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on thE InfULEnCE of GRoUnd MotIon PREdICtIvE EqUAtIonS on PRobAbILIStIC SEISMIC hAzARd AnALySIS, PARt 2: tEStInG And SCoRInG PASt And RECEnt AttEnUAtIon ModELSS. Barani1, D. Albarello2, M. Massa3, D. Spallarossa11Dipartimento di Scienze della Terra dell’Ambiente e della Vita, Università di Genova, Italy

2Dipartimento di Scienze Fisiche della Terra e dell’Ambiente, Università di Siena, Italy3Istituto Nazionale di Geofisica e Vulcanologia, Milano, Italy

Foreword and scope of work. As known, ground motion prediction equations (GMPE) are stochastic models that estimate the probability distribution associated to the possible shaking levels induced at a site by an earthquake as a function of several parameters, such as magnitude, source-to-site distance, style of faulting, and ground type. Their parameterization implies statistical analyses on a large number of observations which, in turn, are subjected to a heavy work of processing in order to achieve uniform data sets. The signal processing and the homogenization of data coming from different institutions are certainly the most critical steps in the derivation of a GMPE. Signals have to be corrected and filtered; earthquake magnitudes are estimated using a uniform scale as well as distances are determined adopting a uniform distance metrics; site conditions at recording stations have to be determined (at least in the form of soil categories) along with the fault mechanism of the relevant seismic source.

Despite of the great efforts in developing GMPEs, it is not so unusual to listen that predictions are biased because of inaccuracies in the regression data sets. For instance, it is anything but a joke to listen that ground motion values are wrong due to a wrong setup (e.g., wrong seismometer’s generator constant) of the recording instruments. It is more frequent to discuss that the reliability and accuracy of predictions is affected by gross site classifications based on large-scale geological mapping. It is also frequent listening that GMPEs neglect topographic effects or, better, that ridges and crests are lost inside the large number of sites considered in the definition of a GMPE (e.g., Barani et al., 2014). The sensation of the writers is that the time goes by and regression data sets become larger and larger (Fig. 1a), functional forms are increasingly complex, and the variability of ground motion increases (Fig. 1b) although additional explanatory variables (e.g., variables that allow for soil nonlinear behavior, rupture directivity, high-frequency attenuation) are incorporated into the mathematical models. Throughout this proliferation of data sets and GMPEs, scientists (including the writers) are losing sight of the limitations of their models and, possibly, the steady improvement in the performance of brand new GMPEs. This is reflected in Probabilistic Seismic Hazard (PSH)

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estimates and, particularly, in the logic trees, which are increasingly leafy. Are GMPE branches really healthy or do they act as knots making the wood timber to sound worse?

The previous question is intentionally provocative, although it reflects a common feeling. The purpose of this work is to compare dated and recent GMPEs (see Tab. 1) in order to examine their impact (and that of the relevant aleatory sigma) on the hazard and to quantify their predictive power with reference to real case studies via a statistical scoring test.

Tab. 1 - List of GMPEs: Hm is for maximum horizontal, GM is for geometric mean, GMRotI50 indicates that the geometric mean is determined from the 50th percentile of the geometric means computed for all non-redundant rota-tion angles, RotD50 is the median single-component horizontal ground-motion calculated over all non-redundant azimuths.

Fig. 1 – a) Number of data used to calibrate the GMPEs considered in this study and b) values of the aleatory sigma for each GMPE. GMPEs are plotted on the X axis following a temporal order.

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Improvement in ground motion predictions and effect on seismic hazard. A first answer to the provocative question posed above may be given by analyzing the residuals between observed and predicted ground motion values. In this study, we apply the method proposed by Spudich et al. (1999) which uses the maximum likelihood formalism to calculate the mean value of the residuals (bias) and their dependence on magnitude and distance. The residual analysis (Fig. 2) is carried out for the seismic stations AQP (L’Aquila) and MRN (Mirandola), which recorded the 2009 L’Aquila sequence and the 2012 Emilia seismic crisis, respectively. Analyzing Fig. 2 in conjunction with Fig. 1b indicates that, although sigma has been increasing with time, the (absolute) residuals between observed and predicted ground motion values tend to decrease, thus suggesting an improvement in the GMPE performance (i.e., in the predictions) that will be reflected in the hazard results.

Fig. 2 – Residuals (absolute values) between observed and expected ground motion for the test sites of L’Aquila (AQP) and Mirandola (MRN). Residuals for BOR13 are not yet available.

In order to assess the effect of each GMPE on the hazard, we carried out different computational runs by varying one GMPE at a time while keeping constant the remaining PSH input models (e.g., source zone model) and parameter values (e.g., b-values, Mmax). The reference seismic hazard model considers the same set of input models and parameters adopted by Barani et al. (2009) for the disaggregation of the Italian ground motion hazard maps (Gruppo di Lavoro MPS, 2004). This set of inputs is that providing hazard results closer to the median values obtained using the entire logic tree (Gruppo di Lavoro MPS, 2004). If necessary, magnitude

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scale and distance conversions were applied. Moreover, GMPEs were corrected to predict the geometric mean of the horizontal components (Beyer and Bommer, 2006). Following good practice, the aleatory variability associated to conversion equations was carried across into the aleatory variability of each GMPE (Bommer et al., 2005).

Analyzing the hazard curves in Fig. 3, one may observe the largest uncertainty in the results (the spread between the hazard curves is an index of the epistemic uncertainty affecting the results) produced by older GMPEs (black curves in Fig. 3). Independently of the site, recent GMPEs (red curves in Fig. 3) appear to lead to a lower dispersion in the results, with hazard curves showing similar trend; after all, this was partly expectable given our previous observations concerning Fig. 2.

Fig. 3 – PSH curves for PGA and Sa(1s) for the sites of Barisciano (BRS) and Malcesine (MLC).

Scoring GMPEs. In order to evaluate the actual improvement in the GMPE performance (i.e., their effectiveness in predicting the ground motion), at least for application to the Italian area, we tested and scored different hazard models, each of which uses one of the GMPEs in Tab. 1. Given a set E of seismic occurrences (Evidence) and assuming that model outcomes are independent, the likelihood that in the i-th model the evidence E occurs (score) is given by (Albarello and D’Amico, 2008):

(1)

where:

(2)

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Ps are model outcomes in the form of exceedance probabilities (a Poisson process is assumed here) of any ground motion value gs in a fixed exposure time Ts at the s-th site; N* indicates the number of times that gs is exceed by observations at S sites during the time period Ts.

The statistical test can be also applied to evaluate the feasibility of the models (i.e., probability p that N* or less exceedances are expected to occur if the i-th model is “correct”).

The scoring procedure was applied taking into account the PGA values recorded at 73 accelerometric stations (belonging to the RAN – Rete Accelerometrica Nazionale) operating in Italy for at least 25 years. For these sites, the PGA hazard was calculated accounting for local soil conditions. Results (for PGA only) are presented in Tab. 2 and discussed in the next section.

Discussion and conclusions. Two decades of research efforts on GMPEs seem to have lead to fruitful results:

1 - with the exception of CF08 and AB10, recent GMPEs (i.e., hazard models based on recent GMPEs) are found to be more effective in providing PGA hazard estimates supported by available observations, at least for short-to-medium mean return periods;

2 - BND 13 performs better than previous models based on European and Middle East data;

3 - BOR13 performs better than its predecessor BA08.

Tab. 2 - Results of the scoring test. The values in each cell indicate the likelihood of each model. They may be adopted to select and weight GMPEs in a logic tree scheme.

In addition to the previous observations, it is worth observing that:a) ITA08 is found to be the most effective model. The lower performance of ITA10 could

be attributed to the distance metrics adopted. ITA08 uses Repi, a distance measure that is fully compatible with the way the earthquake sources (area sources in this application) are modeled in the code used for PSH analysis;

b) PGA hazard models based on GMPEs that ignore the contribution of M < 5 (nearby) events (SP96, AMB05, CF08, and AB10) tend to underestimate observations;

c) among dated GMPEs, AMB96 is found to be the most effective model. However, at lower mean return periods, it tends to provide PGA hazard values that overestimate observations (see also Fig. 3).

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Acknowledgements. This study has benefited from funding provided by the Italian Presidenza del Consiglio dei Ministri - Dipartimento di Protezione Civile (DPC).

ReferencesAkkar S. and Bommer J.J.; 2010: Empirical equations for the prediction of PGA, PGV and spectral accelerations in

Europe, the Mediterranean region and the Middle East. Seismological Research Letters, 81, 195-206.Albarello D. and D’Amico V.; 2008: Testing probabilistic seismic hazard estimates by comparison with observations:

an example in Italy. Geophysical Journal International, 175, 1088-1094.Ambraseys N.N., Douglas J., Sarma S.K. and Smit P.M.; 2005: Equations for the estimation of strong ground

motions from shallow crustal earthquakes using data from Europe and the Middle East: horizontal peak ground acceleration and spectral acceleration. Bulletin of Earthquake Engineering, 3, 1-53.

Ambraseys N.N., Simpson K.A. and Bommer J.J.; 1996: Prediction of horizontal response spectra in Europe. Earthquake Engineering and Structural Dynamics, 25, 371-400.

Barani S., Spallarossa D. and Bazzurro P.; 2009: Disaggregation of Probabilistic Ground-Motion Hazard in Italy. Bulletin of the Seismological Society of America, 99, 2638-2661.

Barani S., Massa M., Lovati S. and Spallarossa D.; 2014: Effects of surface topography on ground shaking prediction: implications for seismic hazard analysis and recommendations for seismic design. Geophysical Journal International, 197, 1551-1565.

Beyer K. and Bommer J.J.; 2006: Relationships between median values and between aleatory variabilities for different definitions of the horizontal component of motion. Bulletin of the Seismological Society of America, 96, 1512-1522.

Bindi D., Luzi L., Massa M. and Pacor F.; 2010: Horizontal and vertical ground motion prediction equations derived from the Italian Accelerometric Archive (ITACA). Bulletin of Earthquake Engineering, 8, 1209-1230.

Bindi D., Pacor F., Luzi L., Puglia R., Massa M., Ameri G. and Paolucci R.; 2011: Ground motion prediction equations derived from the Italian strong motion database. Bulletin of Earthquake Engineering, 9, 1899-1920.

Bindi D., Massa M., Luzi L., Ameri G., Pacor F., Puglia R. and Augliera P.; 2013: Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods up to 3.0 s using the RESORCE dataset. Bulletin of Earthquake Engineering, doi 10.1007/s10518-013-9525-5.

Bommer J.J., Scherbaum F., Bungum H., Cotton F., Sabetta F. and Abrahamson N.A.; 2005: On the use of logic trees for ground-motion prediction equations in seismic hazard analysis. Bulletin of the Seismological Society of America, 95, 377-389.

Boore D.M. and Atkinson G.M.; 2008: Ground motion prediction equations for the mean horizontal component of PGA, PGV and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s. Earthquake Spectra, 24, 99-138.

Boore D.M., Stewart J.P., Seyhan E. and Atkinson G.M.; 2013: NGA-West2 equations for predicting response spectral accelerations for shallow crustal earthquakes. PEER Report 2013/05, Pacific Earthquake Engineering Research Center, University of California, Berkeley.

Cauzzi C. and Faccioli E.; 2008: Broadband (0.05 to 20s) prediction of displacement response spectra based on worldwide digital records. Journal of Seismology, 12, 453-475.

Gruppo di Lavoro MPS; 2004: Redazione della mappa di pericolosità sismica prevista dall’Ordinanza PCM 3274 del 20 marzo 2003, Rapporto conclusivo per il dipartimento di Protezione Civile, INGV, Milano—Roma, aprile 2004, 65 pp. + 5 appendici, http://zonesismiche.mi.ingv.it/documenti/rapporto_conclusivo.pdf.

Massa M., Morasca P., Moratto L., Marzorati S., Costa G. and Spallarossa D.; 2008: Empirical ground motion prediction equations for Northern Italy using weak and strong motion amplitudes, frequency content and duration parameters. Bulletin of the Seismological Society of America, 98, 1319-1342.

Sabetta F. and Pugliese A.; 1996: Estimation of response spectra and simulation of nonstationary earthquake ground motions. Bulletin of the Seismological Society of America, 2, 337-352.

Spudich P., Joyner W.B., Lindh A.G., Boore D.M., Margaris B.M. and Fletcher J.B.; 1999: SEA99: a revised ground motion prediction relation for use in extensional tectonic regimes. Bulletin of the Seismological Society of America, 89, 1156-1170.

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