Abstract. 1 Introduction

Transcription

1 Macroseismic intensity versos distance: constraints to the attenuation model L. Peruzza CNR, Gruppo Nazionaleper la Difesa dai Terremoti, at OGS, 2077, Abstract Constraints in the way of deriving attenuation parameters for macroseismic intensity are applied to Italian data: statistical analyses on macroseismic data points, and fitting of models in a pseudo intensity versus distance plane increase the capability of reconstructing the actual damage distribution starting from earthquake catalogues. As a consequence, propagation property analyses as well as reliable seismic hazard studies can be performed. 1 Introduction Efespite the increase of strong-motions records, intensity attenuation versus epicentral distance is a cornerstone parameter in seismic hazard assessment, because its semi-empirical approach to the interaction between earthquakes and environment expands to historic times the observation period. Traditionally, the attenuation model formulation, and the ways of deriving their own parameters too, start from isoseismal maps and isoseismal radii. In the last years, an extensive criticism on the criteria of drawing isoseismal lines, as well as of mathematical treatment of the intensity values, enhances the handling of the intensity data points directly. Plotting intensities as a function of the epicentral distances, dispersion of data may cause serious doubts on the statistical meaning of their correlation; Fig. 1 is an intensity versus distances graph of a XVIII century Italian earthquake (from Postpischl [1]). Attenuation parameters are often derived from the speedy treatment of these macroseismic points; for a given model, ordinary

2 216 Soil Dynamics and Earthquake Engineering algorithms of linear, or non-linear fitting, try to suit the data considering intensity a numerical, equispaced value, where uncertain attributions of intensity build intermediate classes. As too many equally good curves can be drawn through these data, the seismologists' debate about what is the best intensity decay model becomes useless OJ c. 60 c O) CJ ' o * I n + $ i * x i x S ; : x f 7 i 1 i J i ; $! t 1 i t i i " O i o III + IV x V VI + VII o VIII 0 IX A X i i o 1 II 4 I macroseismic intensity (MCS) Figure 1: 1781/06/03 Qgli (Northern Apennines) earthquake (Postpischl [1]); epicentral distance of the points versus macroseismic intensity (Mercalli-Chncani-Sieberg MCS). This paper presents some methodological guidelines in assessing intensity attenuation characteristics, starting from macroseismic data of Italian earthquakes. Two basic assumptions are followed: 1) intensity at a site is a categorical, ordered quantity, not a real number: each intensity point belongs to a set, or to sets-intersection for uncertain attribution. Gbmputing the intensity decay involves the use of an arbitrary axis, where values can be considered numerical, equispaced ones: we call it pseudo-intensity axis for clearness. Ch its side, epicentral intensity is another questionable parameter, biased as it is by considerations (tectonic, related to the seismic source, to the distribution of the maximum damage, etc.) extraneous to observations. For these reasons epicentral intensity will be here considered to lie on the same numerical axis of pseudo-intensity. 2) the attenuation relation is the relation existing between the different sets of equal in tensity points: considering the seismic hazard purposes of this study, no inversion of the "source parameters" (location of the epicentre, epicentral intensity) is performed. In such a way, the model is derived from earthquake catalogue parameters, and easily can be applied to the same "source", satisfying an important, and often disregarded condition for damage distribution reconstruction.

3 Soil Dynamics and Earthquake Engineering Statistical analysis of the intensity sets Be the N macroseismic points of an earthquake defined by an intensity value and a distance (computed from a given epicentre quoted in the earthquake catalogue); a routine statistical analysis for each intensity class can be performed,earthquake by earthquake, being the distance a continuous quantity. In Table I and Fig. 2 an example (from Postpischl [1]) of the 1920 Garfagnana earthquake is given. Uncertain attributions of intensity, such as VII-VIII, are splitted into two (or more) classes of intensity and contribute to both the sets. A visual comparison of the "shape" of the data and the probabilistic models is performed with cumulative histogram and CEF. Then Chi-square (%2) and Kblmogorov- Smirnov tests are applied to evaluate the differences between data and model. 300 IV V VI VII VIII IX X Hgure 2: 1920/09/07 Garfagnana (Tuscanian Apennines) earthquake: statistical representation of distances population. Box encloses 50% of the data with the median value of the variable displayed as a horizontal line; the error bars indicate the range of values given by 15 times the interquartile distance; outliers are displayed as individual points. Table I: Statistics of the intensity classes for the 1920 earthquake. Minimum Maximum Points Mean Median RMS StdEev. Skewn ess Kurtosis III IV V VI VII VIII IX X

4 218 Soil Dynamics and Earthquake Engineering a) 300 b) Rgure 3: Cumulative frequency (symbols) and CCF (lines) for intensity classes: a) 1980/11/23 Irpinia earthquake, with lognormal distribution; b) 1638/03/27 Calabria eqs, with Weibull and Gamma functions. In Kg. 3 two examples are given: the intensity sets of the 1980 Irpinia earthquake arefittedby a lognormal distribution in Hg. 3a, while in Kg. 3b the 1638 Qlabria (Southern Apennines) earthquake is modelled by a combination of Weibull and Gamma distributions. In Rg. 4 histograms of one single intensity class show in a more comprehensible way how data do appear. In theory, every intensity class of each earthquake can exhibit a different behaviour in term of probabilistic model. In practice, the number of observed values strongly limits the model choice. Usually, the highest classes of damage are poorly represented, and reliable statistics need the "stacking" of many earthquakes of the same epicentral intensity. A general outlook on the data-set (55 earthquakes, from GNDT [2], by an average number of 6 classes of intensity each)

5 Soil Dynamics and Earthquake Engineering 219 suggests the lognormal model to be the more suitable to treat with the same model all the intensity sets, being, on the contrary of the normal distribution, non-symmetrical; obviously, when a single distribution is chosen, a circular propagation is invoked. A possible a-priori assumption of non-circular intensity decay, linked to the source mechanism as well as to a regional propagation anisotropy, can be modelled when data show a bimodal behaviour, for example by using a proper combination of distributions. Although anisotropy is easily invoked when drawing isoseismal lines, its existence hardly can be demonstrated in a statistical meaning. In fact, bimodal distribution of data is a necessary but not sufficient condition and azimuthal analyses are expected to confirm anisotropy.look what happens in Rg. 5 where azimuths versus distance are given for the macroseismic data points: the lack of coverage suggests a false azimuthal attenuation dependence in the case of the 1980 earthquake (Rg. 5a), while distance distribution is far from being bimodal (Rg. 4a): on the contrary, a bimodal behaviour in the case of the 1638 earthquake (Rg. 4b) is not clearly testified by the azimuthal analysis (Rg. 5b). The present study does not consider anisotropy hypothesis rh Rgure 4: Histogram of macroseismic points distance of a single intensity class; same data of Rg. 3; a) 1980/11/23 Irpinia earthquake; b) 1638/03/27 Calabria earthquake. 3 Fitting a given decay model Qice the probabilistic model has been chosen, distances expected not to be exceeded at a given probability level can be obtained for each intensity class, the level depending from the desired caution, or from the way of application of an intensity decay relationship. In this way, each intensity set of an earthquake is represented by a single value of distance. The reference value of the lognormal probabilistic model here b)

6 220 Soil Dynamics and Earthquake Engineering chosen is at 50%probability: the following methodological considerations are independent from both the kind of distribution and probability level Then, the relationship between the different sets of intensity is carried on by fitting the attenuation model in a pseudo-in tensity/distance plane. Cbpending from the model, fitting can be performed using linear, or non-linear algorithms; the unknowns represent the model coefficients. Rg. 6 shows that the data can be fitted equally well by different intensity decay models; the solid squares are fitted by the Hake [3] model (thick dashed line) and the Gandori [4] one (thin solid line). The seismologist' debate about the best fitting model, becomes how to compute efficiently the model coefficients & 120 0) "D e - i o 60 e * b) Rgure 5: Clockwise azimuth of the intensity points with respect to epicentre is given from Nord in the range : central symmetry is invoked to test elliptical models. a)l Irpinia earthquake; b) 1638/03/27 Qlabria earthquake.

7 Soil Dynamics and Earthquake Engineering 221 Many authors developed attenuation relations to compute some hypocentral parameters; this is the case, for example, of the Hake model [2] where h has to be considered the depth of the focus. Fitting intensity versus distance (dashed line on open circles again in Rg. 6) requires the evaluation of the parameters a and h: to reach the data fitting the epicentral intensity has to be considered unknown as well. The learned experience in treating macroseismic data suggests to handle with care the model coefficients (such h in this example) implying physical assumptions, and to avoid the regression of epicentral intensity. Cbviously,in the previous case, only using the triplet of unknowns (a, h and computed epicentral intensity), the damage distribution can be reconstructed M >s '(75 g cz M 0) T 6 O g 4 C/) Q. - O Figure 6: Fitting the 1781 earthquake. Q)en circles represent intensity values, solid squares pseudo-in tensity decay with respect to epicentral intensity given in the catalogue. 4 Considerations on Italian data The described methodology has been applied to 55 earthquakes; they have been selected from the seismogenic zoning (Scandone et al. [5]) developed in the frame of the GNDT (National Qoup for Ebfence against Earthquakes) activities. The Qandori [4] attenuation relationship has been used. The statistics allow us to define a mean behaviour of intensity propagation, where the influence of anomalous points is greatly reduced: moreover the distance at a given probability level can be considered an efficient and well-constrained procedure for replacing isoseismal radii. No problems in fitting the decay of intensity versus distance have been found. This demonstrates the capability of the

8 222 Soil Dynamics and Earthquake Engineering method in adjusting the model to different propagation characteristics. Qi the other side, equal attenuation curves can be modelled by different combination of coefficients: this stresses that model coefficients have an essentially mathematical meaning. The damage distribution is well reproduced, using the earthquake catalogue parameters and the characteristic model coefficients: residuals (observed minus computed intensity) are in most cases symmetrically distributed around the null value, and, even more important, in all the intensity classes. The method avoids the weight surplus of intensity classes that have more samples, even if some intensity sets have poor statistical robustness. Acknowledgements The research has been developed under the framework of the CNR's CNDT activities. Thanks to Max Stucchi and Ebrio Slejko who encouraged the study, and livio Sirovich for useful suggestions and comments. References 1. Postpischl, D. (ed). Atlas of isoseismal maps of Italian earthquakes, CNRPF Ceod in arnica, Qraficoop, Bologna, Quppo Nazionale per la Dtfesa dai Terremoti. Macroseismic intensity database, Milano, Blake, A. On the estimation of focal depth from macroseismic data, Bullettin ofseism ological Society of A m erica, 1941,31, Qrandori, G, Perotti, F. & Tagliani, A. Qi the attenuation of macroseismic intensity with epicentral distance, in Ground Motion and Engineering Seismology (ed A.S. C&kmak), pp.581 to594,3rd Int. G)nf. on Soil Dynamics and Earthquake Big., Princeton,,USA, 1986, Hsevier, Amsterdam, Scandone,P.,Patacca,E, Meletti, C, Bellatalla, M., Perilli, N. & Santini, U. Struttura geologica, evoluzione cinematica e schema sismotettonico della penisola italiana, in Zanazione e riclassificazione sismica (ed CM)T),pp.ll9 tol33,am^/g?nv^n<9,pisa,itaua,1990,ambiente, Bologna, 1992.