as greatly as the two areas investigated (i.e., one facing the Tyrrhenian Sea and the other facing the Adriatic Sea) should display approximately the same apparent Q~behaviour, if this parameter is practically dependent only on the scale of heterogeneity of the lithosphere, and on the physical size of the scattering elements. The net increase with frequency found for Q by analysing the Irpinia accelerometric data confirms the correlation observed by Aki (1980b, 1981) between level of tectonic activity and degree of dependence on frequency: also in the present case,
An early version of this work was presented as a Short Communication at the International School of Applied Geophysics (Erice, Italy, 1982). The author thanks the Organizing Committee and in particular Prof. R. Cassinis for this opportunity. Particular gratitude is expressed to Prof. I.P. Kosminskaya for many helpful discussions and for precious Russian material concerning turbidity and seismic-attenuation research. Thanks are due to Prof. E. Boschi for continuous encouragement and support to this research work.
References Aki, K., 1980a. Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys. Earth Planet. Inter., 21: 50—60. Aki, K., 1980b. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res., 85: 6496—6504. Aki, K., 1981. Scattering and attenuation of high-frequency body waves (1—25 Hz) in the lithosphere. Phys. Earth Planet. Inter., 26: 241—243. Aki, K. and Chouet, B., 1975. Origin of coda waves: source, attenuation and scattering effects. J. Geophys. Res., 80: 3322—3342. Berardi, R., Berenzi, A. and Capozza, F., 1981. Terremoto Campano—Lucano del 23 Nov. 1980: registrazioni accelerometriche della scossa principale e loro elaborazioni. Annu. Meet., Progetto Finalizzato Geodinamica Udine (Ital 1981 Calcagnile, G. and Panza, G.F., 1979. The lithosphere— asthenosphere system in the Italian area. Proc. 8th Symp. Eur. Geophys. Soc., Vienna, 1979. Clements, J.R., 1982. Intrinsic and its frequency dependence. Phys. Earth Planet. Inter. 27: 286—299. . . Cohen, T.J., 1970. Source-depth determinations spectral, pseudo-autocorrelation and cepstral analysis.using Geophys. J.,
)
Q
R. Astron. Soc., 20: 223—231. Console, R. and Rovelli, A., 1981. Attenuation parameters for
217 Friuli region from strong-motion accelerogram spectra. Bull. Seismol. Soc. Am., 71: 1981—1991. Dainty, AM., 1981. A scattering model to explain seismic observations in the lithosphere between I and 30 Hz. Geophys. Res. Lett., 8: 1126—1128. Dainty, A.M. and Toksoz, M.N., 1981. Seismic codas on the Earth and the Moon: a comparison. Phys. Earth Planet. Inter., 26: 250—260. Der, Z.A., McElfresh, T.W. and O’Donnell, A., 1982. An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the United States in the 0.5—4 Hz band. Geophys. J., R. Astron. Soc., 69: 67—99. Fedotov, S.A. and Boldyrev, S.A., 1969. Frequency dependence of the body-wave absorption in the crust and the upper mantle of the Kurili Island chain. Izv. Akad. Sci. USSR, Phys. Solid Earth, 9: 17—33. Hermann, RB., 1980. estimates using the coda of local earthquakes. Bull. Seismol. Soc. Am., 70: 447—468. Kikuchi, M., 1981. Dispersion and attenuation of elastic waves due to multiple scattering from cracks. Phys. Earth Planet, Inter., 27: 100—105. Kovach, R.L., 1978. Seismic surface waves and crustal and upper mantle structure. Rev. Geophys. Space Phys., 16: I — 13. Mitchell, B.J., 1980. Frequency dependence of shear wave internal friction in the continental crust of eastern North
Q
Q
America. J. Geophys. Res., 85: 5212—5218. Mitchell, B.J., 1981. Regional variation and frequency dependence of Q in the crust of the United States. Bull. Seismol. Soc. Am., 71: 153 1—1538. Nicolaev, A.V., 1968. Seismic properties of weakly heterogeneous media. Izv. Akad. Sci. USSR, Phys. Solid Earth, 8: 83—87. Nuttli, O.W., 1980. The excitation and attenuation of seismic crustal phases in Iran. Bull. Seismol. Soc. Am., 70: 469—485. O’Connell, R.J. and Budianski, B., 1977. Viscoelastic properties of fluid-saturated cracked solids. J. Geophys. Res., 82: 57 19—5735. Progetto Finalizzato Geodinamica, 1981. Il terremoto Campano—Lucano del 23 Nov. 1980: elaborazione preliminare dei dati sismometrici. Consiglio Nazionale delle Ricerche, Rome (Italy). Rautian, T.G. and Khalturin, V.1., 1978. The use of the coda for determination of the earthquake source spectrum. Bull. Seismol. Soc. Am., 68: 923—948. Rovelli, A., 1982. On the frequency dependence of Q in Friuli from short-period digital records. Bull. Seismol. Soc. Am., 72: 2369—2372. Spencer, T.W., Sonnad, J.R. and Butler, T.M., 1982. Seismic stratigraphy or dissipation. Geophysics, 47: 16—24. Tsujiura, M., 1978. Spectral analysis of the coda waves from local earthquakes. Bull. Earth Res. Inst., Tokyo Univ., 53: 1—48.
Q: