We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activit

A. Carpinteri

A. Corral

A. Manuello

C. F. Richter

D. Krajcinovic

G. Lacidogna

G. Niccolini

T. Utsu

Y. Y. Kagan

English

We present a comparative statistical analysis between the time series of the acoustic emission (AE) events
detected from the ancient Greek Athena temple in Syracuse (Eastern Sicily, UNESCO World Heritage List
since 2005), and the time series of small and intermediate earthquakes occurred in this part of Sicily during
the AE monitoring period. The waiting-time distributions for both time series and different magnitude
thresholds are described by a unique scaling function indicating self-similarity over a wide range of
magnitude scales. The similarity between the waiting times in AEs and earthquakes suggests a correlation
between the microfracturing process accompanying ageing and deterioration of the monument and the
regional seismicity. Our results reveal that the structure of the Athena temple is particularly sensitive to the
normal seismic activity, suggesting structural AE monitoring as a useful tool for seismic hazard assessment

NICCOLINI, Gianni

LACIDOGNA, GIUSEPPE

MANUELLO BERTETTO, AMEDEO DOMENICO BERNARDO

CARPINTERI, Alberto

G. DURIN

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

AE monitoring of the Syracuse Athena Temple: Scale invariance in the timing of ruptures

We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions
for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activity

08 November 2022POLITECNICO DI TORINORepository ISTITUZIONALEAcoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures / Niccolini,Gianni; Carpinteri, Alberto; Lacidogna, Giuseppe; MANUELLO BERTETTO, AMEDEO DOMENICO BERNARDO. - In:PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - STAMPA. - 108503:(2011), pp. 1-4.[10.1103/PhysRevLett.106.108503]OriginalAcoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing ofRupturesPublisher:PublishedDOI:10.1103/PhysRevLett.106.108503Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2412928 since:Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariancein the Timing of RupturesG. NiccoliniIstituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, ItalyA. Carpinteri, G. Lacidogna, and A. ManuelloDepartment of Structural Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy(Received 14 June 2010; published 10 March 2011)We perform a comparative statistical analysis between the acoustic-emission time series from theancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparentassociation between acoustic-emission bursts and the earthquake occurrence. The waiting-time distribu-tions for acoustic-emission and earthquake time series are described by a unique scaling law indicatingself-similarity over a wide range of magnitude scales. This evidence suggests a correlation between theaging process of the temple and the local seismic activity.DOI: 10.1103/PhysRevLett.106.108503 PACS numbers: 91.62.Ty, 62.20.mj, 89.75.Da, 91.30.DkIntroduction.—Fracture in heterogeneous materials oc-curs as the culmination of progressive damage due toloading conditions or harsh environments. Damage growthis accompanied by the spontaneous release of stored strainenergy in the form of transient elastic waves [acousticemission (AE)] [1–3]. Thus, as it provides informationon the internal state of a material, AE monitoring is usedsuccessfully for the structural integrity assessment of ma-terials and also large-sized structures (buildings, bridges,etc.) before they become safety hazards [3,4]. This predic-tive power can be exploited to protect the Italian culturalheritage, as historic buildings and monuments are exposedto seismic risk. Many structures may undergo acceleratedaging and deterioration due to the action of small andintermediate earthquakes, rather frequent in SouthernItaly. The triggered damage, often inaccessible for visualinspection, eventually results in increased vulnerability tostrong earthquakes. Here, the results of AE monitoringof the Athena temple in Syracuse (Eastern Sicily) arepresented. We analyze the time correlation between theAE bursts from a temple pillar and the occurrence ofnearby earthquakes. Furthermore, we investigate consis-tency of scaling laws between AE and Eastern Sicilyearthquake waiting-time distributions.AE Monitoring of the Syracuse Cathedral.—In the sev-enth century, the Cathedral of Syracuse (on the UNESCOWorld Heritage List since 2005) was built onto the ruins ofthe ancient and famed Athena temple and afterward re-peatedly modified as a consequence of damages caused byearthquakes. The structure currently exhibits an extendeddamage pattern, especially in four pillars at the end of thenave, showing repaired areas, replacements, and also sev-eral cracks. The AE activity in one of the nave pillars wasmonitored over a four-month period by means of six piezo-electric transducers working in the range of 50–500 kHzattached to the pillar surface.After setting an appropriate detection threshold to filterout environmental background noise, we started data ac-quisition storing two quantities for each AE signal: thearrival time, determined by using the first threshold cross-ing of the signal, and the peak amplitude Vmax (expressedin V), which defines the magnitude of the AE event asM ¼ logðVmax=1 VÞ [3].Figure 1 displays the accumulated number of AE events,the AE instantaneous rate (averaged over 1 h), and theearthquake sequence as functions of time. Here, only earth-quakes with hypocentral distance  60 km from Syracuseare considered (Fig. 2 and Table I). There appears to be acorrelation in time between AE activity on the Cathedraland local seismicity, as AE bursts often follow the occur-rence of nearby seismic events.There appear to be some seismic events which followAE bursts and, then, which do not trigger AE activity onthe Cathedral. The occurrence of increased AE activity inseveral case histories from Italy was observed byCarpinteri, Lacidogna, and Niccolini and Gregori et al.Accumulated number of AE events AE rate ( events/hour)5000 3000 35002500200015001000t (hours) 5 1034 1033 1031 10302 10350 100 150 200 0300 Magnitude 1.0 2.0 3.04.0 5.0 FIG. 1 (color online). Accumulated number (black line), in-stantaneous AE rate averaged over 1 h (red line) in the templepillar, and nearby earthquake occurrence (triangles) as functionsof time.PRL 106, 108503 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 20110031-9007=11=106(10)=108503(4) 108503-1  2011 American Physical Societybefore large earthquakes [4,6]. In this case, AE burstsapparently indicate crustal stress crises affecting areas ofa few hundred kilometers radius during the preparation of aseismic event. In spite of intrinsic difficulties in high-frequency propagation through disjointed media (in par-ticular, at the ground-building foundation interface), part ofthe AE activity from the structures might derive fromprecursive microseismic activity. A rigorous investigationof causal relationships between AE bursts and earthquakeswould require simultaneous operation of suitable arrays ofAE monitoring sites, adequately placed in the territory,e.g., on the order of 1000 over a large regional area.Several studies established that the total rate of damage,as measured, for instance, by the accumulated AE releasedenergy, increases as a power law of the time to failureon the approach to the structural collapse [7,8]. Here, theabsence of a critical power-law behavior in the accumu-lated number of AE events in time, with two episodicabrupt increments at about 1800 and 2900 h (see Fig. 1),suggests that the structure experiences damage but is stillfar from unstable conditions.Scaling law for AE and earthquake waiting-timedistributions.—Space-time organization of AE and theearthquake source process is ruled by different powerlaws, among them, the Gutenberg-Richter law for themagnitude distribution [9], the Omori law for the rate ofaftershocks as a function of time from the main shock [10],and the fractal distribution law for the epicenters [11].However, power laws and critical exponents are not theonly scaling predictions for fracture processes. Startingfrom the pioneer work of Bak et al. [12], Corral foundthat the distributions of waiting times between consecutiveearthquakes follow a universal scaling law in differentregions of the world and earthquake catalogs if appropri-ately rescaled [13]. There has been an ongoing debatein the seismological community about the extent to whichuniversal scaling of earthquake temporal occurrence ap-plies to AE time series in laboratory fracture [14–18]. Thissuggests that timing of fractures might be self-similar overa larger range of magnitude than had been suggestedearlier. Here, the rescaling and collapsing procedure forwaiting-time distributions in a sequence of rupture eventsis illustrated. We select the NðMthÞ events with magnitudeM above a certain threshold Mth. The sequence is trans-formed into a point process where events occur at times tiwith 1  i  NðMthÞ  N, and therefore, the waitingtime between consecutive events can be obtained asi  ti  ti1. Thus, we compute the waiting-time proba-bility density function (PDF) as pMthðÞ  Probð waiting time< þ dÞ=d. Measuring the time in unitsof the mean waiting time hiMth  ðtN  t1Þ=ðN  1Þ,i.e., performing the transformation  ! =hiMth , changesalso the units of the PDF: pMthðÞ ! hiMthpMthðÞ.This rescaling procedure is applied to PDFs obtained forFIG. 2 (color online). Map of Sicily showing the location ofthe monitored site (yellow square) and epicenters (black circles)of nearby earthquakes (listed in Table I) that occurred during themonitoring period.TABLE I. List of earthquakes with hypocentral distance from Syracuse  60 km (extractedfrom the Eastern Sicily earthquake catalog [5]). Richter magnitude,ML;H, hypocenter depth; d,distance of monitoring site to the hypocenter; NAE, AE rate.Date Time Epicentral coordinates H (km) d (km) ML1 2006/09/19 03:20 37.09 15.35 20.2 21.4 2.02 2006/09/22 15:52 37.37 14.95 4.1 42.9 1.83 2006/09/26 16:59 37.62 15.14 13.6 62.0 2.54 2006/09/26 17:08 37.65 15.13 16.0 66.5 2.35 2006/10/14 23:55 37.25 14.78 18.4 50.8 3.06 2006/10/16 02:21 37.14 15.25 17.9 19.1 1.37 2006/10/16 03:40 37.05 14.76 16.7 48.5 1.68 2006/11/05 22:01 37.25 14.77 18.3 51.5 1.39 2006/12/05 05:01 37.06 15.61 24.3 38.8 2.910 2006/12/05 15:31 37.31 14.94 9.9 39.7 1.511 2006/12/07 16:23 37.34 14.93 0.0 40.9 1.612 2006/12/23 00:33 37.15 15.23 18.1 20.1 1.213 2006/12/25 08:02 37.23 15.17 16.1 24.6 1.814 2006/12/28 10:56 37.14 15.17 9.5 14.4 1.515 2007/01/09 09:57 37.08 15.57 14.0 30.1 1.916 2007/01/11 05:15 37.03 15.09 20.2 26.6 1.617 2007/01/14 23:23 36.90 14.98 17.6 37.2 1.9PRL 106, 108503 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 2011108503-2several values ofMth. If all the rescaled PDFs collapse ontoa single curve f, we can establish the fulfilment of a scalinglaw [13]:pMthðÞ ¼ fð=hiMthÞ=hiMth : (1)The mean waiting time can be expressed in terms of theGutenberg-Richter law [13,15]:hiMth ¼ T10aþbMth ; (2)where T  ðtN  t1Þ.By inserting Eq. (2), Eq. (1) takes the formpMthðÞ ¼ 10bMth ~fð10bMthÞ; (3)where ~fð10bMthÞ  kfðk10bMthÞ and k  T110a.If we consider events separated by waiting times  forM  Mth and 0  10b for M  M0th  Mth þ 1 and in-sert these particular arguments, (0; M0th) and (; Mth), intoEq. (3), we obtainpMthðÞ ¼ 10bpMthþ1ð10bÞ: (4)Equation (4) expresses self-similarity of the distributions,as they can be obtained from each other by a similaritytransformation [15]. The scaling function f is well ap-proximated by a generalized gamma distribution, whichis a common parameterization for all fracture systems fromthe microscopic scale (AEs) to the seismic scale (earth-quakes) [13–16]:fðÞ / ð1Þ exp½ð=xÞn; (5)where  is the rescaled waiting time:   =hiMth .Although the parameterization of Eq. (5) is valid for allfracture processes, from AE in laboratory experiments toearthquakes, the values of fitting parameters , x, and ngenerally depend on the window of observation [13]. Inparticular, the power-law exponent 1  indicates theclustering degree in time of events. For example, whenaftershock sequences or earthquake swarms dominate theselected time window T, the power-law exponent is high(1  ¼ 1:5 [18] against 0.3 for stationary activity orslowly varying event rates [13–16]), indicating that earth-quakes are close in time.Previously, Kagan [19–21] in a different approachpointed out that the number of short waiting times betweenlarge earthquakes exceeds the number expected for mem-oryless Poisson recurrence. This behavior, indicating clus-tering, is the opposite of the regularity or quasiperiodicityderived from the idea of the seismic cycle. A surprisingconsequence of clustering is the paradoxical result that thelonger it has been since the last earthquake, the longerthe expected time until the next [13,19–21]. Here, below,the temporal occurrence of rupture events at differentsize scales will be investigated. First, we analyze thefracture process of a Syracuse limestone cylindricalspecimen (base diameter 120 mm and height 120 mm).The specimen was subjected to uniaxial compression at aconstant displacement rate of 0:1 ms1, by using aservo-hydraulic press with a maximum capacity of500 kN. We set the AE detection threshold to filter outbackground noise. In this way, we ensured that no spuriousAE signals would be detected before the beginning ofthe test.In Fig. 3, the solid line represents the stress vs timediagram, characterized by irregular trend and stress dropsdue to damage accumulation before the specimen failure.Such quasibrittle behavior characterize heterogeneous ma-terials [22]. The dashed line represents the accumulatednumber of AE events as a function of time. Stress dropswere followed by as many drops in the AE activity, sug-gesting momentary relaxation until the stress exceeds theprevious reached values (Kaiser effect [23]).We analyze the AE time series until the peak stress,when the specimen fails, and also for the complete durationof the experiment. The PDFs of waiting times are calcu-lated from both sequences and the corresponding rescaleddistributions that appear in Fig. 4. In both cases, the datacollapse illustrates the validity of a scaling law of the typeof (5), although the scaling function f is different. The fityields  ¼ 0:23 0:02, x ¼ 2:23 1:00, and n ¼ 1:150:16 before peak load and  ¼ 0:46 0:04, x ¼ 5:613:15, and n ¼ 0:99 0:14 for the whole duration ofexperiment. In the first case, the power-law exponent isTime (s) 10 20 30 40 50 00.5 1031.0 1031.5 1032.0 1032.5 1033.0 1030 103 1 103 2 103 3 103 4 103 5 103 6 1030.0 103NAE(t)Stress (MPa) t (s) Load AE FIG. 3. Applied load (solid line) and accumulated number ofAE events (dashed line) as functions of time.10310110–110–3f (Mth)(dimensionless)10–5              10–3               10–1              101                   / Mth (dimensionless)(a)Mth)(dimensionless)10–3                 10–1                   101 /f (Mth (dimensionless)(b) 10210010–210–4FIG. 4 (color online). Rescaled waiting-time PDFs for theperiod preceding the peak load (a) and for the whole durationtest (b), for several Vth values, equivalent to Mth ¼logðVth=1 VÞ. The data collapse illustrates the fulfilment of ascaling law, where the solid line is the scaling function of Eq. (5).PRL 106, 108503 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 2011108503-3higher (1   0:77 against 0.54) because of the largenumber of AE events close in time which typically precedethe specimen failure.Now, we use the scaling approach to study the AE eventsfrom the pillar and the Eastern Sicily earthquakes. ThePDFs of rescaled waiting times are calculated for both timeseries and appear in Fig. 5. The good quality of the datacollapse demonstrates that a common scaling law describesboth AE and earthquake time recurrence (the fit yields ¼ 0:35 0:02, x ¼ 1:15 0:42, and n ¼ 0:530:04). This finding indicates the existence of a nontrivialcorrelation between small-scale AE activity in the templepillar and nearby earthquake activity.Conclusions.—An apparent correlation in time betweenAE bursts and the occurrence of nearby earthquakes isfound. Therefore, the structure of the temple might beparticularly sensitive to the action of nearby earthquakes.The demonstration that a common scaling law describestemporal recurrence of AE and earthquake activities sup-ports the conjecture that both respond to critical values ofstress in the same manner. The presented study suggeststhat the AE structural monitoring coupled with the analysisof local earthquake activity can be a tool of crucial im-portance in earthquake damage mitigation. The similaritybetween microfractures and seismicity could even haveimplications for understanding the triggering mechanismof earthquakes of all types by other earthquakes.[1] C. H. Scholz, J. Geophys. Res. 73, 1417 (1968).[2] D. Lockner, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.30, 883 (1993).[3] S. Colombo, I. G. Main, and M.C. Forde, J. Mater. CivilEng. 15, 280 (2003).[4] A. Carpinteri, G. Lacidogna, and G. Niccolini, Nat.Hazards Earth Syst. Sci. 7, 251 (2007).[5] Available at http://www.ct.ingv.it/ufs/analisti/gridsismMysql.asp.[6] G. P. Gregori, G. Paparo, M. Poscolieri, and A. Zanini,Nat. Hazards Earth Syst. Sci. 5, 777 (2005).[7] A. Guarino, A. Garcimartin, S. Ciliberto, M. Zei, and R.Scorretti, Eur. Phys. J. B 26, 141 (2002).[8] D. L. Turcotte, W. I. Newman, and R. Shcherbakov,Geophys. J. Int. 152, 718 (2003).[9] C. F. Richter, Elementary Seismology (Freeman, SanFrancisco, 1958).[10] T. Utsu, Y. Ogata, and S. Matsu’ura, J. Phys. Earth 43, 1(1995).[11] J. Weiss, Surv. Geophys. 24, 185 (2003).[12] P. Bak, K. Christensen K, L. Danon, and T. Scanlon, Phys.Rev. Lett. 88, 178501 (2002).[13] A. Corral, in Modelling Critical and CatastrophicPhenomena in Geoscience, edited by P. Bhattacharyyaand B.K. Chakrabarti, Lect. Notes Phys. Vol. 705(Springer, Berlin, 2006), p. 191.[14] J. Davidsen, S. Stanchits, and G. Dresen, Phys. Rev. Lett.98, 125502 (2007).[15] G. Niccolini, F. Bosia, A. Carpinteri, G. Lacidogna, A.Manuello, and N. Pugno, Phys. Rev. E 80, 026101 (2009).[16] G. Niccolini, A. Schiavi, P. Tarizzo, A. Carpinteri, G.Lacidogna, and A. Manuello, Phys. Rev. E 82, 046115(2010).[17] P. Diodati, F. Marchesoni, and S. Piazza, Phys. Rev. Lett.67, 2239 (1991).[18] S. Hainzl, J. Geophys. Res. 107, 2338 (2002).[19] Y. Y. Kagan and D.D. Jackson, Bull. Seismol. Soc. Am.89, 1147 (1999).[20] Y. Y. Kagan, Physica (Amsterdam) 77D, 160 (1994).[21] Y. Y. Kagan, in Modelling Critical and CatastrophicPhenomena in Geoscience, edited by P. Bhattacharyyaand B.K. Chakrabarti, Lect. Notes Phys. Vol. 705(Springer, Berlin, 2006), p. 303.[22] D. Krajcinovic, Damage Mechanics (Elsevier,Amsterdam, 1996).[23] J. Kaiser, Dr.-Ing. dissertation, Fakultät fürMaschinenwesen und Elektrotechnik der TechnischenUniversität München (TUM), 1950.10–110–310–510–710–9100                   102                  104                  106(s)p  Mth () (s–1)10–5            10–3              10–1             101 / Mth (dimensionless)10410210010–210–410–6f (Mth)    (dimensionless) )b()a(FIG. 5 (color online). Waiting-time PDFs for five seismicmagnitude thresholds Mth and four AE signal thresholds Vth(a) and their collapse onto a single curve illustrating the fulfil-ment of a common scaling law (b).PRL 106, 108503 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending11 MARCH 2011108503-4

Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures

Crossref

Physical Review Letters

Niccolini, Gianni

Carpinteri, Alberto

Lacidogna, Giuseppe

Manuello, A.

PORTO Publications Open Repository TOrino

Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance
in the Timing of Ruptures
G. Niccolini
Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy
A. Carpinteri, G. Lacidogna, and A. Manuello
Department of Structural Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
(Received 14 June 2010; published 10 March 2011)
We perform a comparative statistical analysis between the acoustic-emission time series from the
ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We ﬁnd an apparent
association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distribu-
tions for acoustic-emission and earthquake time series are described by a unique scaling law indicating
self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the
aging process of the temple and the local seismic activity.
DOI: 10.1103/PhysRevLett.106.108503 PACS numbers: 91.62.Ty, 62.20.mj, 89.75.Da, 91.30.Dk
Introduction.—Fracture in heterogeneous materials oc-
curs as the culmination of progressive damage due to
loading conditions or harsh environments. Damage growth
is accompanied by the spontaneous release of stored strain
energy in the form of transient elastic waves [acoustic
emission (AE)] [1–3]. Thus, as it provides information
on the internal state of a material, AE monitoring is used
successfully for the structural integrity assessment of ma-
terials and also large-sized structures (buildings, bridges,
etc.) before they become safety hazards [3,4]. This predic-
tive power can be exploited to protect the Italian cultural
heritage, as historic buildings and monuments are exposed
to seismic risk. Many structures may undergo accelerated
aging and deterioration due to the action of small and
intermediate earthquakes, rather frequent in Southern
Italy. The triggered damage, often inaccessible for visual
inspection, eventually results in increased vulnerability to
strong earthquakes. Here, the results of AE monitoring
of the Athena temple in Syracuse (Eastern Sicily) are
presented. We analyze the time correlation between the
AE bursts from a temple pillar and the occurrence of
nearby earthquakes. Furthermore, we investigate consis-
tency of scaling laws between AE and Eastern Sicily
earthquake waiting-time distributions.
AE Monitoring of the Syracuse Cathedral.—In the sev-
enth century, the Cathedral of Syracuse (on the UNESCO
World Heritage List since 2005) was built onto the ruins of
the ancient and famed Athena temple and afterward re-
peatedly modiﬁed as a consequence of damages caused by
earthquakes. The structure currently exhibits an extended
damage pattern, especially in four pillars at the end of the
nave, showing repaired areas, replacements, and also sev-
eral cracks. The AE activity in one of the nave pillars was
monitored over a four-month period by means of six piezo-
electric transducers working in the range of 50–500 kHz
attached to the pillar surface.
After setting an appropriate detection threshold to ﬁlter
out environmental background noise, we started data ac-
quisition storing two quantities for each AE signal: the
arrival time, determined by using the ﬁrst threshold cross-
ing of the signal, and the peak amplitude Vmax (expressed
in  V), which deﬁnes the magnitude of the AE event as
M ¼ logðVmax=1  VÞ [3].
Figure 1 displays the accumulated number of AE events,
the AE instantaneous rate (averaged over 1 h), and the
earthquakesequence asfunctions of time.Here, only earth-
quakes with hypocentral distance   60 km from Syracuse
are considered (Fig. 2 and Table I). There appears to be a
correlation in time between AE activity on the Cathedral
and local seismicity, as AE bursts often follow the occur-
rence of nearby seismic events.
There appear to be some seismic events which follow
AE bursts and, then, which do not trigger AE activity on
the Cathedral. The occurrence of increased AE activity in
several case histories from Italy was observed by
Carpinteri, Lacidogna, and Niccolini and Gregori et al.
A
c
c
u
m
u
l
a
t
e
d
 
n
u
m
b
e
r
 
o
f
 
A
E
 
e
v
e
n
t
s
 
A
E
 
r
a
t
e
 
(
e
v
e
n
t
s
/
h
o
u
r
)
500 0 3000 3500 2500 2000 1500 1000
t (hours) 
5 10
3
41 0
3
31 0
3
11 0
3
0
21 0
3
50 
100 
150 
200 
0
300 
M
a
g
n
i
t
u
d
e
 
1.0 
2.0 
3.0
4.0 
5.0 
FIG. 1 (color online). Accumulated number (black line), in-
stantaneous AE rate averaged over 1 h (red line) in the temple
pillar, and nearby earthquake occurrence (triangles) as functions
of time.
PRL 106, 108503 (2011) PHYSICAL REVIEW LETTERS
week ending
11 MARCH 2011
0031-9007=11=106(10)=108503(4) 108503-1  2011 American Physical Societybefore large earthquakes [4,6]. In this case, AE bursts
apparently indicate crustal stress crises affecting areas of
a few hundred kilometers radius during the preparation of a
seismic event. In spite of intrinsic difﬁculties in high-
frequency propagation through disjointed media (in par-
ticular,attheground-buildingfoundationinterface),partof
the AE activity from the structures might derive from
precursive microseismic activity. A rigorous investigation
of causal relationships between AE bursts and earthquakes
would require simultaneous operation of suitable arrays of
AE monitoring sites, adequately placed in the territory,
e.g., on the order of  1000 over a large regional area.
Several studies established that the total rate of damage,
as measured, for instance, by the accumulated AE released
energy, increases as a power law of the time to failure
on the approach to the structural collapse [7,8]. Here, the
absence of a critical power-law behavior in the accumu-
lated number of AE events in time, with two episodic
abrupt increments at about 1800 and 2900 h (see Fig. 1),
suggests that the structure experiences damage but is still
far from unstable conditions.
Scaling law for AE and earthquake waiting-time
distributions.—Space-time organization of AE and the
earthquake source process is ruled by different power
laws, among them, the Gutenberg-Richter law for the
magnitude distribution [9], the Omori law for the rate of
aftershocks as a function of time from the main shock [10],
and the fractal distribution law for the epicenters [11].
However, power laws and critical exponents are not the
only scaling predictions for fracture processes. Starting
from the pioneer work of Bak et al. [12], Corral found
that the distributions of waiting times between consecutive
earthquakes follow a universal scaling law in different
regions of the world and earthquake catalogs if appropri-
ately rescaled [13]. There has been an ongoing debate
in the seismological community about the extent to which
universal scaling of earthquake temporal occurrence ap-
plies to AE time series in laboratory fracture [14–18]. This
suggests that timing of fractures might be self-similar over
a larger range of magnitude than had been suggested
earlier. Here, the rescaling and collapsing procedure for
waiting-time distributions in a sequence of rupture events
is illustrated. We select the NðMthÞ events with magnitude
M above a certain threshold Mth. The sequence is trans-
formed into a point process where events occur at times ti
with 1   i   NðMthÞ N, and therefore, the waiting
time between consecutive events can be obtained as
 i   ti   ti 1. Thus, we compute the waiting-time proba-
bility density function (PDF) as pMthð Þ Probð   
waiting time < þ d Þ=d . Measuring the time in units
of the mean waiting time h iMth  ð tN   t1Þ=ðN   1Þ,
i.e., performing the transformation   !  =h iMth, changes
also the units of the PDF: pMthð Þ!h  iMthpMthð Þ.
This rescaling procedure is applied to PDFs obtained for
FIG. 2 (color online). Map of Sicily showing the location of
the monitored site (yellow square) and epicenters (black circles)
of nearby earthquakes (listed in Table I) that occurred during the
monitoring period.
TABLE I. List of earthquakes with hypocentral distance from Syracuse   60 km (extracted
from the Eastern Sicily earthquake catalog [5]). Richter magnitude, ML; H, hypocenter depth; d,
distance of monitoring site to the hypocenter; NAE, AE rate.
Date Time Epicentral coordinates H (km) d (km) ML
1 2006/09/19 03:20 37.09 15.35 20.2 21.4 2.0
2 2006/09/22 15:52 37.37 14.95 4.1 42.9 1.8
3 2006/09/26 16:59 37.62 15.14 13.6 62.0 2.5
4 2006/09/26 17:08 37.65 15.13 16.0 66.5 2.3
5 2006/10/14 23:55 37.25 14.78 18.4 50.8 3.0
6 2006/10/16 02:21 37.14 15.25 17.9 19.1 1.3
7 2006/10/16 03:40 37.05 14.76 16.7 48.5 1.6
8 2006/11/05 22:01 37.25 14.77 18.3 51.5 1.3
9 2006/12/05 05:01 37.06 15.61 24.3 38.8 2.9
10 2006/12/05 15:31 37.31 14.94 9.9 39.7 1.5
11 2006/12/07 16:23 37.34 14.93 0.0 40.9 1.6
12 2006/12/23 00:33 37.15 15.23 18.1 20.1 1.2
13 2006/12/25 08:02 37.23 15.17 16.1 24.6 1.8
14 2006/12/28 10:56 37.14 15.17 9.5 14.4 1.5
15 2007/01/09 09:57 37.08 15.57 14.0 30.1 1.9
16 2007/01/11 05:15 37.03 15.09 20.2 26.6 1.6
17 2007/01/14 23:23 36.90 14.98 17.6 37.2 1.9
PRL 106, 108503 (2011) PHYSICAL REVIEW LETTERS
week ending
11 MARCH 2011
108503-2several values of Mth. If all the rescaled PDFs collapse onto
a single curvef,we canestablish the fulﬁlment ofa scaling
law [13]:
pMthð Þ¼fð =h iMthÞ=h iMth: (1)
The mean waiting time can be expressed in terms of the
Gutenberg-Richter law [13,15]:
h iMth ¼ T10 aþbMth; (2)
where T  ð tN   t1Þ.
By inserting Eq. (2), Eq. (1) takes the form
pMthð Þ¼10 bMth ~ fð10 bMth Þ; (3)
where ~ fð10 bMth Þ kfðk10 bMth Þ and k   T 110a.
If we consider events separated by waiting times   for
M   Mth and  0   10b  for M   M0
th   Mth þ 1 and in-
sert these particular arguments, ( 0; M0
th) and ( ; Mth), into
Eq. (3), we obtain
pMthð Þ¼10bpMthþ1ð10b Þ: (4)
Equation (4) expresses self-similarity of the distributions,
as they can be obtained from each other by a similarity
transformation [15]. The scaling function f is well ap-
proximated by a generalized gamma distribution, which
is a common parameterization for all fracture systems from
the microscopic scale (AEs) to the seismic scale (earth-
quakes) [13–16]:
fð Þ/  ð1  Þ exp½ð  =xÞn ; (5)
where   is the rescaled waiting time:      =h iMth.
Although the parameterization of Eq. (5) is valid for all
fracture processes, from AE in laboratory experiments to
earthquakes, the values of ﬁtting parameters  , x, and n
generally depend on the window of observation [13]. In
particular, the power-law exponent 1     indicates the
clustering degree in time of events. For example, when
aftershock sequences or earthquake swarms dominate the
selected time window T, the power-law exponent is high
(1     ¼ 1:5 [18] against 0.3 for stationary activity or
slowly varying event rates [13–16]), indicating that earth-
quakes are close in time.
Previously, Kagan [19–21] in a different approach
pointed out that the number of short waiting times between
large earthquakes exceeds the number expected for mem-
oryless Poisson recurrence. This behavior, indicating clus-
tering, is the opposite of the regularity or quasiperiodicity
derived from the idea of the seismic cycle. A surprising
consequence of clustering is the paradoxical result that the
longer it has been since the last earthquake, the longer
the expected time until the next [13,19–21]. Here, below,
the temporal occurrence of rupture events at different
size scales will be investigated. First, we analyze the
fracture process of a Syracuse limestone cylindrical
specimen (base diameter 120 mm and height 120 mm).
The specimen was subjected to uniaxial compression at a
constant displacement rate of 0:1  ms  1, by using a
servo-hydraulic press with a maximum capacity of
500 kN. We set the AE detection threshold to ﬁlter out
background noise. In this way, we ensured that no spurious
AE signals would be detected before the beginning of
the test.
In Fig. 3, the solid line represents the stress vs time
diagram, characterized by irregular trend and stress drops
due to damage accumulation before the specimen failure.
Such quasibrittle behavior characterize heterogeneous ma-
terials [22]. The dashed line represents the accumulated
number of AE events as a function of time. Stress drops
were followed by as many drops in the AE activity, sug-
gesting momentary relaxation until the stress exceeds the
previous reached values (Kaiser effect [23]).
We analyze the AE time series until the peak stress,
whenthespecimen fails,and also forthe completeduration
of the experiment. The PDFs of waiting times are calcu-
lated from both sequences and the corresponding rescaled
distributions that appear in Fig. 4. In both cases, the data
collapse illustrates the validity of a scaling law of the type
of (5), although the scaling function f is different. The ﬁt
yields   ¼ 0:23   0:02, x ¼ 2:23   1:00, and n ¼ 1:15  
0:16 before peak load and   ¼ 0:46   0:04, x ¼ 5:61  
3:15, and n ¼ 0:99   0:14 for the whole duration of
experiment. In the ﬁrst case, the power-law exponent is
Time (s) 
10 
20 
30 
40 
50 
0
0.5 10
3
1.0 10
3
1.5 10
3
2.0 10
3
2.5 10
3
3.0 10
3
0 10
3 1 10
3 2 10
3 3 10
3 4 10
3 5 10
3 6 10
3
0.0 10
3
N
A
E
(
t
)
S
t
r
e
s
s
 
(
M
P
a
)
 
t (s) 
Load 
AE 
FIG. 3. Applied load (solid line) and accumulated number of
AE events (dashed line) as functions of time.
10
3
10
1
10
–1
10
–3
f
 
(
M
t
h
)
(
d
i
m
e
n
s
i
o
n
l
e
s
s
)
10
–5              10
–3               10
–1              10
1      
               / Mth (dimensionless)
(a)
M
t
h
)
(
d
i
m
e
n
s
i
o
n
l
e
s
s
)
10
–3                 10
–1                   10
1
 /
f
 
(
Mth (dimensionless)
(b) 
10
2
10
0
10
–2
10
–4
FIG. 4 (color online). Rescaled waiting-time PDFs for the
period preceding the peak load (a) and for the whole duration
test (b), for several Vth values, equivalent to Mth ¼
logðVth=1  VÞ. The data collapse illustrates the fulﬁlment of a
scaling law, where the solid line is the scaling function of Eq. (5).
PRL 106, 108503 (2011) PHYSICAL REVIEW LETTERS
week ending
11 MARCH 2011
108503-3higher (1       0:77 against 0.54) because of the large
number of AE events close in timewhich typically precede
the specimen failure.
Now, we use the scaling approach to study the AE events
from the pillar and the Eastern Sicily earthquakes. The
PDFs of rescaled waiting times are calculated for both time
series and appear in Fig. 5. The good quality of the data
collapse demonstratesthatacommonscalinglawdescribes
both AE and earthquake time recurrence (the ﬁt yields
  ¼ 0:35   0:02, x ¼ 1:15   0:42, and n ¼ 0:53  
0:04). This ﬁnding indicates the existence of a nontrivial
correlation between small-scale AE activity in the temple
pillar and nearby earthquake activity.
Conclusions.—An apparent correlation in time between
AE bursts and the occurrence of nearby earthquakes is
found. Therefore, the structure of the temple might be
particularly sensitive to the action of nearby earthquakes.
The demonstration that a common scaling law describes
temporal recurrence of AE and earthquake activities sup-
ports the conjecture that both respond to critical values of
stress in the same manner. The presented study suggests
that the AE structural monitoring coupled with the analysis
of local earthquake activity can be a tool of crucial im-
portance in earthquake damage mitigation. The similarity
between microfractures and seismicity could even have
implications for understanding the triggering mechanism
of earthquakes of all types by other earthquakes.
[1] C.H. Scholz, J. Geophys. Res. 73, 1417 (1968).
[2] D. Lockner, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
30, 883 (1993).
[3] S. Colombo, I.G. Main, and M.C. Forde, J. Mater. Civil
Eng. 15, 280 (2003).
[4] A. Carpinteri, G. Lacidogna, and G. Niccolini, Nat.
Hazards Earth Syst. Sci. 7, 251 (2007).
[5] Available at http://www.ct.ingv.it/ufs/analisti/
gridsismMysql.asp.
[6] G.P. Gregori, G. Paparo, M. Poscolieri, and A. Zanini,
Nat. Hazards Earth Syst. Sci. 5, 777 (2005).
[7] A. Guarino, A. Garcimartin, S. Ciliberto, M. Zei, and R.
Scorretti, Eur. Phys. J. B 26, 141 (2002).
[8] D.L. Turcotte, W.I. Newman, and R. Shcherbakov,
Geophys. J. Int. 152, 718 (2003).
[9] C.F. Richter, Elementary Seismology (Freeman, San
Francisco, 1958).
[10] T. Utsu, Y. Ogata, and S. Matsu’ura, J. Phys. Earth 43,1
(1995).
[11] J. Weiss, Surv. Geophys. 24, 185 (2003).
[12] P. Bak, K. Christensen K, L. Danon, and T. Scanlon, Phys.
Rev. Lett. 88, 178501 (2002).
[13] A. Corral, in Modelling Critical and Catastrophic
Phenomena in Geoscience, edited by P. Bhattacharyya
and B.K. Chakrabarti, Lect. Notes Phys. Vol. 705
(Springer, Berlin, 2006), p. 191.
[14] J. Davidsen, S. Stanchits, and G. Dresen, Phys. Rev. Lett.
98, 125502 (2007).
[15] G. Niccolini, F. Bosia, A. Carpinteri, G. Lacidogna, A.
Manuello, and N. Pugno, Phys. Rev. E 80, 026101 (2009).
[16] G. Niccolini, A. Schiavi, P. Tarizzo, A. Carpinteri, G.
Lacidogna, and A. Manuello, Phys. Rev. E 82, 046115
(2010).
[17] P. Diodati, F. Marchesoni, and S. Piazza, Phys. Rev. Lett.
67, 2239 (1991).
[18] S. Hainzl, J. Geophys. Res. 107, 2338 (2002).
[19] Y.Y. Kagan and D.D. Jackson, Bull. Seismol. Soc. Am.
89, 1147 (1999).
[20] Y.Y. Kagan, Physica (Amsterdam) 77D, 160 (1994).
[21] Y.Y. Kagan, in Modelling Critical and Catastrophic
Phenomena in Geoscience, edited by P. Bhattacharyya
and B.K. Chakrabarti, Lect. Notes Phys. Vol. 705
(Springer, Berlin, 2006), p. 303.
[22] D. Krajcinovic, Damage Mechanics (Elsevier,
Amsterdam, 1996).
[23] J. Kaiser, Dr.-Ing. dissertation, Fakulta ¨tf u ¨r
Maschinenwesen und Elektrotechnik der Technischen
Universita ¨tM u ¨nchen (TUM), 1950.
10–1
10–3
10–5
10–7
10–9
10
0                   10
2                  10
4                  10
6
(s)
p
 
M
t
h
 
(
)
 
(
s
–
1
)
10
–5            10
–3              10
–1             10
1
 / Mth (dimensionless)
104
102
100
10–2
10–4
10–6
f
 
(
M
t
h
)
 
 
 
 
(
d
i
m
e
n
s
i
o
n
l
e
s
s
)
 
) b ( ) a (
FIG. 5 (color online). Waiting-time PDFs for ﬁve seismic
magnitude thresholds Mth and four AE signal thresholds Vth
(a) and their collapse onto a single curve illustrating the fulﬁl-
ment of a common scaling law (b).
PRL 106, 108503 (2011) PHYSICAL REVIEW LETTERS
week ending
11 MARCH 2011
108503-4

Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures

Abstract

Similar works

Full text

Available Versions

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

Crossref

PORTO Publications Open Repository TOrino