#
Correlation between Earthquakes and AE Monitoring of Historical Buildings in Seismic Areas^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Description of Chapel XVII and Asinelli Tower

**Figure 2.**The Asinelli and the adjacent Garisenda Towers in the city center of Bologna. The Asinelli tower is the tallest one on the right.

## 3. Acoustic Emission Monitoring

#### 3.1. Chapel XVII

**Figure 3.**Chapel XVII. View of the monitored areas. Left side: sensors 5, 6, and the fresco detachment. Right side: sensors 1–4 and the vertical crack.

**Figure 4.**Chapel XVII: AE rate (blue chart) and nearby earthquake (red dots) occurrences as functions of time. The AE rate chart illustrates the number of AE events (averaged over 1 h), while seismic events are marked by points indicating occurrence time and Richter magnitude.

#### 3.2. Asinelli Tower

**Figure 5.**Front views and axonometric view of Asinelli Tower. Faces (

**1**) South; (

**2**) East; (

**3**) North; (

**4**) West; (

**5**) Axonometric view. The AE transducers were applied to the northeast corner of the tower, in the zones marked with a circle.

**Figure 6.**Asinelli Tower: AE rate (blue chart) and nearby earthquake (red dots) occurrences as functions of time. The AE rate chart illustrates the number of AE events (averaged over 1 h), while seismic events are marked by points indicating occurrence time and Richter magnitude.

## 4. Grassberger-Procaccia Algorithm

_{L}≥ 1.2, was driven by completeness criteria.

**Figure 7.**Correlation integral C(r) vs. r (km) and its slope D in bi-logarithmic scale for Varallo regional seismicity (

**a**) and Bologna regional seismicity (

**b**).

## 5. Space-Time Correlation between AE and Seismic Events

_{AE}event bursts {x

_{0}, t

_{j}}, with x

_{0}being the coordinate vector of the monitoring site, while k runs over all the N

_{EQ}seismic events {x

_{k}, t

_{k}}, with x

_{k}being the epicentral coordinate vector.

_{0}, t

_{j}) and a seismic event (x

_{k}, t

_{k}) with mutual epicentral distance │x

_{0}− x

_{k}│ ≤ r and time intervals│t

_{j}− t

_{k}│ ≤ τ among all N

_{AE}and N

_{EQ}possible pairs, C(r,τ) can easily be interpreted as the probability of an AE burst and an earthquake occurring with an inter-distance ≤r and a time interval ≤τ.

_{t}and D

_{s}can be defined similarly to Equation (2):

_{t}(r, τ) characterizes the time-coupling of AE bursts to the earthquakes occurring up to a given distance r from the AE monitoring site, whereas the space correlation dimension D

_{s}(r, τ) characterizes the spatial distribution of nearby earthquakes with separation in time from AE bursts not exceeding a given τ.

_{j}− t

_{k}│ ≤ τ does not specify the chronological order between the two types of event. On the other hand, the AE time series and the sequence of nearby earthquakes are two very closely interrelated sets in the time domain. Therefore, a given AE burst might be either due to structural damage triggered by a seismic event or due to precursive microseismic activity. In spite of intrinsic difficulties in high-frequency propagation across disjointed media (in particular at the ground-building foundation interface), AE bursts apparently indicate widespread crustal stress crises during the preparation of a seismic event [9,12], when part of the related deformation energy stored in the Earth’s crust might be transferred to the building foundations.

^{+}(r, τ), for example, gives the occurrence probability of an AE burst followed by an earthquake in the next interval τ and within a radius r of the monitoring site.

^{±}(r, τ) as functions of time C

^{±}

_{r}(τ) for different values of range r. This provides two-dimensional plots, which are easier to read than a three-dimensional representation of C

^{±}(r, τ).

^{+}

_{r}> C

^{−}

_{r}for all considered values of range r, suggesting that AE bursts are more likely to precede earthquakes than to follow them. The interpretation of this evidence is that the monitored structures behave as receptors of microseismic precursive activity during the preparation of a seismic event, i.e., as sensitive earthquake receptors.

**Figure 9.**Modified correlation integrals C

^{±}

_{r}(τ), both considering AEs as earthquake “precursors” (+) and as “damage aftershocks” (−), plotted as functions of the time separation τ for different values of the spatial range r for: (

**a**) Chapel XVII and area around the city of Varallo; (

**b**) Asinelli Tower and area around the city of Bologna.

## 6. AE Clustering in Time as a Seismic Precursor or an Aftershock

^{±}

_{r}(τ) are represented in a time domain ranging from 1 to 14–16 weeks, shorter values of τ are further investigated.

_{t}for τ ranging from 3 to 24 h after an earthquake occurrence, and from 10 min to 24 h before an earthquake occurrence.

_{t}of Log C

^{−}vs. Log τ reveals that the AE activity following seismic events is not equally probable over the time (see Figure 10a,b). For short time delays, τ = 3–10 min, high values of the time fractal dimension, D

_{t}= 1.38 and 1.24, indicate tight coupling of the AE activity to the earthquakes. In other words, AE bursts following an earthquake are more likely to occur within τ = 3–10 min after the seismic event. Then, such short time delays suggest a triggering action exerted by nearby earthquakes on damage processes of Chapel XVII and the Asinelli Tower. Contrarily, for τ ranging from 1.0 × 10

^{3}to 1.440 × 10

^{3}min, the obtained low values of D

_{t}, 0.48 and 0.45, suggest that the effects of nearby earthquakes on the structural damage evolution disappear after 24 h.

^{+}(D

_{t}= 1.06 and 0.94) shown in Figure 11 describe a uniform probability density of finding AE events prior to an earthquake for a wide range of time intervals, up to τ = 1.440×10

^{3}min. In other words, we observe a constant AE activity in the 24 h preceding an earthquake. The absence of accelerating precursive activity in the presented case studies confirms the need for further investigation, possibly with the aid of electromagnetic seismic precursors.

**Figure 10.**Analysis of time-clustering features of AE events considered as “seismic aftershocks” by the time correlation dimension D

_{t}, as a local slope of Log C

^{−}vs. Log τ. The time range for τ is 3 min to 24 h. The selected seismic events are all those considered during the defined monitoring periods. (

**a**) Chapel XVII (Varallo); (

**b**) Asinelli Tower (Bologna).

**Figure 11.**Analysis of time-clustering features of AE events considered “seismic precursors” by the time correlation dimension D

_{t}, as the local slope of Log C

^{+}vs. Log τ. The time range for τ is 10 min to 24 h. The selected seismic events are all those considered during the defined monitoring periods. (

**a**) Chapel XVII (Varallo); (

**b**) Asinelli Tower (Bologna).

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Niccolini, G.; Carpinteri, A.; Lacidogna, G.; Manuello, A. Acoustic emission monitoring of the Syracuse Athena Temple: Scale invariance in the timing of ruptures. Phys. Rev. Lett.
**2011**. [Google Scholar] [CrossRef] [PubMed] - Carpinteri, A.; Lacidogna, G.; Invernizzi, S.; Accornero, F. The Sacred Mountain of Varallo in Italy: Seismic risk assessment by Acoustic Emission and structural numerical models. Sci. World J.
**2013**, 2013, 1–10. [Google Scholar] [CrossRef] [PubMed] - Carpinteri, A.; Lacidogna, G.; Manuello, A.; Niccolini, G. A study on the structural stability of the Asinelli Tower in Bologna. Struct. Control HLTH
**2015**. [Google Scholar] [CrossRef] - Bak, P.; Christensen, K.; Danon, L.; Scanlon, T. Unified scaling laws for earthquakes. Phys. Rev. Lett.
**2002**, 88, 178501–178504. [Google Scholar] [CrossRef] [PubMed] - Parson, T. Global Omori law decay of triggered earthquakes: Large aftershocks outside the classical aftershock zone. J. Geophys. Res.
**2002**, 107, 2199–2218. [Google Scholar] [CrossRef] - Corral, A. Long-term clustering, scaling and universality in the temporal occurrence of earthquakes. Phys. Rev. Lett.
**2004**. [Google Scholar] [CrossRef] [PubMed] - Tosi, P.; de Rubeis, V.; Loreto, V.; Pietronero, L. Space-time combined correlation integral and earthquake interactions. Ann. Geophys.
**2004**, 47, 1–6. [Google Scholar] - Grassberger, P.; Procaccia, I. Characterization of strange attractors. Phys. Rev. Lett.
**1983**, 50, 346–349. [Google Scholar] [CrossRef] - Carpinteri, A.; Lacidogna, G.; Niccolini, G. Acoustic emission monitoring of medieval towers considered as sensitive earthquake receptors. Nat. Hazard Earth Syst. Sci.
**2007**, 7, 251–261. [Google Scholar] [CrossRef] - Carpinteri, A.; Lacidogna, G. Structural monitoring and integrity assessment of medieval towers. J. Struct. Eng.
**2006**, 132, 1681–1690. [Google Scholar] [CrossRef] - Scholz, C.H. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am.
**1968**, 58, 399–415. [Google Scholar] - Gregori, G.P.; Paparo, G. Acoustic emission (AE). A diagnostic tool for environmental sciences and for non destructive tests (with a potential application to gravitational antennas). In Meteorological and Geophysical Fluid Dynamics; Schroeder, W., Ed.; Science Edition: Bremen, Germany, 2004; pp. 166–204. [Google Scholar]
- Kagan, Y.Y.; Knopoff, L. Spatial distribution of earthquakes: The two-point correlation function. Geoph. J. Roy. Astron. Soc.
**1980**, 62, 303–320. [Google Scholar] [CrossRef] - Hirata, T. A correlation between the b-value and the fractal dimension of earthquakes. J. Geophys. Res.
**1986**, 94, 7507–7514. [Google Scholar] [CrossRef] - Carpinteri, A.; Lacidogna, G.; Niccolini, G.; Puzzi, S. Morphological fractal dimension versus power-law exponent in the scaling of damaged media. Int. J. Damage Mech.
**2009**, 18, 259–282. [Google Scholar] [CrossRef] - Italian Seismological Instrumental and Parametric Data-Base (ISIDE). Available online: http://iside.rm.ingv.it/iside/standard/result.jsp?rst=1&page=EVENTS#result (accessed on 5 December 2015).
- Burrato, P.; Vannoli, P.; Fracassi, U.; Basili, R.; Valensise, G. Is blind faulting truly invisible? Tectonic-controlled drainage evolution in the epicentral area of the May 2012, Emilia-Romagna earthquake sequence (northern Italy). Ann. Geophys. Italy
**2012**, 55, 525–531. [Google Scholar] - Carpinteri, A.; Xu, J.; Lacidogna, G.; Manuello, A. Reliable onset time determination and source location of acoustic emissions in concrete structures. Cem. Concr. Compos.
**2012**, 34, 529–537. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Lacidogna, G.; Cutugno, P.; Niccolini, G.; Invernizzi, S.; Carpinteri, A.
Correlation between Earthquakes and AE Monitoring of Historical Buildings in Seismic Areas. *Appl. Sci.* **2015**, *5*, 1683-1698.
https://doi.org/10.3390/app5041683

**AMA Style**

Lacidogna G, Cutugno P, Niccolini G, Invernizzi S, Carpinteri A.
Correlation between Earthquakes and AE Monitoring of Historical Buildings in Seismic Areas. *Applied Sciences*. 2015; 5(4):1683-1698.
https://doi.org/10.3390/app5041683

**Chicago/Turabian Style**

Lacidogna, Giuseppe, Patrizia Cutugno, Gianni Niccolini, Stefano Invernizzi, and Alberto Carpinteri.
2015. "Correlation between Earthquakes and AE Monitoring of Historical Buildings in Seismic Areas" *Applied Sciences* 5, no. 4: 1683-1698.
https://doi.org/10.3390/app5041683