Impact of Uncertainty on Loss Estimates for a Repeat of the 1908 Messina-Reggio Calabria Earthquake in Southern Italy

Transcription

1 Impact of Uncertainty on Loss Estimates for a Repeat of the 1908 Messina-Reggio Calabria Earthquake in Southern Italy Guillermo Franco a, BingMing Shen-Tu a, Agostino Goretti b, Paolo Bazzurro a, and Gianluca Valensise c a AIR Worldwide Corporation, 131 Dartmouth Street, Boston, MA Send correspondence to: gfranco@air-worldwide.com b Seismic Risk Office, CPD, Rome, Italy c Institute of Geophysics and Vulcanology (INGV), Rome, Italy Abstract. Increasing sophistication in the insurance and reinsurance market is stimulating the move towards catastrophe models that offer a greater degree of flexibility in the definition of model parameters and model assumptions. This study explores the impact of uncertainty in the input parameters on the loss estimates by departing from the exclusive usage of mean values to establish the earthquake event mechanism, the ground motion fields, or the damageability of the building stock. Here the potential losses due to a repeat of the 1908 Messina-Reggio Calabria event are calculated using different plausible alternatives found in the literature that encompass 12 event scenarios, 2 different ground motion prediction equations, and 16 combinations of damage functions for the building stock, a total of 384 loss scenarios. These results constitute the basis for a sensitivity analysis of the different assumptions on the loss estimates that allows the model user to estimate the impact of the uncertainty on input parameters and the potential spread of the model results. For the event under scrutiny, average losses would amount today to about to million Euros. The uncertainty in the model parameters is reflected in the high standard deviation of this loss, reaching approximately 45%. The choice of ground motion prediction equations and vulnerability functions of the building stock contribute the most to the uncertainty in loss estimates. This indicates that the application of non-local-specific information has a great impact on the spread of potential catastrophic losses. In order to close this uncertainty gap, more exhaustive documentation practices in insurance portfolios will have to go hand in hand with greater flexibility in the model input parameters. Keywords: Loss Estimation, Earthquake Risk Modeling, Uncertainty, Italy. INTRODUCTION At the February 2008 meeting of the Reinsurance Association of America in Tampa, Florida, Dr. Peter Taylor presented Ten Key Issues Facing Catastrophe Modelers, a collection of challenges that the catastrophe modeling community faces under progressively more sophisticated demands from the insurance and reinsurance market [1]. This paper addresses two of those ten items, in particular the sensitivity of catastrophe models to uncertainty in the input parameters and the development of models with knobs that permit the selection of different plausible assumptions for a catastrophic scenario instead of imposing a single deterministic hypothesis.

2 Parting from the usual estimation of a mean expected loss for a specific event, in this study knobs are implemented in three of the main blocks that constitute a typical earthquake risk loss estimation model. The resulting framework is applied towards obtaining expected losses due to an earthquake event similar to that of December 28th, 1908 in the Messina Straits, Italy. In this study the main earthquake event characteristics, the ground motion calculation, and the damage functions that determine the vulnerability of the building stock at risk are considered adjustable within a reasonable range that captures several different, well established alternatives found in the literature (see Figure 1). FIGURE 1. Flowchart of the loss sensitivity analysis. The rectangles with a bold frame and bold type represent the blocks with knobs, where uncertainty is explicitly considered in this study. LOSS SIMULATION SCENARIOS Two of the most widely accepted hypotheses for the source mechanism of the 1908 event serve as the basis to establish the event parameters. From these two fundamental hypotheses twelve plausible event scenarios are defined. In addition, two ground motion prediction equations are considered to obtain two sets of ground motion fields for each event scenario. To represent the vulnerability of the building stock, which is dominated by reinforced concrete and masonry structures, sixteen different hypotheses are considered. A detailed description of the input parameters and assumptions for these different scenarios follows in the next sections. Earthquake Event Definition The 1908 earthquake is one of the rare historic events that was captured by a network of seismographs and covered by several geodetic surveys. In fact, the 1908 event is generally considered the first European earthquake to have been fully documented instrumentally. The two source mechanisms proposed by Capuano et al. [2] and Boschi et al. [3] have found significant acceptance as plausible explanations for the 1908 rupture. Both solutions fit the geodetic and seismological data as well as other proposed alternatives while retaining considerable simplicity. The mechanism suggested by Boschi et al. was adopted by Valensise and Pantosti [4] and later by the Italian Database of Individual Seismogenic Sources (DISS) [5]. This solution draws on the observation of the local geological setting and establishes the hypothesis that the Messina Straits was formed by the repeated occurrence of events similar to that of The refinement of this solution proposed in the DISS database [5] ensures agreement with large scale recent geological and landscape features as well as with most instrumental observations. On the other hand, waveform modeling of regional

3 seismograms by Pino et al. [6] and joint inversion of first motion P-wave polarity data and coseismic surface displacement by Amoruso et al. [7] seem to show a greater agreement with the solution presented by Capuano et al. From the two base scenarios presented above a set of twelve variations are considered here with regard to the location of the hypocenter and the magnitude of the event (see tables 1 and 2). TABLE 1. Scenarios corresponding to the DISS database [5] after Boschi et al. [3]. Parameter Latitude Longitude M W Azimuth ( ) Dip Angle ( ) Depth (km) Rupture Length (km) TABLE 2. Earthquake source parameters corresponding to Capuano et al. [2]. Parameter Latitude Longitude M W Azimuth ( ) Dip Angle ( ) Depth (km) Rupture Length (km) Ground Motion Calculation The ground motion fields are computed using the ground motion prediction equations (GMPEs) proposed by Ambraseys et al. [8] and Sadigh et al. [9]. The GMPE of Ambraseys et al. was developed based on strong motion data observed in Europe, although it has been used in other regions of the world as well. Sadigh et al. s GMPE was developed based on California strong motion data for shallow crustal earthquakes and is applicable to magnitude and distance values that bracket those of the scenarios considered here. The latter equation is, however, well suited to predict the ground motion generated by shallow crustal earthquakes in active tectonic environments like the one under scrutiny. Therefore, it is considered as an alternative to Ambraseys et al. s equation, which applies to an average of widely different tectonic environments. Shallow site conditions (soil amplification) are considered in all ground motion calculations and all exposure sites are classified according to NEHRP soil types based on local geological data. Exposure Distribution and Vulnerability The replacement value of the existing exposure in the epicentral region that comprises the provinces of Messina and Reggio di Calabria is estimated using census and insurance market statistics at about million Euros. The data suggest that there are small percentages of residential wood and industrial steel construction, a 3% and a 6% in terms of the total replacement value, respectively. However, the

4 residential and commercial stock at risk is dominated by a 60% of reinforced concrete and a 31% of masonry construction in terms of replacement cost, typically low- and mid- rise buildings of 2 to 5 stories, and the losses calculated here refer to those two groups of construction classes. The hypotheses on the damageability of the building stock aim to capture the different alternatives available to characterize the behavior of these two most represented construction classes. Vulnerability is expressed here through a damage function, a curve that associates a damage ratio, DR (i.e. cost of repairs divided by the cost of replacement) with a level of a ground motion intensity measure, in this case Peak Ground Acceleration (PGA). The choice of this variable is due to the fact that many of the damage functions available in the literature are given in terms of PGA and, pursuing simplicity, these are used without adaptations here. Earthquake risk models typically use spectral displacements and spectral accelerations instead of PGA as measures of the ground motion. Four alternatives are considered for the damage functions for reinforced concrete. Three of these are derived from the study by Rossetto and Elnashai [10], which collects a series of fragility curves for reinforced concrete buildings that resemble the typical structural systems used in Europe. These fragility curves, which are empirically derived, are based on a number of damage surveys of various countries. Here, such fragility curves are used to obtain a damage function by assigning a damage ratio to each damage level. The values of DR associated with each damage level, based on those damage indices suggested by Rossetto and Elnashai, are chosen as: 10% (slight), 30% (light), 60% (moderate), 85% (extensive), and 100% (partial and total collapse). The mean damage function, the upper, and the lower 90% confidence bounds presented by Rossetto and Elnashai are considered here as plausible (even though perhaps extreme) alternatives to represent the damageability of reinforced concrete. These three solutions are referred to here as Europe L90, Mean, and U90. The fourth alternative was derived via convolution of the primary vulnerability (physical damage conditioned upon seismic intensity and building type) [11] and secondary vulnerability (probability of consequences conditional upon damage and building type) as reported for the Italian RC building stock [12]. This solution, which represents the mean behavior of RC in Southern Italy, is named here South Italy RC. Four alternatives are also considered for the masonry building damage functions. Three are obtained using the same convolution approach mentioned earlier that is presented in [11] and [12]. They represent an average behavior for three types of masonry construction, namely A (poor quality), B (medium), and C (good). These three damage functions will be referred to as South Italy A, B, and C, respectively. The distribution of masonries A, B, and C for the regions of Messina and Reggio Calabria is known to be approximately 15%, 10%, and 75%, respectively. The sensitivity analysis will however show the results that are obtained if one does not have this information (as it occurs for most regions worldwide) and approximates all masonry behavior with a single curve. For comparison with the Italy specific data, a damage function is derived applying the same DR values mentioned above to the

5 fragility curves developed by D Ayala et al. [13] for the Alfama district in Lisbon. Figure 2 collects the eight damage functions used for the vulnerability analysis. 100% Reinforced Concrete Damage Functions 100% Masonry Damage Functions Damage Ratio 80% 60% 40% South Italy RC Europe (U90) Europe (Mean) Europe (L90) Damage Ratio 80% 60% 40% 20% 0% PGA (cm/s 2 ) 20% 0% Lisbon, Portugal South Italy A South Italy B South Italy C PGA (cm/s 2 ) FIGURE 2. Vulnerability alternatives used for concrete (left) and masonry structures (right). DISCUSSION AND SENSITIVITY ANALYSIS The combination of source parameters (12 scenarios) with the GMPEs (2 alternatives) and the damage functions considered (16 combinations of RC and masonry) result in 384 loss estimates. The average event in this set of scenarios produces about million Euros in loss with a 51% standard deviation, causing an approximate dwellings to collapse and rendering homes totally unusable. As these damages ensue, it is estimated that, on average, this event would cause about casualties and that people would be in need of shelter. In order to compare the impact of choosing a specific GMPE, a first sensitivity analysis is conducted with the losses obtained by using the Ambraseys et al. and the Sadigh et al. separately. These groups of losses are plotted in Figure 3 in the form of a histogram. The choice of the GMPE, as expected, has a clear impact on estimated losses. The losses obtained using Ambraseys et al. are centered at million Euros with a standard deviation of 38%, while those computed with Sadigh et al. are centered at million Euros and display a higher standard deviation of 44%. The choice of a GMPE has also a strong impact on the geographic distribution of uncertainty, as shown in the plots of the geographic distribution of the standard deviation of loss of Figure 4. Both footprints show a low deviation near the epicenter since the PGAs predicted by both equations in those areas are high and all the damage functions look similarly in the high range of PGA. However, in regions with more moderate PGAs, different GMPE cause a differentiated spread of loss. The correct quantification of the quality of masonry structures plays a considerable role in the estimation of losses as well. Figure 5 shows the losses grouped by the choice of damage function under both GMPE scenarios. Dispersion in the results is high due to the uncertainty in the construction quality of reinforced concrete buildings and, especially, of masonry buildings. Comparison of the results for the D Ayala et al. results versus the Italy-specific curves indicates that the assumption of damage

6 functions not developed specifically for the study region may over or underestimate the losses considerably. Using a distribution-weighted damage function to collect the information on the regional masonry quality described above, the mean results in about million Euros with a standard deviation of 40%. This standard deviation is now mainly the product of the different GMPEs. Indeed, choosing one GMPE the deviation is reduced to 28% and the means obtained are million for Sadigh et al. and million for Ambraseys et al. In the frequent absence of locally specific data, however, choosing the most appropriate vulnerability relationships and an accurate quality distribution becomes a challenge and the uncertainty grows Ambraseys et al Sadigh et al Count Count Loss in 1,000 Million Euro Loss in 1,000 Million Euro FIGURE 3. Histogram of losses for the Ambraseys et al. (left) and for the Sadigh et al. scenarios. FIGURE 4. Geographic distribution of the standard deviation of loss. 20 Ambraseys et al. Sadigh et al. Reinforced Concrete 20 Masonry Ambraseys et al. Sadigh et al. Loss (1,000 Million Euro) Loss (1,000 Million Euro) Europe (L90) Europe (Mean) Europe (U90) South Italy RC 0 Lisbon, Portugal South Italy A South Italy B South Italy C FIGURE 5. Sensitivity due to the choice of damage functions for reinforced concrete (left) and for masonry structures (right), considering both GMPEs.

7 With the objective of identifying the parameters that, under complete certainty, reduce the spread of the losses, an analysis is performed on selected groups of results. Table 3 summarizes these analyses obtained by fixing one parameter and leaving the rest variable. For instance, the row associated with RC Europe (Mean) imposes that all RC building stock behaves as dictated by this damage function but does include all the results for different event parameters, the two GMPEs, and the four masonry damage functions. The statistics associated with those scenarios in which the RC damage function is thus defined show a dispersion of million Euros. Fixing the masonry damage curve, on the other hand, tends to produce a higher reduction of the loss spread, for instance to million Euros in the choice of the South Italy C curve. This is a consequence of the composition of the building stock that is dominated by masonry structures. The consideration of one event set of parameters versus the other does not seem to reduce the uncertainty significantly, however, pointing at the fact that while choosing the correct event parameters is important, the uncertainty in the final loss estimates are dominated by the vulnerability and ground motion prediction equation choices. TABLE 3. Statistics resulting from fixing a parameter in the sensitivity analysis. Losses are expressed in thousands of millions of Euros ( Euro). Fixed Parameter Average Min Max Max-Min St. Dev. Boschi et al. [3] % Event Capuano et al. [2] % Ground Ambraseys et al. [8] % Motion Sadigh et al. [9] % Europe (L90) [10] % Europe (Mean) [10] % Europe (U90) [10] % RC Damage Functions Masonry Damage Functions South Italy RC [11,12] % Lisbon, Portugal [13] % South Italy A [11,12] % South Italy B [11,12] % South Italy C [11,12] % CONCLUSIONS Today, an event similar to the 1908 Messina Straits quake would likely cause an average loss to the building stock in the environs of to million Euros. However, the deviation from this estimate due to the choice of vulnerability functions or ground motion prediction equations is large, of the order of 45%. The ground motion prediction equations play an important role and additional analyses using more modern equations such as those by Ambraseys et al. [14] and Akkar and Bommer [15, 16] will be performed 1. Similarly, although uncertainty in the building stock distribution and its cost of replacement has not been included in this analysis, their effect on the loss outcomes needs to be evaluated. For practical purposes, however, much of this uncertainty can be reduced with an in-depth 1 These results will be included in the oral presentation of this paper.

8 knowledge and proper documentation of the quality of the building stock in the region of interest. Insurance portfolios often lack the precision that is necessary to reduce this uncertainty. Therefore, models with knobs, which allow the variation of the damage functions for a portfolio lacking in specificity of the property s characteristics may lead to results with a high dispersion. This evidence might have an impact on underwriting practices inspiring a more exhaustive documentation of the structural characteristics of the insured properties to progressively close the uncertainty gap. REFERENCES 1. P. Taylor, Ten Key Issues Facing Catastrophe Modellers, presented at the Catastrophe Modeling 2008 Conference, Reinsurance Association of America, Tampa, Florida, Feb , P. Capuano, G. De Natale, P. Gasparini, F. Pingue, and R. Scarpa, A Model for the 1908 Messina Straits (Italy) Earthquake by Inversion of Levelling Data, Bulletin of the Seismological Society of America 78 (6), (1988). 3. E. Boschi, D. Pantosti, and G. Valensise, Modello di Sorgente per il Terremoto di Messina del 1908 ed Evoluzione Recente dell Area dello Stretto, Procceedings of the 8 th Meeting of the GNGTS, pp , Rome, G. Valensise and D. Pantosti, A 125 kyr-long geological record of seismic source repeatability: the Messina Straits (southern Italy) and the 1908 earthquake (Ms 71/2), Terra Nova, 4, pp (1992). 5. DISS Working Group, Database of Individual Seismogenic Sources (DISS), Version 3.0.3: A compilation of potential sources for earthquakes larger than M 5.5 in Italy and surrounding areas, INGV 2005 (2007). 6. N. A. Pino, D. Giardini, and E. Boschi, The December 28, 1908, Messina Straits, Southern Italy, Earthquake: Waveform Modeling of Regional Seismograms, Journal of Geophysical Research, 105 (B11), pp. 25,473-25,492 (2000). 7. A. Amoruso, L. Crescentini, and R. Scarpa, Source Parameters of the 1908 Messina Straits, Italy, Earthquake from Geodetic and Seismic Data, J. of Geophys. Res., 107 (B4), p. 2,080 (2002). 8. N. N. Ambraseys, K. A. Simpson, and J. J. Bommer, Prediction of Horizontal Response Spectra in Europe, Earthquake Eng. Struct. Dyn. 25, pp (1996). 9. K. Sadigh, C.-Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs, Attenuation Relationships for Shallow Crustal Earthquakes Based on California Strong Motion Data, Seism. Res. Lett., 68 (1), pp (1997). 10. T. Rossetto and A. Elnashai, Derivation of Vulnerability Functions for European-Type RC Structures Based on Observational Data, Engineering Structures 25, (2003). 11. E. Speranza, A. Goretti, and M. Dolce, Historical Damage Data and Microzonation: An Application to 1930 Senigallia Earthquake, Proc. 1 st ECEES, #1267, Geneva, Switzerland, G. Di Pasquale and A. Goretti, "Functional and Economic Building Vulnerability Observed in Recent Italian Earthquakes," X National Conf. Earthquake Eng., Potenza-Matera, 9-13 Sep D. D Ayala, R. Spence, C. Oliveira, and A. Pomonis, Earthquake Loss Estimation for Europe s Historical Town Centres, Earthquake Spectra, 13 (4), pp (1997). 14. N. N. Ambraseys, J. Douglas, P. Smit, and S. K. Sarma, 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, Bull. Earthquake Eng., 3 (1), pp (2005). 15. S. Akkar and J. J. Bommer, Prediction of elastic displacement response spectra in Europe and the Middle East, Earthq. Eng. Struct. Dyn., 36, pp (2007). 16. S. Akkar and J. J. Bommer, Empirical prediction equations for peak ground velocity derived from strong motion records from Europe and the Middle East, Bull. Seism. Soc. Am., 97 (2), pp (2007).