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IntensItY-attenuatIon relatIonshIPs for strongaPennInes earthQuaKes: QuestIonIng the staBIlItY of regressIonCoeffICIents over tIme and sPaCe Based on mCs and esI sCalesM.F. Ferrario, A.M. Michetti, F. LivioUniversità degli Studi dell’Insubria, Dipartimento di Scienza e Alta Tecnologia, Como, Italy

Introduction. The reliable evaluation of historical earthquakes is pivotal for seismic hazard assessment, and macroseismic observations are the only data available for the estimation of location and magnitude of historical events. Seismic parameters for pre-instrumental earthquakes included in the Italian catalogue (CPTI15, Rovida et al., 2016) are estimated on the basis of well-constrained empirical relations between Io and Mw, and also through dedicated algorithms (i.e., Boxer code; Gasperini et al., 1999, 2010).

However, the application of traditional, damage-based macroseismic scales (i.e., MCS – Mercalli Cancani Sieberg; MMI – Modified Mercalli; EMS98 – European Macroseismic Scale) to contemporary earthquakes suffer some limitations such as the saturation at higher degrees and a strong dependence on the spatial distribution of human settlements. Most pertinent for this research, these scales are significantly influenced by the large variability of building vulnerability as a function of age and local economy.

In this sense, the seismic sequence occurred in Emilia Romagna region in 2012 is particularly relevant. Seismic parameters estimated from the MCS and EMS survey do not match those instrumentally recorded or expected from the application of general empirical regressions (e.g., Galli et al., 2012; Graziani et al., 2015). This has been attributed to the concomitant role exerted by the local geologic setting and the characteristics of the building stock, or to overestimated intensity of strong seismic events in the historical catalogue.

A complementary approach is provided by the ESI07 (Environmental Seismic Intensity) scale. This scale is based solely on Earthquake Environmental Effects (EEEs), which have the significant advantage of still increase in their dimensions also close to full scale and to respond consistently in time and space (Michetti et al., 2007).

The goal of this note is twofold: (i) evaluate the reliability of EEEs attenuation with distance using a preliminary dataset of Italian strong earthquakes with normal kinematic and (ii) pursue the integration of MCS and ESI scales, which result in a more comprehensive picture of the historical and modern seismic events. We focus on the MCS scale, for which a much larger database is available; arguably, the preliminary results described in the following apply also to the other damage-based scales.

The investigated database. We gathered data of all the events in the Italian Apennines for which both MCS and ESI macroseismic data points (MDPs) are available; the database consists of 14 normal faulting earthquakes (Tab. 1) in the magnitude range 6.0 – 7.1, occurred between 1688 and 2016 AD, for a total of 6419 and 431 MDPs for MCS and ESI scales, respectively. MDPs range from intensity 2 to 11 for MCS and from 3 to 11 for ESI. Traditional intensities were compiled from the DBMI database (Locati et al., 2016; for the Amatrice 2016 event: Galli et al., 2016; 2017), whereas ESI values were collected from the EEE catalogue (Guerrieri et al., 2011) and published literature (Serva et al., 2007; Comerci et al., 2015).

Macroseismic epicenter. The macroseismic epicenter was calculated with Boxer algorithm (v. 3.3) for the 2 separate datasets, as the barycenter of MDPs with highest intensity (“Method 0” in Gasperini et al., 2010). MCS-based epicenters were collected from CPTI database, while ESI-based ones were computed in this study. The ESI-derived macroseismic epicenter agrees well with the MCS-derived one, with mean differences of 12.2 ± 10.9 km.

The epicenter calculated from ESI data should be more closely connected to the surface projection of the seismogenic source than the MCS epicenter. This proved true for at least the most recent events, i.e., those where the seismogenic source is well-known, and earthquake surface faulting has been observed (Colfiorito 1997; L’Aquila 2009; Amatrice 2016).

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Intensity attenuation with distance and estimation of epicentral intensity. We calculated epicentral distance for each MDP (half degrees were not considered and intensities lower than 4 were filtered out) and we computed regression equations using the intensity-level binning proposed by Bakun and Wentworth (1997). The average epicentral distance for MCS data points is 61.28 ± 28.63 km, and the maximum value is 636 km. Environmental effects are indeed documented mainly in the near-field, at average distances of 27.76 ± 18.93 km (maximum value: 210 km).

Attenuation relations were calculated as regressions through a least squares method, in the linear form:

I = a * D + b (1)Where I is the intensity (in MCS or ESI scale), D the epicentral distance (in km), a and b

are free parameters. Despite several forms have been proposed for traditional intensity scales (i.e., logarithmic, bi-linear, square and cubic root, log-linear; see Pasolini et al., 2008 for a comprehensive review), we here adopted the linear form.

The slope [coefficient a in Eq. (1)] is higher for ESI-derived equations in respect of MCS-derived ones: values are of -0.070 ± 0.047 for MCS and -0.120 ± 0.072 for ESI, corresponding to a decrease of one degree of intensity every 14 and 8 km, respectively.

It is worth noting that I0 and Imax values for the MCS scale are always equal or higher than ESI ones (Tab. 1). On the contrary, the b parameter of Eq. (1), which represents the intensity predicted at the epicenter, is higher for ESI in 9 out of 14 earthquakes. The comparison between I0 and b furnishes some insight, but should be treated only in a qualitative way, due to the different nature of I0 (which can assume only discrete values, i.e., integer or half degrees) and the b coefficient (which instead is a continuous variable). For the MCS scale, the predicted

Tab. 1 - Summary characteristics of the investigated earthquakes. Epicentral intensity (I0), maximum intensity (Imax) and the intensity predicted at the epicenter (i.e., b coefficient of the derived equations) are shown for both the MCS and ESI scales. I0 for the ESI scale was computed with the same criteria adopted in the CPTI15 for the MCS scale (Rovida et al., 2016).

Epicentralintensity(I0) Maximumintensity(Imax) Intensitypredictedat Difference epicenter(bcoefficient) (I0–b)

Date Locality MCS ESI (MCS-ESI) MCS ESI (MCS-ESI) MCS ESI (MCS-ESI) MCS ESI

24/0�/201� Amatrice 10,� �,0 1,� 10,� �,0 1,� �,2� �,44 -0,14 1,21 -0,44

0�/04/200� L’Aquila �,� �,0 0,� �,� �,0 0,� �,�� �,�4 -0,0� 0,�� 0,1�

2�/0�/1��� Colfiorito �,� �,0 0,� �,0 �,0 0,0 �,33 �,�4 -1,22 0,1� -1,�4

23/11/1��0 Irpinia 10,0 10,0 0,0 10,0 10,0 0,0 �,3� �,4� 0,�1 0,�2 1,�2

23/0�/1�30 Irpinia 10,0 10,0 0,0 10,0 10,0 0,0 10,12 10,41 -0,2� -0,12 -0,41

13/01/1�1� Fucino 11,0 10,0 1,0 11,0 10,0 1,0 10,�� 11,1� -0,�0 0,43 -1,1�

2�/12/1�0� Messina 11,0 10,0 1,0 11,0 11,0 0,0 10,04 11,0� -1,04 0,�� -1,0�

1�/12/1��� Basilicata 11,0 10,0 1,0 11,0 10,0 1,0 10,23 �,�� 3,3� 0,�� 3,12

2�/0�/1�0� Molise 10,0 10,0 0,0 10,0 10,0 0,0 �,�3 �,14 0,�� 0,0� 0,��

0�/02/1��3 Calabria 11,0 11,0 0,0 11,0 11,0 0,0 10,�� 10,�1 0,24 0,1� 0,3�

02/02/1�03 L’Aquila 10,0 10,0 0,0 10,0 10,0 0,0 �,�4 12,�� -2,�4 0,2� -2,��

14/01/1�03 Norcia 11,0 11,0 0,0 11,0 11,0 0,0 10,22 12,�0 -2,3� 0,�� -1,�0

0�/0�/1��4 Irpinia 10,0 �,0 1,0 10,0 10,0 0,0 �,3� �,�� -0,�0 0,�1 -0,��

0�/0�/1��� Sannio 11,0 �,0 3,0 11,0 �,0 3,0 11,�� �,3� 2,�� -0,�� -1,3�

Mean �,22 �,�� 0,41 -0,3�

Stddev 1,00 1,14 0,�4 1,4�

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epicentral intensity is half degree lower than the observed one (I0 – b, data in Tab. 1). For the ESI scale, the trend is opposite and predicted epicentral intensity is about half degree higher than the observed one.

Intensity attenuation with distance: generalization. In order to properly compare events with different I0, we follow the approach used by Gasperini (2001) on the database of macroseismic observations provided by Monachesi and Stucchi (1997). The difference between epicentral and local intensity has been computed for each MDP, in the form:

ΔI = I0 - Ii (2)where I0 is the epicentral intensity and Ii the local intensity at the i-th point.

Hypocentral distances were calculated from epicentral distances and assuming a fixed depth of 10 km, in analogy with the work by Gasperini (2001).

Fig. 1 shows ΔI as a function of the hypocentral distance, where a distance binning of 5 km is adopted. For MCS data, we found the same result of Gasperini (2001), i.e., a difference in slope around 45 km, that we define as the boundary between near- and far-field. ESI data show indeed a linear trend up to 75 km.

Fig. 1 - Differences between hypocentral and local intensity (ΔI) as a function of distance, for the MCS and ESI database. Mean values averaged in 5 km bins are shown as black circles. Only the intervals with at least 5 occurrences are considered.

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Fig. 2 - Close-up on the epicentral area and comparison with the equations of Gasperini (2001).

In Fig. 2 we compared our dataset with the general equations by Gasperini (2001). The most striking difference is in the near-field: here, the ESI-based regression mimics the results of Gasperini whereas MCS data show the same slope, but higher ΔI values.

We explore two possibilities for explaining the underestimation of MCS scale in the near-field: (i) the saturation at higher degrees and (ii) the presence of significant differences when comparing events occurred several centuries apart from each other. The former hypothesis is time-independent, while in the latter case a time-dependent behavior is expected. Thus, we divided the database into subsets, according to the timing of earthquake occurrence. We found a clear mismatch between MCS post-2000 (i.e., L’Aquila 2009 and Amatrice 2016 events) and previous events, which suggests the reliability of the second hypothesis.

Conclusions and perspectives. MCS and ESI scales show opposite strength and limitations, which are counterbalanced when the two datasets are considered together. ESI scale is more robust in the near-field and possibly in evaluating epicentral intensity, I0, while MCS behaves better in the far-field.

We suggested the existence of a bias in intensity assessment with MCS scale for contemporary earthquakes in respect of older ones. We argue that the integration of effects on the natural and the human environment is the best approach to assess overall earthquake intensity. Our results prompt to the need for a reassessment of earthquake effects in a renowned perspective, assuring the consistency between modern and historical events.

The preliminary results described here look particularly promising and future developments include the following issues:

- different functional forms and a more accurate assessment of errors and uncertaintiesdifferent functional forms and a more accurate assessment of errors and uncertainties should be performed;

- new case histories, within and outside the Italian Apennines, need to be analyzed to widennew case histories, within and outside the Italian Apennines, need to be analyzed to widen the available database and different tectonic regimes should be considered as well;

- development of surveying strategies and methodologies that take into consideration effectsdevelopment of surveying strategies and methodologies that take into consideration effects on buildings and the natural environment;

- particular attention should be paid to recent (instrumental) events, which provideparticular attention should be paid to recent (instrumental) events, which provide independent estimates of magnitude. This will enable to relate magnitude with ESI and MCS data, and to derive better magnitude estimates for pre-instrumental events, in analogy to the current practice, which is based on traditional scales only.

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