ROSE SCHOOL SENSITIVITY ANALYSIS IN PROBABILISTIC SEISMIC HAZARD ASSESSMENT

Transcription

1 Istituto Universitario di Studi Superiori Università degli Studi di Pavia EUROPEAN SCHOOL FOR ADVANCED STUDIES IN REDUCTION OF SEISMIC RISK ROSE SCHOOL SENSITIVITY ANALYSIS IN PROBABILISTIC SEISMIC HAZARD ASSESSMENT A Dissertation Submitted in Partial Fulfilment of the Requirements for the Master Degree in EARTHQUAKE ENGINEERING by ARGYRO THEODORAKATOU Supervisor: Dr FABIO SABETTA May, 2007

2 The dissertation entitled Sensitivity Analysis in Probabilistic Seismic Hazard Assessment, by Argyro Theodorakatou, has been approved in partial fulfilment of the requirements for the Master Degree in Earthquake Engineering. Dr. Fabio Sabetta Dr. Carlo Lai

3 Abstract ABSTRACT The scope of this thesis is to define those parameters that are the most important input in a Seismic Hazard Analysis. The subject of the current work was provoked from the great differences that were detected between the two hazard maps that have been recently produced in Italy, one of them conducted from the Department of Civil Protection [D. Albarello et al., 1999] and the other one more recently produced from the National Institute of Geophysics and Volcanology [M. Stucchi et al., 2004]. The latter of the hazard maps shows significantly lower values in the whole of the Italian peninsula, than the respective ones of the former. Since the introduction of the new Italian Hazard map, no detailed sensitivity analysis has been implemented, in order to become clear what the main reasons of the discrepancies are. Between the two Hazard Maps, a number of different choices in the selection of the input parameters have occurred, making it impossible to ascribe the discordances into one or more of the data entering the Seismic Hazard Assessment that produced the maps. Through this work it will become clear, how much, if any, is the contribution of each input parameter to the final outcome. A number of factors will be examined and the most decisive ones for the abrupt reduction of Peak Ground Acceleration values will be pointed out. i

4 Acknowledgements ACKNOWLEDGEMENTS To begin with, I would like to thank my supervisor, Dr. Fabio Sabetta. His help has been more than I could have hoped for. Always available and willing to offer his assistance even beyond scientific matters has been exactly what every student would need. Antonio Lucantoni has been an important ally to this work. His support with everything that was unfamiliar to me helped me every time I came across obstacles. Both his and Dr. Sabetta s comments contributed to appreciable improvements in this manuscript. My very good friend Sophia has been very brave to have endured me for more than a year. Rose School would have been a so much more difficult without you, and all those moments we had together. And last but most important, I must thank my family: my parents Makis and Katerina, my siblings Lenna and Dimitris and my companion, Christos. Nothing I have done and been through could have been accomplished without them. This work is dedicated to my mother. I hope you are proud. ii

5 Index TABLE OF CONTENTS Page ABSTRACT...i ACKNOWLEDGEMENTS...ii TABLE OF CONTENTS...iii LIST OF FIGURES...v LIST OF TABLES...xi 1. INTRODUCTION METHODOLOGY Description of Cornell Methodology Seismic Hazard Calculations Main Data and Parameters Affecting the Final Results Seismic Source Zones Earthquake Catalogue and Completeness Recurrence Relations Attenuation Relationships Software Used Logic Trees and Treatment on Uncertainties in Probabilistic Seismic Hazard Assessment DATA Italian Seismic Source Zones Magnitude Scales and Italian Seismic Earthquake Catalogues Historical and Statistical Completeness Maximum Magnitude Attenuation Relation Site Selection...36 iii

6 Index 4. SENSITIVITY ANALYSIS ON HAZARD CURVES AND UNIFORM HAZARD SPECTRA Seismic Zonation Seismic Catalogue Catalogue Completeness Magnitude Scale Maximum Magnitude Attenuation Relation SENSITIVITY ANALYSIS ON HAZARD MAPS Seismic Zonation Seismic Catalogue Catalogue Completeness Magnitude Scale Maximum Magnitude Attenuation Relation DISCUSSION & CONCLUSIONS...83 REFERENCES...87 iv

7 Index LIST OF FIGURES Page Figure 1.1: SSN-GNDT Hazard Map-Values of PGA(g) with a probability of exceedance 10% in 50 years (Return Period of 475 years)...1 Figure 1.2: INGV Hazard Map- Values of PGA (g) with a probability of exceedance 10% in 50 years (Return Period of 475 years)...1 Figure 2.1: Parameters which determinate Seismic Risk [Sabetta 2005, Lecture Notes, Pavia 2005]...3 Figure 2.2: Basic steps of Probabilistic Seismic Hazard Assessment [Reiter, 1990]...6 Figure 2.3: Steps in a non-parametric historic hazard method [McGuire R. K.]...7 Figure 2.4: Seismic source zones defined by different groups of researchers for the Sannio-Matese region of southern Italy [Barbano et al., 1989]...9 Figure 2.5: Major structural features of Italy [Cinti et al., 2004]...10 Figure 2.6: First example of a macroseismic map describing the earthquake effects on a four grade scale (1603 in Puglia earthquake)...11 Figure 2.7: Estimation of Completeness Period T c...12 Figure 2.8: Gutenberg-Richter recurrence law showing the meaning of parameters a and b...13 Figure 2.9: Truncated Gutenberg-Richter recurrence law...14 Figure 2.10: Comparison of Truncated and Bounded Gutenberg-Richter Recurrence Relation [Sabetta 2005, Lecture Notes, Pavia 2005]...15 Figure 2.11: Schematic illustration of conditional probability of exceeding a particular value of a ground motion parameter for a given magnitude and distance [Kramer S. L. 1996]...17 Figure 2.12: CRISIS user-friendly interface...18 Figure 2.13: Example of logic tree application to derive multiple hazard curves [McGuire R. K.]...21 Figure 3.1: Location and geometry of seismic zones for zonation ZS Figure 3.2: Location and geometry of seismic zones for zonation ZS Figure 3.3: Saturation of various magnitude scales: Mw (Moment Magnitude), ML (Richter Local Magnitude), MS (Surface Wave Magnitude), mb (short-period Body Wave Magnitude), mb v

8 Index (long-period Body Wave Magnitude) and MJMA (Japanese Meteorological Agency Magnitude) [Idriss, 1985]...25 Figure 3.4: Location of earthquake events with M S magnitude greater than 5.50, of NT4.1 earthquake catalogue...26 Figure 3.5: Location of earthquake events with M as magnitude greater than 5.50, of CPTI04 earthquake catalogue...26 Figure 3.6: Attenuation of PGA (T S =0sec) with distance, for the three relations, ±σ and for magnitude= Figure 3.7: Attenuation of PSA (T S =2sec) with distance, for the three relations, ±σ and for magnitude= Figure 3.8: Attenuation of PGA (T S =0sec) with distance, for the three relations, ±σ and for magnitude= Figure 3.9: Attenuation of PSA (T S =2sec) with distance, for the three relations, ±σ and for magnitude= Figure 3.10: Response spectra for the three attenuation relations, for 5% damping, M w =5.0 and D=3km...35 Figure 3.11: Response spectra for the three attenuation relations, for 5% damping, M w =7.0 and D=3km...35 Figure 3.13: Response spectra for the three attenuation relations, for 5% damping, M w =7.0 and D=85km...35 Figure 3.14: Variation of σ with respect to period for the three attenuationrelations and for M w = Figure 3.15: Variation of σ with refigure 3.12: Response spectra for the three attenuation relations, for 5% damping, M w =5.0 and D=85km...35 Figure 3.16: Variation of σ with respect to magnitude for the three attenuation relations and for T=0sec...36 Figure 3.17: Variation of σ with respect to magnitude for the three attenuation relations and for T=0.5sec...36 Figure 3.18: Location of the six selected sites...37 Figure 3.19: INGV Hazard Map-Values of PGA (g) with a probability of exceedance 10% in 50 years (T R = 475 years)...38 Figure 3.20: SSN-GNDT Hazard Map-Values of PGA (g) with a probability of exceedance 10% in 50 years (T R = 475 years)...38 Figure 3.21: Location of sites and seismic zonation ZS Figure 3.22: Location of sites and seismic zonation ZS Figure 3.23: Identification of zones of interest for seismic zonation ZS Figure 3.24: Identification of zones of interest for seismic zonation ZS vi

9 Index Figure 4.1: Hazard curves for Benevento for two spectral periods and for zonations ZS4 and ZS Figure 4.2: Hazard curves for Vibo Valentia for two spectral periods and for zonations ZS4 and ZS942 Figure 4.3: Hazard spectra for Benevento for two return periods and for zonations ZS4 and ZS Figure 4.4: Hazard spectra for Vibo Valentia for two return periods and for zonations ZS4 and ZS9 43 Figure 4.5: Seismic zones around Benevento with zonations ZS Figure 4.6: Seismic zones around Benevento with zonations ZS Figure 4.7: Seismic zones around Vibo Valentia with zonations ZS Figure 4.8: Seismic zones around Vibo Valentia with zonations ZS Figure 4.9: Hazard curves for Benevento for two spectral periods and for catalogues NT4 and CPTI Figure 4.10: Hazard curves for Vibo Valentia for two spectral periods and for catalogues NT4 and CPTI Figure 4.11: Hazard spectra for Benevento for two return periods and for catalogues NT4 and CPTI Figure 4.12: Hazard spectra for Vibo Valentia for two return periods and for catalogues NT4 and CPTI Figure 4.13: Gutenberg-Richter regression relations for Benevento with both old and new catalogue 47 Figure 4.14: Gutenberg-Richter regression relations for Vibo Valentia with both old and new catalogue...47 Figure 4.15: Hazard curves for Pavia for two spectral periods and for completenesses historical and statistical...49 Figure 4.16: Hazard curves for Vibo Valentia for two spectral periods and for completenesses historical and statistical...49 Figure 4.17: Hazard spectra for Pavia for two return periods and for completenesses historical and statistical...50 Figure 4.18: Hazard spectra for Vibo Valentia for two return periods and for completenesses historical and statistical...50 Figure 4.19: Gutenberg-Richter relations for Pavia with both completenesses...51 Figure 4.20: Gutenberg-Richter relations for Vibo Valentia with both completenesses...51 Figure 4.21: Hazard curves for Rome for two spectral periods, attenuation Ambraseys et al and for magnitude scales M S and M w...52 Figure 4.22: Hazard curves for Benevento for two spectral periods, attenuation Ambraseys et al and for magnitude scales M S and M w...52 Figure 4.23: Hazard spectra for Rome for two return periods, attenuation Ambraseyset al and for magnitude scales M SA and M w...53 vii

10 Index Figure 4.24: Hazard spectra for Benevento for two return periods, attenuation Ambraseys et al and for magnitude scales M SA and M w...53 Figure 4.25: Gutenberg-Richter relations for Rome (zone 922) with both magnitude scales...54 Figure 4.26: Gutenberg-Richter relations for Benevento (zone 927) with both magnitude scales...55 Figure 4.27: Gutenberg-Richter relation for Vibo Valentia (zone 929) with both magnitude scales...56 Figure 4.28: Hazard curves for Nocera Umbra for two spectral periods and for maximum magnitude from G-R and from INGV...58 Figure 4.29: Hazard curves for Venzone for two spectral periods and for maximum magnitude from G- R and from INGV...58 Figure 4.30: Hazard spectra for Nocera Umbra for two return periods and for maximum magnitude from GR and from INGV...59 Figure 4.31: Hazard spectra for Venzone for two return periods and for maximum magnitude from GR and from INGV...59 Figure 4.32: Hazard curves for Nocera Umbra, structural period T S =0 and M max from GR and one, two and three classes above it...60 Figure 4.33: Hazard curves for Nocera Umbra, structural period T S =4 and M max from GR and one, two and three classes above it...60 Figure 4.34: Hazard spectra for Nocera Umbra, return period T r =475y and M max from GR and one, two and three classes above it...60 Figure 4.35: Hazard spectra for Nocera Umbra, return period T r =10,000y and M max from GR and one, two and three classes above it...60 Figure 4.36: Hazard curves for Rome for spectral period T S =0sec and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.37: Hazard curves for Rome for spectral period T S =2sec and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.368: Hazard curves for Venzone for spectral period T S =0sec and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.39: Hazard curves for Venzone for spectral period T S =2sec and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.40: Hazard spectra for Rome for return period T r =475y and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.41: Hazard spectra for Rome for return period T r =10,000y and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.42: Hazard spectra for Vezone for return period T r =475y and for attenuations Sabetta&Pugliese, Ambraseys et al and viii

11 Index Figure 4.43: Hazard spectra for Vezone for return period T r =10,000y and for attenuations Sabetta&Pugliese, Ambraseys et al and Figure 4.44: Hazard estimates for San Francisco using three different ground-motion models with and without random uncertainty σ [Reiter; 1990]...64 Figure 5.1: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the ZS4 (Figure 5.1a) and ZS9 seismic zonation (Figure 5.1b)...65 Figure 5.2: Difference between the PGA values (in g) obtained by the ZS4 and the ZS9 seismic zonation...66 Figure 5.3: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by NT4 (Figure 5.3a) and CPTI04 earthquake catalogue (Figure 5.3b)...67 Figure 5.4: Difference between the PGA values (in g) obtained by the NT4 and the CPTI04 earthquake catalogue...68 Figure 5.5: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the statistical (Figure 5.5a) and historical completeness (Figure 5.5b)...69 Figure 5.6: Difference between the PGA values (in g) obtained by the statistical and the historical completeness...70 Figure 5.7: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the M w (Figure 5.7a) and M S (Figure 5.7b) magnitude scale using Ambraseys et al attenuation relation...71 Figure 5.8: Difference between the PGA values (in g) obtained by the M w and the M S magnitude scale using Ambraseys et al attenuation relation...72 Figure 5.9: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the INGV M max (Figure 5.9a) and original M max (Figure 5.9b)...73 Figure 5.10: Difference between the PGA values (in g) obtained by the M max given in the INGV report and the original M max...73 Figure 5.11: Values of PGA (in g) with a probability of exceedance 10% in 50 years (Return Period 475 years) obtained by the M max plus one magnitude class (Figure 5.11a) and M max plus three magnitude classes (Figure 5.11b)...74 Figure 5.12: Difference between the PGA values (in g) obtained by the M max plus one magnitude class and the original M max...75 Figure 5.13: Difference between the PGA values (in g) obtained by the M max plus three magnitude class and the original M max...76 Figure 5.14: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the Sabetta&Pugliese (Figure 5.14a) and the Ambraseys et al attenuation relation (Figure 5.14b)...77 ix

12 Index Figure 5.15: Difference between the PGA values (in g) obtained by the Sabetta&Pugliese 1996 and Ambraseys et al attenuation relation...78 Figure 5.16: Values of PGA (in g) obtained by the Sabetta&Pugliese 1996 (Figure 5.16a) and the Ambraseys et al attenuation relation (Figure 5.16b)...79 Figure 5.17: Difference between the PGA values (in g) obtained by the Sabetta&Pugliese 1996 and the Ambraseys et al attenuation relation...80 Figure 5.18: Values of PSA for T S =1sec (in g) obtained by the Sabetta&Pugliese 1996 (Figure 5.18a) and the Ambraseys et al. 2004attenuation relation (Figure 5.18b)...81 Figure 5.19: Difference between the PSA for T S =1sec values (in g) obtained by the Sabetta&Pugliese 1996 and the Ambraseys et al attenuation relation...81 x

13 Index LIST OF TABLES Page Table 3.1. Years of historical completeness for some of the ZS9 zones and different magnitude classes: class 1 M w =4.76; class 12 M w =7.29 [Stucchi et al. 2004]...28 Table 3.2. Years of statistical completeness for some of the ZS9 zones and different magnitude classes: class 1 M w =4.76; class 12 M w =7.29 [Stucchi et al. 2004]...29 Table 3.3. Procedure followed for the computation of the Gutenberg-Richter relation...30 Table 3.4. Maximum values of magnitudes for the ZS9 as these have been reported in the INGV report (zones )...31 Table 3.5. Maximum values of magnitudes for the ZS9 as these have been reported in the INGV report (zones )...32 Table 3.6. Main characteristics of the Attenuations used...33 Table 3.7. PGA values for the six sites with the SSN-GNDT and the INGV Hazard Map...38 Table 3.8. Zones in which the selected sites fall for both seismic zonations...39 Table 3.9. Zones within the radius of 100 km for each site and for both zonations...40 Table 4.1. Values of hazard curves using zonation ZS4 and ZS9 (T=0sec) in Nocera Umbra...44 Table 4.2. Ratios of events over completeness, for both historical and statistical completeness...50 Table 4.3. Number of events for each magnitude and for both magnitude scales for Rome...54 Table 4.4. Number of events for each magnitude and for both magnitude scales for Benevento...55 Table 4.5. Number of events for each magnitude and for both magnitude scales for Vibo Valentia...56 Table 4.6. Numerical differences in a and b...57 Table 4.7. Ratios of events over completeness, for both historical and statistical completeness...57 Table 4.8. M max Values from G-R and from INGV...58 Table 6.1. Maximum differences (in g) and maximum percentage differences in the PGA values for the hazard maps and for all the parameters that have been modified...83 xi

14 Index Table 6.2. Percentage differences of frequency of exceedance for a particular value of acceleration of the hazard curves and percentage differences of the PGA of the hazard spectra for some of the selected sites and for all the modified parameters...84 xii

15 Chapter 1: Introduction 1. INTRODUCTION The scope of this work is to analyse the sensitivity of the hazard estimates when different choices are considered for the input parameters. The subject of this work was provoked from the great differences that were detected between the two hazard maps that have been recently produced in Italy. The one of them (Figure 1.1), has been realized by Servizio Sismico Nazionale (SSN) and Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [Albarello et al., 2000], while the other and more recent one has been generated by the National Institute of Geophysics and Volcanology [M. Stucchi et al., 2004] and can be seen in Figure 1.2. The latter of the hazard maps shows significantly lower values in the whole of the Italian peninsula, than the respective ones of the former. Since the introduction of the new Italian Hazard map, no detailed sensitivity analysis has been implemented, while between the two Hazard Maps, a number of different choices in the selection of the input parameters have occurred. VENZONE VENZONE PAVIA %a %a N PAVIA %a %a N NOCERA UMBRA NOCERA UMBRA %a %a ROMA %a BENEVENTO ROMA %a BENEVENTO %a %a %a Sites DPC MAP VIBO VALENTIA %a %a Sites INGV MAP VIBO VALENTIA %a Figure 1.1: SSN-GNDT Hazard Map-Values of PGA Figure 1.2: INGV Hazard Map-Values of PGA (g) (g) with a probability of exceedance 10% with a probability of exceedance 10% in 50 years (Return Period of 475 years) in 50 years (Return Period of 475 years) 1

16 Chapter 1: Introduction The choices that can be done for a hazard map are not standard and deserve detailed investigation to quantify their influence in the hazard estimates. Usually, in an engineering project there will not be room for a detailed sensitivity analysis of the different parts of the model, even though a simple disaggregation is usually included in most cases where Probabilistic Seismic Hazard Assessments are employed. This work aims at both the clarification of the parameters, which are most responsible for the final results, as well as at explaining the main reasons for the discrepancies that appear between the two hazard maps of Figures 1.1 and 1.2. This thesis is developed in six chapters. In Chapter 2 the methodology that is going to be followed is illustrated. The Cornell method is presented as well as all the main data and parameters whose effect on the final results will be investigated. Seismic zonation, earthquake catalogue, catalogue completeness, magnitude scale, maximum magnitude and attenuation relationship are the input parameters of the Hazard Calculations which will be studied. Finally, a presentation of the software that will be used is carried out. In Chapter 3 the choices of the input data introduced in the previous Chapter are specified. The different options among which we will alternate are presented, followed by the selection of the Italian sites which will be examined. The following Chapter, forth in position, comprises the results of the hazard calculations in terms of hazard curves and hazard spectra for the selected sites. In Chapter 5 the results of the hazard assessment are presented in the form of hazard maps. All the input parameters that were mentioned in Chapter 3 are used and comparisons among the respective maps are carried out. Finally, in Chapter 6 the most important conclusions that were drawn from the studies are discussed and presented. 2

17 Chapter 2: Methodology 2. METHODOLOGY In the current chapter, the methodology that is going to be followed in this work will be described. Also, all the parameters whose variation of value will affect the outcome of a Probabilistic Seismic Hazard Assessment will be presented and defined. 2.1 Description of Cornell Methodology Seismic risk can be defined as the possibility or probability of losses due to earthquake, whether these losses are human, social or economic. It can be estimated from the following expression: Seismic Risk = Seismic Hazard. Vulnerability. Exposure (2.1) Figure 2.1: Parameters which determinate Seismic Risk [Sabetta 2005, Lecture Notes, Pavia 2005] In the formula above, the seismic hazard represents the expected earthquake ground motion at the site of a structure or any other engineering project. The vulnerability of a structure represents its attitude to be damaged by a given intensity earthquake. The exposure refers to the human activity located in the zones of seismic hazard and represents the quantity and quality of the goods (population, facilities, lifelines, etc.) exposed to risk. 3

18 Chapter 2: Methodology Seismic Hazard Assessment should always be viewed as an integral part of the assessment of seismic risk otherwise it is nothing more than an interesting academic amusement. Consider the following examples: Defining the earthquake loads to be considered in the earthquake-resistant design of standard occupancy structures according to a code of practice. Assessing the seismic safety of a nuclear power plant. Formulating an emergency response plan for a large city in the event of a major earthquake. Assessing the capacity of a hospital to continue to operate and provide medical attention following a major earthquake in the city where it is located. Designing a retrofit scheme for a national monument in an earthquake area. There is no one single approach suitable for application in all of these situations, indeed the Seismic Hazard Assessments in each case may differ significantly in the way they are carried out. In each engineering project, the actual approach adopted should be determined according to the tectonic setting and the level of seismicity, the nature and cost of the project, the consequences of failure under seismic shaking, the conditions of the owner, and the requirements of the law and the perceptions of the public [Sabetta 2005, Lecture Notes, Pavia 2005]. All the calculations and the analyses that will follow in the next chapters are going to be carried out under the prism of Probabilistic Seismic Hazard Assessment. Probabilistic Seismic Hazard Assessment (PSHA) provides a framework in which uncertainties in size, location and rate of occurrence of earthquakes and in variation of ground motion characteristics can be explicitly considered in the evaluation of seismic hazard. These uncertainties can also be identified, quantified and combined in a rational manner. Hazard descriptions are not restricted to scenario-like statements, as is the case of Deterministic Seismic Hazard Assessment (DSHA). On the contrary, they incorporate the effects of all the earthquakes capable to affect the site in question. PSHA integrates over all possible earthquake occurrences and ground motions to calculate a combined probability of exceedance that incorporates the relative frequencies of occurrence of different earthquakes and groundmotion characteristics. This is why, when one selected site is examined, all the zones within a certain radius from the site are being taken into account. Modern PSHA also considers multiple hypotheses on input assumptions and thereby reflects the relative credibilities of competing scientific hypothesis. Another advance of PSHA is that it results in an estimate of the likelihood of earthquake ground motion. This allows the incorporation of PSHA into seismic risk estimates and the quantitative comparison of different options in making decisions. These features of PSHA allow the ground motion hazard to be expressed at multiple sites consistently in terms of earthquake sizes, frequencies of occurrence, attenuation and associated ground motion. 4

19 Chapter 2: Methodology As a result, consistent decisions can be made to choose seismic design or retrofit levels, to make insurance and demolition decisions and to optimize resources to reduce earthquake risk vis-à-vis other causes or loss. A disadvantage of PSHA is that the concept of a design earthquake scenario is lost. There is no single event, specified in terms of magnitude and distance that represents the earthquake threat at a given level of return period. Still, there is a well established procedure for determining earthquake scenarios to associate with the probabilistic ground motion. This procedure is referred to as Deaggregation. Without a deaggregation, the probabilistic evaluation gives the ground motion level without information on the earthquake scenarios that can cause that ground motion [McGuire, R. K., 1995]. The basic procedure of PSHA was first defined by Cornell [1968] and although numerous modifications have been made to the process, the basic elements of the calculations remain unchanged. The Cornel method is based on three specific assumptions. Firstly, event magnitude is exponentially distributed ( log λm = a b m ), secondly seismicity is uniformly distributed inside each Seismogenic zone and thirdly, earthquake recurrence times follow a Poisson process. The Poisson model provides a simple framework for evaluating probabilities of events that follow a Poisson process, one that yields values of a random variable describing the number of occurrences of a particular event during a given time interval or in a specified spatial region. Since PSHA deals with temporal uncertainty, the spatial applications of the Poisson model will not be considered further. Poisson processes possess the following properties: (i) the number of occurrences in one time interval are independent of the number that occur in any other time interval, (ii) the probability of occurrence during a very short time interval is proportional to the length of the time interval and (iii) the probability of more than one occurrence during a very short time interval is negligible [Kramer S. L., 1996]. These properties indicate that the events of a Poisson process occur randomly, with no memory of the time, size and location of any preceding event (memory-less process). Investigations of the applicability of Poisson and non-poissonian models have shown that the Poisson model is useful for practical seismic risk analysis except when the seismic hazard is dominated by a single source for which the time interval since the previous significant event is greater than the average inter-event time and when a source displays strong characteristictime behavior. Each one of the more sophisticated models counting for prior seismicity (Renewal Models, Time-Predictable models, Slip-Predictable models, Marcov models, Semi- Marcov models, etc) uses a pattern of earthquake occurrence to reconcile their computed probabilities with the mechanics of the elastic rebound process. As a result, each requires additional parameters whose values must be evaluated from historical and instrumental seismicity records that are, in most cases, too sparse to permit accurate evaluation. For this and other reasons related to simplicity, ease of use and lack of sufficient data to support more sophisticated models, the Poisson model is most widely used in contemporary PSHA. 5

20 Chapter 2: Methodology Also, it has not been yet affirmed whether the world seismicity and consequently the earthquakes generation is increasing or decreasing. Keeping all these in mind, the Poisson model seems suitable for use in a PSHA. Figure 2.2: Basic steps of Probabilistic Seismic Hazard Assessment [Reiter, 1990] The conceptual steps of the Cornell methodology are the following: Identification and characterization of all earthquake sources capable of producing significant ground motion at the site of interest. Source characterization includes definition of each source s geometry and earthquake potential, which will be uniform, that is, the earthquakes have an equal probability of occurring at any point within the seismic source zone. Source may range from clearly understood faults, to less well defined geological structures, to hypothetical seismotectonic provinces or zones. Each source is characterized by an earthquake probability distribution or recurrence relationship, which specifies the average rate at which a given size earthquake will be exceeded. The recurrence relation may accommodate the maximum size earthquake but it does not limit consideration to that earthquake. The ground motion produced at the site by earthquakes of any possible size occurring at any possible point in each source zone must be determined with the use of predictive relations. The uncertainty inherent in the predictive relation is also considered in the PSHA. Finally, different uncertainties in earthquake location, earthquake size and ground motion prediction parameter are combined to obtain the probability that the ground motion parameter will be exceeded during a particular time period [Sabetta 2005, Lecture Notes, Pavia, 2005]. 6

21 Chapter 2: Methodology These four steps are schematically presented in Figure Seismic Hazard Calculations Methods of seismic hazard calculations fall into two categories. The first consists of historic methods, which are based on historical earthquake occurrences and which do not use interpretations of faults, seismic sources or seismicity parameters. The second are called deductive methods, because interpretations are made to deduce the causes of earthquakes (faults and areal sources) and their characteristics (the seismicity parameters). An outline of the non-parametric historic method is shown in Figure 2.4. In the top left, the earthquake catalogue in the vicinity of the site is plotted. In the top right, a ground motion attenuation function is adopted that predicts ground motion intensity as a function of epicentral intensity I 0 and distance. For each historic earthquake, using its value of M (or I 0 ) and distance R, the distribution of ground motion is estimated, as shown in the bottom right. This gives the historical rate at which different levels of ground motion are exceeded. Figure 2.3: Steps in a non-parametric historic hazard method [McGuire R. K.] Finally, this function is divided by the number of years in the catalogue in order to obtain an annual rate of exceedance, which for small values of is a good approximation to the annual probability of exceedance (illustrated in the bottom left of Figure 2.3). This method has the advantage that seismic sources and seismicity parameters are not needed, so it involves fewer interpretations than the deductive method. Its primary disadvantage though, is its unreliability at lower annual probabilities than the inverse period of the catalogue. 7

22 Chapter 2: Methodology Practical applications of the historic method are more complicated than portrayed in Figure 2.3 because, for example, earthquake catalogues typically are complete for different time periods at different intensity levels [McGuire R. K.]. The steps involved in the deductive method were illustrated in Figure 2.3, where the basic steps of PSHA were presented. The results of a PSHA can be expressed in many different ways. All of them involve some level of probabilistic computations to combine the uncertainties in earthquake size location, frequency and effects to estimate seismic hazards. A common approach involves the development of seismic hazard curves, which indicate the annual probability of exceedance of different values of a selected ground motion parameter. The seismic hazard curve can then be used to compute the probability of exceeding the selected ground motion parameter in a specified period of time. Hazard curves are the outcome of the procedure illustrated in Figure 2.2. Seismic hazard curves can be obtained for individual source zones and combined to express * the aggregate hazard at a particular site. The probability of exceeding a particular value, y, of a ground motion parameter,y, is calculated for one possible earthquake at one possible source location and then multiplied by the probability that that particular magnitude earthquake would occur at that particular location. The process is then repeated for all possible magnitudes and locations with the probabilities of each summed. The required calculations are described in the following paragraphs [Kramer S. L., 1996]. For a given earthquake occurrence, the probability that a ground motion parameter Y will * exceed a particular value y can be computed using the total probability theorem, that is: P [ ] [ ] [ ] ( ) [ Y > y ] = P Y > y * X P X = P Y y * X f X dx * > x (2.2) where X is a vector of random variables that influencey. In most cases the quantities in X are limited to the magnitude, M, and distance, R. Assuming that M and R are independent, the probability of exceedance can be written as: P [ Y > y ] = P Y > y * m, r f ( m) f ( r) dmdr [ ] * (2.3) where P [ Y > y * m, r] is obtained from a predictive attenuation relationship and f M (m) and f R (r) are the probability density functions for magnitude and distance, respectively. If the site of interest is in a region of N s potential earthquake sources, each of which has an average rate of threshold magnitude exceedance, ν i [ = exp( ai βim 0 )], the total average exceedance rate for the region will be given by: λ y = N s i= 1 ν i [ > y m, r] P Y M R * f ( m) f ( r) dmdr (2.4) This method is called the deductive method of seismic hazard analysis because we deduce what are the causative sources, characteristics and ground motions for future earthquakes. This method was first published by Cornell [1968], with many applications since. Mi Ri 8

23 Chapter 2: Methodology It is preferred over the historic method for low probabilities, because it can account for hypotheses such as migration of seismicity, seismic gaps, cyclical strain release and nonstationary seismicity that may not be captured by historic methods. Still, the individual components of Equation 2.4 are, for virtually all PSHAs, sufficiently complicated that the integrals cannot be evaluated analytically (only in simple cases of point or line sources). Numerical integration is therefore required and this can be done by a variety of computer programs, some of the most used ones being SEISRISK III [Bender and Perkins, 1987] and CRISIS [M. Ordaz et al., 2003] 2.3 Main Data and Parameters Affecting the Final Results Seismic Source Zones The first step for a SHA is to define seismic source zones. These are regions defined by polygons within which it is assumed that seismicity is uniform in terms of the type and distribution of earthquakes. The criteria for determining the boundaries of the seismic zones include the distribution of instrumental and historical seismicity, the tectonic configuration and the location of known active faults [Sabetta 2005, Lecture Notes, Pavia, 2005]. Figure 2.4: Seismic source zones defined by different groups of researchers for the Sannio-Matese region of southern Italy [Barbano et al., 1989] It is almost impossible to prescribe a standard procedure for the definition of seismic source zones, since the process involves a high degree of subjective judgement. In Figure 2.4, different zonations for the same region are shown, adopted by six different groups of researchers. Even renowned experts in the field will rarely agree on the limits of appropriate source zones. A proper way to overcome the high degree of subjectivity which characterises such matters would be to input the different options into a logic tree where every different seismic zonation will be represented by a different branch. The use of logic trees provides a convenient framework for the explicit treatment of model uncertainties since it allows the use of alternative models, each of which is assigned a weighting factor that is interpreted as the relative likelihood of that model being correct. Another and better option instead of the use of seismic zones is the use of single active seismic faults, if possible. 9

24 Chapter 2: Methodology However, in spite of the increased availability of geological, paleoseismological, geodetic and seismometric data, it is very rare that in Europe (with its complex seismotectonics and a large number of buried faults) PSHA could be based essentially on active faults, as it could be perhaps done in California, where the seismicity of the area is dominated from S. Andreas well known fault [Sabetta 2005, Lecture Notes, Pavia 2005]. Figure 2.5: Major structural features of Italy [Cinti et al., 2004] Earthquake Catalogue and Completeness The next step after the definition of the seismic zonation in a seismic hazard assessment, regardless of the methodological approach to be used, is to compile an earthquake catalogue for the region under study. This catalogue must give the origin time, location (epicentral coordinates and focal depth) and magnitude of the earthquakes that have occurred in or near to the region of interest. Catalogues may be instrumental, historical or mixture of both types [Sabetta 2005, Lecture Notes, Pavia, 2005]. (a) Instrumental. Instrumental earthquake catalogues covering most of the twentieth century are easily obtainable for any part of the world from a number of national and international agencies (International Seismological Centre/ISC, National Geophysical Data Centre/NGDC, National Earthquake Information Centre/NEIC, National Institute of Geophysics and Volcanology/INGV). These kinds of catalogues contain events whose location, origin time and magnitude have been recorded by instruments. It is often tempting to obtain an earthquake catalogue for the region of interest and then to proceed directly to the hazard calculations, but it is always necessary to first assess the reliability of the data in the catalogue. Agencies such as those listed above are producing routine earthquake locations that may easily carry an error of km in the epicentral location and more in the focal depth. 10

25 Chapter 2: Methodology (b) Historical. The era of instrumental seismicity is considered to have begun around the end of XIX century, meaning that the instrumental record of earthquake activity is at very best just over 100 years in length. Compared with the time-scale of the geological processes underlying earthquake generation, this is a very short period of observation. Historical seismicity is the term given to the study of earthquakes that occurred before the end of the nineteenth century. The key to this study is the collection of contemporary reports of earthquakes and earthquake effects in newspapers, diaries, church records, etc. The retrieval of historical information often requires a painstaking translation from ancient language and descriptions, into numerical values of intensity and the filtering of useful and factual reports from those that are erroneous. It is not uncommon for sources written long after an earthquake to report the date incorrectly or to confuse and mix different reports. In order to satisfy the hypothesis of independence of events that is at the basis of the Cornell method (Poisson process) the foreshocks and aftershocks preceding and following the main large earthquake should be removed from the earthquake catalogues. This is a procedure referred to as space and time de-clustering. For example, de-clustering can be performed by filtering the catalogue, around each main event, with a space-time window of a certain radius and ± a period of days. Figure 2.6: First example of a macroseismic map describing the earthquake effects on a four grade scale (1603 in Puglia earthquake) De-clustering, however, is often not a straightforward matter because it is common for earthquakes to occur in series, such as the 1997 Umbria-Marche earthquakes in Italy, whence none of the events is clearly identifiable as a main shock, although the events are evidently not independent. Due to the lack of complete documentation, the probability of lost earthquakes increases as one goes back in time making the catalogue progressively less representative of actual seismicity. An earthquake catalogue is defined as complete if all the earthquakes happened during the time period covered are effectively reported in the catalogue. For instrumental data detection capability is the determining factor. 11

26 Chapter 2: Methodology For historical data, evolution in time of socio-cultural environment, population density, and record keeping are the key factors. The most common method for estimating completeness period (T c ) has been proposed by Stepp (1972) and consists of making plots of the cumulative number of events against time, from which, the period since present during which reporting has been complete, can be judgmentally estimated (Fig. 2.7). Estimation of T c is often difficult and involves a high degree of subjective judgment [Sabetta 2005, Lecture Notes, Pavia, 2005] Ms= Ms= Ms= Ms= cumulative earthq. N cumulative earthq. N Year Year Figure 2.7: Estimation of Completeness Period T c Several authors have proposed different statistical methodologies for the evaluation of completeness time intervals [Stepp, 1972; Bath, 1983; Tinti & Mulargia, 1985; Mulargia et al., 1987]. Any statistical approach based exclusively on catalogue data is in some way a vicious circle because you are using an incomplete data base to evaluate its incompleteness. The only way to avoid this circle would be to use independent historical information, based on the knowledge of the variation during historical time of the availability of historical sources that is rarely accessible. Normally to overcome the problem an a priori assumption on the stationary characteristics of the seismicity (allowed by the de-clustering) is made, so that the incompleteness is attributed to the deviation of the seismicity reported in the catalogue from the assumed theoretical stationary model. In this way the completeness test is transformed in a stationarity test. Completeness periods are generally dependent on geographical locations according to their different socio-cultural history. The effect of the completeness time interval T c on the final results of SHA is strongly dependent on the particular time-distribution of earthquakes for the considered seismic zone [Sabetta 2005, Lecture Notes, Pavia, 2005] Recurrence Relations Once an earthquake source is identified and its corresponding source zone characterized, the seismic hazard analyst s attention is turned towards the evaluation of the size of earthquakes that the source zone can be expected to produce. All source zones have a maximum earthquake magnitude that cannot be exceeded; it can be large for some zones and small for others. In general, the source zone will produce earthquakes of different sizes up to the maximum earthquake, with smaller earthquakes occurring more frequently than larger ones. 12

27 Chapter 2: Methodology The strain energy may be released aseismically, or in the form of earthquakes. The distribution of earthquake sizes in a given period of time is described by a Recurrence Relation. A basic assumption of PSHA is that the recurrence relation obtained from past seismicity is appropriate for the prediction of future seismicity. One of the recurrence relations available is the Gutenberg-Richter [Kramer S. L., 1996]. Gutenberg and Richter (1944) gathered data from southern California earthquakes over a period of many years and organized the data according to the number of earthquakes that exceed different magnitudes during that time period. They divided the number of exceedances of each magnitude by the length of the period in order to define a mean annual rate of exceedance, λ m of an earthquake of magnitude m. As would be expected, the mean annual rate of exceedance of small earthquakes is greater than that of large earthquakes. The reciprocal of the annual rate of exceedance is referred to as Return Period of earthquakes exceeding that magnitude. When the logarithm of the annual rate of exceedance of southern California earthquakes was plotted against earthquake magnitude, a linear relationship was observed. The resulting Gutenberg-Richter relation for earthquake recurrence was expressed as: log λ = a b m (2.5) m where λ m is the mean annual rate of exceedance of magnitude m, 10 is the mean yearly number of earthquakes with magnitude greater than or equal to zero and b describes the relative likelihood of large and small earthquakes. In particular, the parameter a represents the seismic activity and as its value increases so does the seismicity of the region. As the b value increases (by absolute value), the number of larger magnitude earthquakes decreases compared to those of smaller magnitude. The b value varies with the seismicity of the region and is usually close to 1.0. The standard Gutenberg-Richter relation and the meaning of the parameters entering equation 2.2 are illustrated in Figure 2.8. a Figure 2.8: Gutenberg-Richter recurrence law showing the meaning of parameters a and b 13

28 Chapter 2: Methodology The standard G-R recurrence relationship may also be expressed as: λ m =10 a-bm =e a-βm (2.6) where a = a and β = b. Equation 2.6 shows that the Gutenberg-Richter law implies that earthquake magnitudes are exponentially distributed. The resulting probability distribution of Magnitude for this Gutenberg-Richter recurrence relation can be expressed in terms of the Cumulative Distribution Function (CDF): F M βm [ ] ( m) = P M < m = 1 e (2.7) or the Probability Density Function (PDF): f M d ( m) = FM ( m) = βe β dm m (2.8) The standard Gutenberg-Richter relation covers an infinite range of magnitudes, from to +. For engineering purposes though, the effects of very small earthquakes are of little interest and it is common to disregard those magnitudes that are not capable of causing significant damage, for example all earthquakes with magnitudes smaller than a given value of magnitude M0. At the other end of the magnitude scale, the standard Gutenberg-Richter relation predicts nonzero mean rates of exceedance for magnitudes up to infinity. Still, some maximum magnitude M max is associated with all source zones. The introduction of M 0 and M max leads to the so called Truncated Gutenberg -Richter relation (TGR). If the Truncated Gutenberg -Richter Relation is plot in semi-log scale, the model is a straight line truncated at M= M max and λ 0 will be the magnitude exceedance rate for M= M 0. The graphic representation of the Truncated Gutenberg -Richter Relation can be seen in Figure 2.9. Figure 2.9: Truncated Gutenberg-Richter recurrence law 14

29 Chapter 2: Methodology Besides the Standard and the Truncated Gutenberg-Richter recurrence relation there is also the Bounded Gutenberg-Richter. To avoid the abrupt truncation at M= M max, a Bounded Gutenberg Richter relation (BGR) can be used. The Bounded Gutenberg-Richter model is very similar to the Truncated Gutenberg-Richter one, for magnitudes close to the M min, but it shows a smooth transaction to zero at the maximum magnitude M max instead of the abrupt drop of the truncated model. If the Bounded Gutenberg-Richter model is used, the mean annual rate of exceedance will be expressed as: λ m e = λ β ( m m0 ) β ( mmax m0 ) e β ( mmax 0 ) 1 e 0 m m m (2.9) 0 m max In this case, the resulting probability distribution of magnitude can be expressed in terms of the Cumulative Distribution Function (CDF) as shown in equation 2.10: F M ( m) = P M 0 1 e [ < m m0 m mmax ] = β ( m m ) 1 e β ( m m ) max 0 (2.10) or the Probability Density Function (PDF): f M βe ( m) = 1 e β ( m m0 ) β ( mmax m0 ) (2.11) The comparison between the Truncated and the Bounded Gutenberg-Richter Recurrence relation can be seen in Figure 2.10 that follows. Figure 2.10: Comparison of Truncated and Bounded Gutenberg-Richter Recurrence Relation [Sabetta 2005, Lecture Notes, Pavia 2005] 15

30 Chapter 2: Methodology Apart from the Gutenberg-Richter recurrence models mentioned above, there are also a number of other recurrence laws that have been proposed. Available evidence is insufficient to determine whether the Gutenberg-Richter or some other recurrence law is correct. Evaluation of which model is most appropriate for a given source is hampered by the brevity of historical and/or instrumental records [Kramer S. L., 1996] Attenuation Relationships Strong-motion attenuation relations are empirical equations that can be used to estimate the values of strong-motion parameters as functions of independent parameters that characterise the earthquake and the site of interest. The name attenuation relationships arises from the fact that the equations describe the decay of the strong motion with distance from the source. A more suitable term would be Ground Motion Scaling Relationships or Ground Motion Prediction Equations. They probably represent the most used tool in Engineering Seismology and Earthquake Engineering for estimating the values of response spectral accelerations for future earthquake scenarios. Attenuation or Predictive Relations are nearly always obtained empirically by least-squares regression on a particular set of strong-motion parameter data. Despite attempts to remove questionable data and the use of quality-based weighting schemes, some amount of scatter in the data, resulting from randomness in the mechanism of rupture and from variability and heterogeneity of the source, travel path, and site conditions, is inevitable. This considerable random uncertainty must be accounted for in PSHA. Scatter in the data is usually quantified by the standard deviation σ of the attenuation relation [Kramer S. L., 1996]. Unfortunately the integrative nature of PSHA is such that only after one examines the results and carries out sensitivity studies, the effect of different ground motion models can be assessed. The probability that a particular ground motion parameter Y exceeds a certain value y* for an earthquake of a given magnitude m, occurring at a given distance r is illustrated graphically in Figure In probabilistic terms, it is given by: ( ) * * [ ] Y ( ) P Y > y m, r = 1 F y (2.12) where F Y y is the value of CDF of Y at m and r. The value of F Y y depends on the probability distribution used to represent Y. In general ground motion parameters are assumed to be log-normally distributed (the logarithm of the parameter is normally distributed). It has to be pointed out that the unbounded characteristics of that distribution can attribute a nonzero probability to unrealistic values of the ground motion parameter. ( ) 16

31 Chapter 2: Methodology Figure 2.11: Schematic illustration of conditional probability of exceeding a particular value of a ground motion parameter for a given magnitude and distance [Kramer S. L. 1996] It is common practice by now to use more than one attenuation relation in hazard studies. As different relations use different definitions both of the dependent variables (selection of a single value from the two horizontal components of motion) and of the independent variables (distance, magnitude, site conditions, and style-of-faulting), empirical conversions rules or adjustments are needed in order to achieve compatibility amongst the relations used. The main point to be kept in mind is that attenuation relationships are crude models that carry very large degrees of scatter. Accounting for this uncertainty in a rational and realistic way is one of the most difficult challenges in seismic hazard assessment. 2.4 Software Used Most of the programs for calculating seismic hazard probabilistically at a site are based on the methodology of Cornell [1968]. Some of the most widely used programs are EQRISK [McGuire, 1976], FRISK [McGuire, 1978], SEISRISK II and III [Bender and Perkins, 1982 and 1987], CRISIS [M. Ordaz et al., 2003] and others. In the present project CRISIS 2003 version.3 software has been used. Below, the main characteristics of this computer code used are presented. CRISIS is an open-source PSHA code that computes the hazard curve and the uniform hazard spectrum for a given site, and the predicted hazard map for a grid of sites [Ordaz et al., 2001]. Seismic sources geometries include point, fault (line), and extended (area) sources. The seismicity model can be poissonian or characteristic. The magnitude distribution included in CRISIS follows a bounded Gutenberg-Richter model, truncated at minimum and exponentially smoothed at maximum magnitudes [Ordaz, 2004]. Moreover, this program allows assigning different strong motion prediction models to different seismogenetic zones. In addition to the classical magnitude and distance formulation considered in PSHA studies described above, CRISIS integrates the distribution of two important input parameters: the slope of the Gutenberg-Richter relation used (b), and the maximum magnitude of each source (M max.) 17

32 Chapter 2: Methodology Recently, a new version of CRISIS 2003 was released, version 3. In this updated version, there are four ways of measuring the source-to-site distance which until now was only considered as focal. This is very useful, since different attenuation relations require distances other than focal. The four types of distances that are now available are: Focal, Epicentral, Joyner and Boore (closest distance to the projection of the fault plane on the Earth s surface) and Closest distance to rupture area. Increasingly, new attenuation laws present values of standard deviation that depend on magnitude. The new version of CRISIS 2003 has also this capability now. Figure 2.12: CRISIS user-friendly interface As input, the program will require: The coordinates of the site or of the grid of sites of interest for which the hazard will be computed, The coordinates of the quadrilateral which define the seismic zones, which will be affecting the sites of interest, Τhe parameter λ m of the Gutenberg-Richter recurrence relationship, which is the mean annual rate of exceedance for earthquakes with magnitude m, the parameter β where β = b ln10, the minimum magnitude M 0 observed and the maximum magnitude expected for each one of the seismic zones entering the analysis, M max 18

33 Chapter 2: Methodology The Attenuation relations in a tabular form which the ground motion is assumed to follow, The type and the number of values for which PSHA has to be computed, The desired return periods and finally, The parameters which control the spatial integration process (triangulation). CRISIS 2003 can generate several output files. The possible output files are: Result file: This file contains a printout of the name of the run, the values assigned to the variables, characteristics of the attenuation models, geometrical and seismicity description of the sources, the data defining the computation grid, etc. It also gives the final results, that is, exceedance rates for each site and type of ground motion (PGA or period of spectral ordinate). It also gives a summary of the computations for each site, indicating which sources are of interest for the site and which sources were skipped. The computer times are also written. Graphics file: This file contains a brief identification header, and the equivalent exceedance rates for the type and levels of ground motion requested. This file can be used as input file to plot ground motion versus equivalent exceedance rate curves. Map file: This file contains ground motion levels for fixed equivalent exceedance rates entered in the data file for each type of ground motion and site. It also gives the coordinates of each site. This file can be used to generate contour or 3D maps of ground motion levels associated to constant exceedance rates. FUE file: This file contains exceedance rates by source for each site. DES file: This file contains results of seismic hazard deaggregation, as a function of magnitude and distance. These disaggregated results indicate which combinations of magnitude and distance contribute more to the seismic hazard at a site, for a given ground motion. 2.5 Logic Trees and Treatment on Uncertainties in Probabilistic Seismic Hazard Assessment Handling uncertainties is a key element of PSHA. Distinction is made between two types of uncertainty in seismic hazard assessment, and these are given the adjectives aleatory and epistemic, terms used to replace and distinguish between the terms randomness and uncertainty, whose use has become ambiguous [Bommer et al. 2005]. Uncertainties that are related to an apparent randomness in nature, such as the scatter associated with empirical relationships, are referred to as aleatory variability. The aleatory variability is the uncertainty that reflects the variability of the outcome of a repeatable experiment. The aleatory variability is inherent in natural processes and cannot be reduced by additional data collection or better modeling. Uncertainties reflecting the incomplete knowledge of, say, seismicity, rupture characteristics and seismic energy excitation, are referred to as epistemic. 19

34 Chapter 2: Methodology The epistemic uncertainty is the uncertainty due to ignorance. It results from statistical or modeling variations and could, in concept, be reduced with additional data or better modeling. There are many epistemic uncertainties in any seismic hazard assessment, including the characteristics of the seismic source zones, the model for the recurrence relationship and the maximum earthquake magnitude [Bommer et al. 2005]. It is important to treat uncertainties in seismic hazard in a logical way so that the hazard results can be used appropriately. Probabilistic seismic hazard analyses have developed significantly in complexity over the years. Still, simpler approaches, including deterministic analyses, are called for at times. In neither case however, will there normally be room for any detailed sensitivity analysis of the different parts of the model, in order to diminish the effect of the variability. These uncertainties are treated differently. If the aleatory variability can be measured, it is then straightforward to incorporate this variability directly into the hazard calculations. The most important aleatory variability in SHA is that associated with ground-motion prediction equations, which is generally represented by the standard deviation of the logarithmic residuals of the predicted parameter. The seismic hazard analysis, integrates over the aleatory variability to calculate the seismic hazard curve. On the other hand, the epistemic variability is treated by multiple hypotheses and distributions of hazard curves. The epistemic variability is expressed as a confidence level for the hazard results. The established procedure in PSHA is to incorporate the epistemic uncertainty into the calculations through the use of logic trees. The logic tree is set up so that for each of the steps in which there is epistemic uncertainty, separate branches are added for each of the choices that the analyst considers feasible. To each of these a normalized weight is assigned that reflects the analyst s confidence, that is the most correct model, and the weights are generally, but not necessarily, centered on a best estimate. The hazard calculations are then performed following all the possible branches through the logic tree, each analysis producing a single hazard curve showing ground motion against annual frequency of exceedance [Bommer et al. 2005]. The weighting of each hazard curve is determined by multiplying the weights along all the component branches. The results allow the definition of a mean and a median hazard curve, as well as similar curves for different confidence intervals. For every branch added to a logic tree, a penalty is paid in terms of additional calculations; if there are multiple branches for each component of the hazard analysis, the total number of hazard calculations can rapidly become very large. For this reason it is advisable to avoid using branches with very small differences between the options that they carry, in cases when these options result in very similar nodes. 20

35 Chapter 2: Methodology Figure 2.13: Example of logic tree application to derive multiple hazard curves [McGuire R. K.]. As an example of a logic tree formulation, the left side of Figure 2.13 illustrates a simple logic tree involving uncertainties in geological interpretations, seismicity assumptions and ground motion models. Each uncertain model or parameter is represented by a node and branches emanating from each node represent discrete alternatives on that model or parameter value. In the example of Figure 2.14, each node has two branches, so there are eight branches, each representing a set of assumptions for which seismic hazard calculations can be made. Once the hazard calculations are completed for the assumptions represented by each end branch, the hazard curves can be plotted as illustrated on the left side of Figure These curves represent the uncertainty in seismic hazard as derived from uncertainties in the input [McGuire R. K.]. 21

36 Chapter 3: Data 3. DATA In Chapter 2, the Methodology that is going to be followed was described, along with the main data and parameters whose variation will be affecting the final results of this parametric study. In the current chapter, the possible choices of these parameters will be presented and analyzed. 3.1 Italian Seismic Source Zones To develop a PSHA, as has already been stated, seismic source zones are necessary. This sensitivity analysis is focusing its results on the Italian peninsula and therefore we will be examining the Italian seismic source zones. The first seismogenic zoning, referred to as ZS4 [Scandone, 1997; Meletti et al., 2000], has been implemented by Gruppo Nationale per la Difesa dai Terremoti (GNDT) special for hazard applications. It is based on a kinematic analysis of quaternary and Cenozoic geological elements and subdivides the Italian peninsula in 80 different Seismogenic zones. The next zonation, referred to as ZS9 [Stucchi et al., 2004], represents an updating of the previous zoning ZS4, based on the most recent knowledge of active tectonics. The number of zones is reduced to 35 from the previous 80 zones included in ZS4, often grouping together the previous zones and sometimes changing completely the geometries, as has happened for example in South-East Italy. This is the result of the most recent acknowledgements in terms of active tectonics and active faults in Italy. The geometry and location of the seismic zones depending if the seismic zonation adopted is ZS4 or ZS9, is shown in Figures 3.1 and 3.2 respectively. From the seismic zonation, the zones that will be affecting each one of the sites that will be selected are going to be defined. All the zones within a certain radius are adding hazard to the sites of interest. Of course, the main characteristics of the site will be those of the zone in which it is located. As a result, the seismic zonation adopted influences the final results since different seismicity data are inputted into the analysis. As we move away from the site, the contribution of the zones is diminishing (according to the attenuation relation adopted) and after a radius of approximately 100 kilometres it will have faded away. Of course, when hazard maps are produced, the whole zonation is inputted into the analysis. As one can therefore assume, the choice of the seismic zonation is crucial for the final outcome of a PSHA, since it is one of the main input needed. 22

37 Chapter 3: Data ZS N ZS N 931 Figure 3.1: Location and geometry of seismic zones for zonation ZS4 Figure 3.2: Location and geometry of seismic zones for zonation ZS9 3.2 Magnitude Scales and Italian Seismic Earthquake Catalogues In order to perform this sensitivity analysis and evaluate those parameters that are crucial for a PSHA, two earthquake catalogues have been used: NT4.1 and the newer catalogue CPTI04. An earthquake catalogue must give origin time, location (epicentral co-ordinates and focal depth) and Intensity/magnitude of the earthquakes that have occurred in or near to the region of interest. Italy has one of the most extended and complete historical catalogues. As we will see later on, the two earthquake catalogues that will be used, include different type of magnitude scales. Magnitude scales are used in order to measure the size of an earthquake. The possibility of obtaining an objective, quantitative measure of the size of an earthquake came about with the development of modern instrumentation for measuring ground motion during earthquakes. Seismic instruments allow an objective and quantitative measurement of earthquake size called earthquake magnitude to be made. The various magnitude scales that have been developed are instrumental scales which measure the amplitude of the ground motion recorded by a seismograph. The magnitude of any type of scale is proportional to the released energy during the rupture. There are several types of magnitudes. The first one to appear was the Local Magnitude M L, introduced by C. Richter in Even though M L has limited applications (calibrated specifically for California, based on a Wood-Anderson seismograph and does not distinguish between different types of waves) particularly for engineers is a very useful scale because it is correlated to short period waves and the extent of earthquake damage is closely related to M L. The magnitude of the earthquake in this case is given from the following expression: ( A) log( A ) M L = log 0 (3.1) 23

38 Chapter 3: Data where A 0 is the amplitude that an earthquake of magnitude zero (1mm amplitude at 100 kilometers distance) would produce at the same epicentral distance. The disadvantages (saturation) of M L can be overcome by the use of Teleseismic Magnitude Scales. One type of Teleseismic Magnitude Scales is based on surface waves and is called Surface Wave Magnitude M S. The surface wave magnitude is based on the maximum ground displacement and is calculated using Equation 3.2: o ( A/ T ) log( ) + 3. Ci M = + (3.2) S log 3 where A/T is the ratio of maximum amplitude and period calculated on surface waves, Q( o o, h) is the calibration factor depending on distance and depth h of the earthquake and a station coefficient which is determined empirically. C i As the total amount of energy released during an earthquake increases, however, the groundshaking characteristics do not necessarily increase at the same rate. For strong earthquakes, the measured ground-shaking characteristics become less sensitive to the size of the earthquake than for smaller earthquakes. This phenomenon is referred to as saturation. The Richter Local M L magnitude scale saturates at magnitudes of 6 to 7 and the Surface Wave magnitude at about M S =8. To describe the size of very large earthquakes, a magnitude scale that does not depend on ground-shaking levels, and consequently does not saturate, would be desirable. The only scale that is not subject to saturation is the Moment Magnitude M w [Kanamori, 1997; Hanks&Kanamori, 1979] since it is based on the Seismic Moment M o which is a direct measure of the factors that produce rupture along the fault. The Seismic Moment M o can be expressed using the following formula: M o = µ A U (3.3) where µ is the shear modulus of the material along the fault, A is the area of the fault rupture and U is the average amount of the slip of the fault. Using the Seismic Moment M o, the Moment Magnitude M w can be expressed using Equation 3.4: M w ( ) 73 2 log M = O (M O in dyne. cm) (3.4) The relationship between the Moment Magnitude and the various magnitude scales can be seen in Figure 3.3. Saturation of the instrumental scales is indicated by their flattening at higher magnitude values. As one can see from this figure, all magnitude scales, apart from M w, saturate for magnitudes grater than 7 approximately. 24

39 Chapter 3: Data Figure 3.3: Saturation of various magnitude scales: M w (Moment Magnitude), M L (Richter Local Magnitude), M S (Surface Wave Magnitude), m b (short-period Body Wave Magnitude), m B (long-period Body Wave Magnitude) and M JMA (Japanese Meteorological Agency Magnitude) [Idriss, 1985] A great effort for a revised and improved global (both historical and instrumental) catalogue for Italy has been made with the help of a well experienced team of historians for an accurate historical interpretation of the ancient descriptions by Camassi and Stucchi [1996], producing the NT4.1 catalogue. This catalogue has been expressly designed for Seismic Hazard Analyses (SHA) and contains 2,488 events, covering a period of time from 1005 until 1992 A.D. with an epicentral intensity greater or equal to V-VI MCS degree or a M S >4.0. It also includes two types of magnitude scales: M s (measured or derived from empirical regressions in terms of macroseismic Intensity) and M m (macroseismic magnitude derived from Intensity) and two types of Intensities: I χ max Intensity, and I o epicentral Intensity. All events have shallow focal depth (<30km). The epicentral parameters are computed to best reproduce all the site intensities observed during the earthquake. There is geographic correlation between this catalogue and the ZS4 Scandone zoning, so that nearly all events of the NT4.1 earthquake catalogue belong to a seismogenic zone. Updates of NT4.1 have been made in 1999 and 2004 leading to the CPTI and CPTI2 respectively (also called CPTI04 since it is a second version of CPTI, released in initials stand for: Parametric Catalogue of Italian Earthquakes). CPTI04 (or CPTI2) includes 2,550 earthquake events which have taken place from 216 B.C. until 2002 A.D. (although only twenty-four events have occurred before 1000 A.D.), with intensities greater or equal to V-VI MCS or a M S >

40 Chapter 3: Data Furthermore it includes three types of magnitude scales: M aw (measured Mw or derived from regressions by Ms), M As (averaged weighted Ms) and M Sp (equal to M L if <=5.5 and equal to Ms if >5.5) and two types of intensities (I mχ and I o ). In this catalogue, all the instrumental seismicities after 1980 have been carefully reassessed and are in correspondence with ZS9 seismic zoning. The selection of earthquake catalogue to be used will also affect the results of the SHA since the two catalogues contain different information for the earthquake events. This can be seen in the two figures that follow, where the difference between the two earthquake catalogues is evident. In Figures 3.4 and 3.5, the location of the main earthquake events (with magnitudes greater than 5.5 degrees) of the NT4.1 and CPTI04 catalogues are shown respectively. NT4.1 Ms= Ms= N CPTI04 Mas= Mas= N Figure 3.4: Location of earthquake events with M S magnitude greater than 5.50, of NT4.1 earthquake catalogue Figure 3.5: Location of earthquake events with M as magnitude greater than 5.50, of CPTI04 earthquake catalogue As one can see from the previous Figures, the two catalogues do not contain exactly the same strong earthquake events and in particular the magnitude values may differ. This is a result of the different processes used in the two catalogues for the data available, and may affect the results of a SHA. Also, in Figure 3.4 M S magnitude scale has been used, whereas in Figure 3.5, the magnitude scale used is M as. As we will see later on, those two scales are more or less equivalent and thus, the two maps are comparable. The magnitude scale is another one of the parameters which will be modified in order to investigate its effect on the PSHA. M S and M w magnitude scales are going to be used. The magnitude scale that is adopted depends on the magnitude scale used in the attenuation relation (see section 3.5). 26

41 Chapter 3: Data As two different magnitude scales will be used, a transformation between them is necessary in order to have comparable results. In this work, in order to transform M S into M w, we have adopted the transformation used from INGV while producing the new hazard map of Italy, shown in Figure 1.2 (see Chapter 1). This transformation is described by the following formulas: M w = M S ( M S < 6.0) M = ( 6.0) w M S M (3.5) S For the other way round conversion from M S to M w, the inverse equation of (3.5) is adopted: M = M M S w ( S < 6.0) M = ( 6.0) S M w M (3.6) S The influence of different magnitude scales adopted in a PSHA will also be examined in the Gutenberg-Richter Regression. Two cases will be studied, where different values of M as and M aw will be chosen from the CPTI04 earthquake catalogue. 3.3 Historical and Statistical Completeness As discussed in Chapter 2, the effect of the completeness time interval T c on the final results of PSHA is strongly dependent on the particular time-distribution of earthquakes for the considered seismic zone. The completeness considered in this sensitivity analysis are those referred to as historical and statistical in the INGV report [Stucchi et al., 2004] where the new hazard map for Italy was computed. In order to determine the historical completeness, specific historical and seismological information relative to 18 Italian localities has been collected and carefully analyzed. In particular, on the basis of an expert judgment, the temporal intervals have been evaluated, for which it is not reliable that effects of an earthquake of the selected intensity have not been reported in the available historical documentation. Afterwards the results have been extrapolated to the seismogenic zones of ZS9 and are reported in Table 3.1 On the other hand, in order to determine the statistical completeness, the methodology of Albarello et al. [2001], similar to the methods described in Chapter 2, has been adopted. Results are shown in table 3.2 where it is evident, comparing with table 3.1, that the statistical completeness is systematically lower (shorter temporal intervals) than the historical one. 27

42 Chapter 3: Data Table 3.1. Years of historical completeness for some of the ZS9 zones and different magnitude classes: class 1 M w =4.76; class 12 M w =7.29 [Stucchi et al. 2004] 28

43 Chapter 3: Data Table 3.2. Years of statistical completeness for some of the ZS9 zones and different magnitude classes: class 1 M w =4.76; class 12 M w =7.29 [Stucchi et al. 2004] 3.4 Maximum Magnitude As mentioned in section 2.4, one of the parameters that need to be inputted in CRISIS software in order to perform the seismic hazard calculations, is the maximum magnitude M max that is expected to occur within each seismic zone. The standard Gutenberg-Richter relation covers in theory an infinite range of magnitudes from 0 to but is generally used between a lower and upper bound (Truncated or Bounded Gutenberg-Richter recurrence relationship). The upper bound magnitude M max is the upper limit of earthquakes of all sizes that will enter the analysis for each source; its function is to truncate the recurrence relationship at the limit of the seismogenic potential of the seismic source. 29

44 Chapter 3: Data The recurrence relationship is effectively an extrapolation of observations of smaller earthquakes to predict the frequency of larger earthquakes; if it is not truncated at M max, then it can predict physically impossible earthquakes. For those faults for which paleoseismological studies have identified a characteristic earthquake, the value of M max is known with some confidence. In other cases, the value of M max is estimated by identifying the length of faults and then using empirical relationships to estimate the magnitude that would be associated with rupture along the entire length considered. The largest historical earthquake is almost always the lower limit for M max. In practice, M max is usually defined by adding an increment m to the largest known magnitude in the source. The value of m should reflect the length and completeness of the earthquake catalogue, the more reliable the seismic record being, the smaller its value. Here, m has been set equal to 0,2 units. In order to examine the effect M max on a SHA, two sets of maximum magnitudes are going to be used: The first set of maximum magnitudes results from the procedure used to define the Gutenberg-Richter recurrence relationship. As we have presented in section (see Chapter 2), Gutenberg & Richter found that there is a logarithmic relationship between the cumulative frequency and the magnitude, known as the magnitude-frequency or recurrence relationship, described by the equation: log λ = a b m (3.7) m For each one of the seismic zones, the rate of occurrence of earthquakes as a function of their magnitude has to be determined: for each magnitude range, the number of earthquakes has to be counted and occurrence rates have to be evaluated through the definition of completeness of the catalogue. The Gutenberg-Richter relation is then derived by means of a linear interpolation of real data. Table 3.3. Procedure followed for the computation of the Gutenberg-Richter relation Zone N Compl. Time f S f C Ms 927 Earthq. Period interval (N/year) cumulated log (f C ) M min 4.30 ± ± ± ± ± ± ± ± ± M max 7.00 ± ± ±

45 Chapter 3: Data For example, this procedure for a given zone would result to a table similar to Table 3.3. In this table, with red colour one can see the maximum magnitude as it results from the Gutenberg-Richter regression calculation. Through this procedure, the maximum magnitude that occurs within the zone, taking into consideration the completeness of the catalogue, is defined. Following this procedure for all the zones, we can evaluate the first set of maximum magnitudes to be used in this parametric study. The second set of maximum magnitudes will be taken from the INGV report, where the new seismic hazard map of Italy was created. In this report, two sets of maximum magnitudes have been developed. These sets of magnitudes have more or less the same values of maximum magnitude with those resulting from the procedure previously mentioned. Some values have been altered though. These set of maximum magnitudes can be seen in the eighth and ninth column of Table 3.4 and 3.5 that follow. In this table, column 3 represents the M max as it derives from the available geological information; columns 4 and 5 include the observed maximum magnitude from the CPTI04 catalogue and its corresponding class. In column 6 the application of the historical completeness intervals has been made, while columns 7 and 9 are the particular cases of class increase. Finally, columns 8 and 10 show the final values of M max, where in column 10 a conservative minimum value of 6.14 has been adopted except for the volcanic zones (922, 928, 936) [Stucchi et al. 2004]. The second set of maximum magnitudes that we have selected to use as input in our parametric study is shown in column 8. Table 3.4. Maximum values of magnitudes for the ZS9 as these have been reported in the INGV report (zones ) 31

46 Chapter 3: Data Table 3.5. Maximum values of magnitudes for the ZS9 as these have been reported in the INGV report (zones ) The SHA will be carried out for both sets of magnitudes and the results will be compared in order to investigate the effect of the maximum magnitude on the final outcome. Furthermore, another set of comparisons will be made. The maximum magnitudes, as they result from the Gutenberg-Richter regression relation calculations for all the seismic zones, will be increased by one, two and three classes, and the seismic hazard calculations will be carried out. Thereinafter, the results from the original maximum magnitudes calculations will be compared from the calculations that result from the increased maximum magnitudes by one, two and three classes, in order to investigate further the impact of maximum magnitude on seismic hazard calculations. 3.5 Attenuation Relation In this study, Sabetta&Pugliese 1996, Ambraseys et al and Ambraseys et al are the attenuations that will be used. As we mentioned previously, the attenuation relationships will also define the magnitude scales that will be used. Ambraseys et al uses M S as a magnitude scale, Ambraseys et al uses M w and Sabetta&Pugliese 1996 uses a double scale: M S for M>5.5 and M L for M<5.5. This adoption was made since at the time the attenuation was formulated, M w was not available for all earthquake events. This double scale fits rather well to M w scale, as it can be seen from Figure 3.3 and thus it was adopted. As different relations use different definitions both of the dependent variables (selection of a single value from the two horizontal components of motion) and of the independent variables (distance, magnitude, site conditions, and style-of-faulting), empirical conversions rules or adjustments are needed in order to achieve compatibility amongst the relations if the choices of dependent and independent variables differ between the attenuations. The main characteristics of the three attenuation relations that will be used have been tabulated in Table

47 Chapter 3: Data Table 3.6. Main characteristics of the Attenuations used Attenuation Relation Ambraseys et al. EESD (1996) Sabetta & Pugliese BSSA (1996) Ambraseys et al. BEE (2004b) Distance range type km R jb (M S >6) R epi (M S 6) Magnitude range type M S km M R S (>5.5) jb M L ( 5.5) km R jb (M S >6) R epi (M S 6) M w Rock definition V S > 750 m/s V S > 800 m/s V S > 750 m/s Style of faulting strike-slip 18% normal 33% reverse 49% strike-slip 7% normal 49% reverse 44% strike-slip, normal thrust, odd (scale factor included) Horizontal component larger envelope larger PGA larger envelope Frequency range Hz Hz Hz The Ambraseys et al.1996 attenuation has resulted after processing 422 records which have taken place in Europe and Middle East, the Sabetta&Pugliese has been generated using 95 records which have occurred in Italy and finally, Ambraseys et al.2004 from the elaboration of 595 records occurring in Europe and Middle East. All three attenuations use data coming from different styles of faulting but Ambraseys et al.2004 includes specifically a coefficient to take into account this effect. As far as the choices of dependent and independent variables are concerned, one can see that: Source-to-site Distance Type: Ambraseys et al and Ambraseys et al use R jb for M S >6 and R epi for M S 6. Sabetta&Pugliese uses R jb for all magnitude ranges. R jb is a distance definition that has become widely used in attenuation relationships and is the shortest horizontal distance to the surface projection of the fault rupture. It has been named R jb after Joyner&Boore [1981], which was the first study to employ this definition of source-site distance. R epi is the epicentral distance from the site to the source, one of the easiest distances to determine after an earthquake. For large magnitude earthquakes though, when the length of the fault rupture is a significant fraction of the distance between the fault ant the site, the epicentral distance may not accurately represent the effective distance. This is why, for M S >6, Ambraseys et al and Ambraseys et al use R jb instead. Still, in PSHA studies, where the earthquake catalogues that are used refer to the epicentres of the occurring earthquakes, the use of R epi would seem more correct. In fact, in previous studies [Albarello Maps, 2000] Sabetta&Pugliese attenuation relation has been used with R epi. Still, in this study, R jb has been used for reasons of simplicity and therefore no conversion for the source-to-site distance is needed between these attenuation relations. Magnitude Type: As Table 3.6 states, Ambraseys et al uses M S as a magnitude scale, Ambraseys et al uses M w and Sabetta&Pugliese 1996 uses a double scale (M S for M>5.5 and M L for M<5.5). Several empirical conversions rules are available in literature to convert among different magnitude scales. The one that will be used here is the one described by Equations 3.5 and

48 Chapter 3: Data Style of faulting: Most attenuation relations are based on data coming from mixed seismotectonic regimes. After choosing the style-of-faulting classification scheme, it is therefore necessary to evaluate the different proportions of normal, strike-slip, and reverse faulting earthquakes included in the relations in order to apply any adjustment. In our case the selected attenuation relations include different styles of faulting in similar proportions. No adjustments were made, since it was deemed not to be the subject of this thesis and furthermore the modifications would result in small changes of the results (less than 5%). Horizontal component: Most attenuations use the geometric mean, or both, or a random selection of the two horizontal components; in this case there is almost no difference. Some attenuations use the larger of the two horizontal components; the difference with respect to the previous case could be as high as 25%. However, since all the selected attenuations use the larger component, even if defined in a slightly different way, there is no need of further adjustment. In order to see how the selected attenuations behave, some diagrams have been plotted. Figures 3.6 to 3.9 show the attenuation of PGA and PSA at T S = 2 sec with respect to distance while Figures 3.10 to 3.13 compare the response spectra that result from the three relationships for a number of magnitude and distance combinations. ACCELERATION (g ATTENUATION OF PGA WITH DISTANCE (M=7) Sabetta&Pugliese 1996 Sabetta&Pugliese σ Sabetta&Pugliese σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ ACCELERATION (g ATTENUATION OF PSA (T=2sec) WITH DISTANCE (M=7) Sabetta&Pugliese 1996 Sabetta&Pugliese σ Sabetta&Pugliese σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ DISTANCE (km) Figure 3.6: Attenuation of PGA (T S =0sec) with distance, for the three relations, ±σ and for magnitude= DISTANCE (km) Figure 3.7: Attenuation of PSA (T S =2sec) with distance, for the three relations, ±σ and for magnitude=7 ACCELERATION (g) ATTENUATION OF PGA WITH DISTANCE (M=5) Sabetta&Pugliese 1996 Sabetta&Pugliese σ Sabetta&Pugliese σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ ACCELERATION (g ATTENUATION OF PSA (T=2sec) WITH DISTANCE (M=5) Sabetta&Pugliese 1996 Sabetta&Pugliese σ Sabetta&Pugliese σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ Ambraseys et al Ambraseys et al σ Ambraseys et al σ DISTANCE (km) Figure 3.8: Attenuation of PGA (T S =0sec) with distance, for the three relations, ±σ and for magnitude= DISTANCE (km) Figure 3.9: Attenuation of PSA (T S =2sec) with distance, for the three relations, ±σ and for magnitude=5 34

49 Chapter 3: Data ACCELERATION (g COMPARISON OF RESPONSE SPECTRA (5% DAMPING, Mw=5.0 AND D=3km) PERIOD (sec) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al ACCELERATION (g COMPARISON OF RESPONSE SPECTRA (5% DAMPING, Mw=7.0 AND D=3km) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al PERIOD (sec) Figure 3.10: Response spectra for the three Figure 3.11: Response spectra for the three attenuation relations, for 5% attenuation relations, for 5% damping, M w =5.0 and D=3km damping, M w =7.0 and D=3km ACCELERATION (g COMPARISON OF RESPONSE SPECTRA (5% DAMPING, Mw=5.0 AND D=85km) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al ACCELERATION (g COMPARISON OF RESPONSE SPECTRA (5% DAMPING, Mw=7.0 AND D=85km) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al PERIOD (sec) PERIOD (sec) Figure 3.12: Response spectra for the three Figure 3.13: Response spectra for the three attenuation relations, for 5% attenuation relations, for 5% damping, M w =5.0 and D=85km damping, M w =7.0 and D=85km As one can observe from the previous diagrams, the selected attenuations show different behaviour for different magnitudes, distances and spectral periods. The effects of each attenuation relation on the PSHA will be analytically examined on the following chapters of this thesis. What is interesting for one to notice is the completely different behaviour of the Ambraseys 2004 attenuation relation when subjected to different magnitudes, high or low. In case of M=5 for PGA and for short distances, Ambraseys 2004 lays above the other two attenuation relations and exhibits much higher acceleration values. On the contrary, for M=7 and for PGA the attenuation that results to the higher acceleration values is the Sabetta&Pugliese one. This phenomenon takes place due to the M dependent factor that Ambraseys 2004 includes in the distance attenuation which gives very high values of PGA for small magnitudes at short distances but decreases very rapidly and becomes very small at large distances. A very important feature of the attenuation relations is the aleatory uncertainty expressed by their standard deviation σ. The effect of aleatory uncertainty (standard deviation of each model) becomes very relevant if compared to the epistemic one (median values of different relations) in hazard studies performed for very long return periods. 35

50 Chapter 3: Data Only Ambraseys et al provides a magnitude dependent sigma, confirming that ground motions from small earthquakes are more variable than those from large. The variation of σ with magnitude and period of the three selected attenuation relations can be seen in the following figures. ST AND ARD DEVIATI ON σ COMPARISON OF σ (Mw =5.0) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al STANDARD DEVIATION σ COMPARISON OF σ (Mw =7.5) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al PERIOD (sec) PERIOD (sec) Figure 3.14: Variation of σ with respect to Figure 3.15: Variation of σ with respect to period for the three attenuation period for the three attenuation relations and for M w =5.0 relations and for M w =7.5 STAN DARD DE VI ATION σ COMPARISON OF σ (PGA T=0sec) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al STANDARD DEVIATION σ COMPARISON OF σ (PSA T=0.5sec) Sabetta&Pugliese 1996 Ambraseys et al Ambraseys et al Mw Figure 3.16: Variation of σ with respect to magnitude for the three attenuation relations and for T=0sec Mw Figure 3.17: Variation of σ with respect to magnitude for the three attenuation relations and for T=0.5sec As it can be seen from the figures above, and in particular from Figure 3.14, for M=5 the sigma of the Ambraseys 2004 attenuation even though varies, is much higher than the respective values of sigma for the other two attenuation relations, until one second spectral period. 3.6 Site Selection In order to perform the sensitivity analysis and evaluate those parameters that have a decisive meaning for a PSHA it is appropriate to select a limited number of sites to be inspected carefully. For the selected sites, hazard curves and uniform hazard spectra will be generated for all the different choices of the parameters presented in this chapter. Thereinafter the curves and spectra will be compared. The six sites that have been selected are: Venzone, Pavia, Nocera Umbra, Roma, Benevento and Vibo Valentia. 36

51 Chapter 3: Data The sites were selected in such a way so that they could be well spread among the Italian peninsula, in order to cover the greater part of it. It was also important that the selected sites would exhibit different levels of seismicity, in order to explore a wider range of seismic activity. Thus, we have very low levels of seismicity near Pavia, intermediate values near Rome, high around the areas of Venzone, Nocera Umbra and Benevento and very high seismicity levels in the vicinity of Vibo Valentia. The location of the six selected sites can be seen on the following map. VENZONE PAVIA N NOCERA UMBRA ROMA BENEVENTO VIBO VALENTIA Sites Figure Location of the six selected sites 37

52 Chapter 3: Data VENZONE VENZONE PAVIA %a %a N PAVIA %a %a N NOCERA UMBRA NOCERA UMBRA %a %a ROMA %a BENEVENTO ROMA %a BENEVENTO %a %a %a Sites INGV MAP VIBO VALENTIA %a %a Sites DPC MAP VIBO VALENTIA %a Figure 3.19: INGV Hazard Map-Values of PGA Figure 3.20: SSN-GNDT Hazard Map-Values of PGA (g) with a probability of exceedance (g) with a probability of exceedance 10% 10% in 50 years (T R = 475 years) in 50 years (T R = 475 years) The PSHA maps of Figures 3.19 and 3.20, already shown in chapter 1, along with the following table, verify the variety of seismic levels that the selected sites exhibit. The values of peak ground acceleration that correspond to the location of the sites for both maps are: Table 3.7. PGA values for the six sites with the SSN-GNDT and the INGV Hazard Map SITE PGA Values from SSN-GNDT Map PGA Values from INGV Map Venzone (0.274) (0.257) Pavia (0.073) (0.070) Nocera Umbra (0.235) (0.234) Roma (0.151) (0.121) Benevento (0.287) (0.255) Vibo Valentia (0.381) (0.266) As it can be seen both from the table and the hazard maps, the values of PGA are quite lower in the map realized by INGV. In the production of the hazard maps, SSN-GNDT used the NT4.1 earthquake catalogue, while INGV used the newer CPTI04 (see paragraph 3.2). Another element of the selected sites is that in the vicinity of some of the sites, strong earthquakes have occurred. This can be observed from Figures 3.4 and 3.5 (paragraph 3.2), where the locations of earthquake events with magnitudes greater than 5.5 were plotted for both earthquake catalogues, NT4.1 and CPTI04 respectively. This is so, especially in the case of Vibo Valentia and somewhat less for Benevento, Nocera Umbra and Venzone. 38

53 Chapter 3: Data In Figures 3.21 and 3.22 the selected sites have been plotted on the Italian map along with the two seismic zonations. In Figure 3.21 zonation ZS4 has been plotted while Figure 3.22 shows zonation ZS9. Table 3.8 shows the zones in which the selected sites are located according to both seismic zonations VENZONE PAVIA NOCERA 32 46UMBRA ROMA BENEVENTO Sites ZS N VIBO VALENTIA VENZONE PAVI907 A NOCERA UMBRA ROMA BENEV924 ENTO Sites ZS VIBO VALENTIA 929 N 931 Figure 3.21: Location of sites and seismic zonation ZS4 Figure 3.22: Location of sites and seismic zonation ZS9 Table 3.8. Zones in which the selected sites fall for both seismic zonations SITE Site Zone According to ZS4 Site Zone According to ZS9 Venzone Pavia - - Nocera Umbra Roma 42 - Benevento Vibo Valentia The sites that were selected as a base for this parametric study, follow the rational mentioned above, that is adequately spreading among Italy and variety of PGA values according to Italian hazard maps. Pavia was chosen as a site outside any seismic zone. Finally, Rome which for zonation ZS9 is located somewhat outside of zone 922, was selected as the biggest Italy s city in terms of population, something that renders it with great importance. As it has been mentioned earlier, the zones that will be affecting each one of the sites will be defined, as the zones within a radius of 100 kilometers around the site of interest. In the two following figures, Figure 3.23 and Figure 3.24, all the zones that will be taken into consideration are shown for both zonations ZS4 and ZS9. 39

54 Chapter 3: Data VENZONE PAVIA NOCERA 32 46UMBRA ROMA BENEVENTO Sites ZS N VIBO VALENTIA VENZONE PAVI907 A NOCERA UMBRA ROMA BENEV924 ENTO Sites ZS VIBO VALENTIA 929 N 931 Figure 3.23: Identification of zones of interest for seismic zonation ZS4 Figure 3.24: Identification of zones of interest for seismic zonation ZS9 From the figures above, we can define the zones whose characteristics are necessary as input for the production of hazard curves and hazard spectra for the selected sites. The zones that will be used for each site are shown in the following table: Table 3.9. Zones within the radius of 100 km for each site and for both zonations SITE Zones According to ZS4 Zones According to ZS9 Venzone 2, 3, 4, 5, 6 904, 905, 906 Pavia 8, 9, 10, 16, 25, 26, 27, 28, 29, , 907, , 915, 916 Nocera Umbra Roma Benevento Vibo Valentia 31, 32, 36, 37, 40, 41, 42, 44, 45, 46, 47, 48, 50, 52, 53, 53 41, 42, 43, 44, 45, 47, 49, 50, 51, 52 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 64, 65, 66, 67, 68, 69, 70, 71, 72, , 915, 916, 917, 918, 919, 920, 921, , 920, 921, 922, , 923, 924, 925, 926, 927, , 930, 932 In the two following chapters, the sensitivity analysis will be carried out and the results from the hazard analyses will be presented. The methodology developed in Chapter 2 will be followed using the data mentioned in the current chapter. The parameters on which all the analyses will be based are: Earthquake catalogue: CPTI04, Earthquake catalogue completeness: Historical, 40

55 Chapter 3: Data Seismic zonation: ZS9, Attenuation relationship: Sabetta&Pugliese 1996, Magnitude scale: M S. It should be noted that all the hazard maps have been calculated for rock-stiff soil conditions. All the analyses will be conducted using these data as a base, with only one parameter changing each time. For example, two hazard curves will be compared where all the parameters remain the same except from the earthquake catalogue, being once the CPTI04 and the next time the NT4.1. The results will be presented into two chapters, one containing uniform hazard curves for some of the selected sites and the other hazard maps for the whole Italian peninsula. 41

56 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra 4. SENSITIVITY ANALYSIS ON HAZARD CURVES AND UNIFORM HAZARD SPECTRA In the previous Chapter all the data that will be use were analytically presented. In this Chapter, using these data, the results from the sensitivity analysis will be introduced for the hazard curves and the uniform hazard spectra for some of the selected sites. In each of the following paragraphs, a comparison is made between two hazard curves and two uniform hazard spectra, the difference of which is produced from the use of the different option of the parameter appearing in the title, while all other input remain the same. 4.1 Seismic Zonation In this paragraph, the results of the hazard analysis will be presented in terms of hazard curves and uniform hazard spectra, when the zonation is either the old ZS4 or the newer ZS9, as these were presented in the previous Chapter. The rest of the required parameters for the hazard analysis will be those apposed in the last part of paragraph 3.6 (see Chapter 3, page 36). In Figures 4.1 and 4.2, the comparison of two hazard curves is made for sites Benevento and Vibo Valentia and for two spectral periods T S =0and T S =2sec, while in Figures 4.3 and 4.4 the comparison of the uniform hazard spectra is shown for the respective selected sites, for two return periods T R =475 and T R =10.000years. ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE ZS4-CPTI04 - T=0sec ZS9-CPTI04 - T=0sec ZS4-CPTI04 - T=2sec ZS9-CPTI04 - T=2sec ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE ZS4-CPTI04 - Ts=0sec ZS9-CPTI04 - Ts=0sec ZS4-CPTI04 - Ts=2sec ZS9-CPTI04 - Ts=2sec 1.0E ACCELERATION (g) Figure 4.1: Hazard curves for Benevento for two spectral periods and for zonations ZS4 and ZS9 1.0E ACCELERATION (g) Figure 4.2: Hazard curves for Vibo Valentia for two spectral periods for zonations ZS4 and ZS9 42

57 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ACCELERATION (g UNIFORM HAZARD SPECTRUM ZS4-CPTI04 - Tr=10,000 years ZS9-CPTI04 - Tr=10,000 years ZS4-CPTI04 - Tr=475 years ZS9-CPTI04 - Tr=475 years ACCELERATION (g UNIFORM HAZARD SPECTRUM ZS4-CPTI04 - Tr=10,000 years ZS9-CPTI04 - Tr=10,000 years ZS4-CPTI04 - Tr=475 years ZS9-CPTI04 - Tr=475 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.3: Hazard spectra for Benevento for two return periods and for zonations ZS4 and ZS9 Figure 4.4: Hazard spectra for Vibo Valentia for two return periods for zonations ZS4 and ZS9 It is obvious from the above figures, even though the size of the figures does not help, that the choice of the older zonation ZS4 instead of the newer ZS9 leads to significantly higher values of acceleration (for the same period) as far as the spectra are concerned and to notably higher frequencies of exceedance (for the same acceleration) as far as the hazard curves are concerned. The choice of the zonation has the same effect on both of these sites as well as on all the rest of the selected sites, whose results are not presented in this paragraph. Regardless of the seismicity of the site, as this was described in the current Italian hazard maps (see Figures 3.19 and 3.20 in Chapter 3), and regardless of the return period, if zonation ZS4 is used, the increase of acceleration seen in the hazard spectra and the equivalent increase in the frequency of exceedance is particularly significant. To be more specific, if we compare the maximum values of each hazard spectrum, we will see that between the two spectra with return period 10,000 years, an increase of approximately 9% has occurred, and for return period 475 years, the increase arises up to 19%! These values refer to Benevento but the same pattern is shown at Vibo Valentia site (20% for T r =10,000 years and 26% for T r =475 years). Of course, the increase of the values of the hazard spectra is not uniform; still the amplification of one of the hazard values is characteristic for the whole spectrum. As far as the hazard curves are concerned, a way to quantify the increase from the use of ZS4 zonation instead of the use of ZS9 could be the selection of one particular ground acceleration and the investigation of the increase of the probability of exceedance for this exact acceleration. The accelerations at which the program calculates the frequencies of exceedance are not always the same. Thus we have to find an acceleration, that is common between the different analyses and compare their respective frequencies of exceedance. In order for this to become clearer, we present the values from two of the hazard curves that have been calculated in this study. From these tables, it is evident that only at one level of acceleration the two curves can be compared with one another (2.19x10-2 g). 43

58 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Table 4.1. Values of hazard curves using zonation ZS4 and ZS9 (T=0sec) in Nocera Umbra Acceleration (g) Frequency of Exccedance Return Period 1.53E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+04 Acceleration (g) Frequency of Exccedance Return Period 2.19E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+05 The comparison of two particular frequencies of exceedance that refer to the same level of acceleration which is equal to 7.14x10-2 g for the hazard curves of Figure 4.1 shows an augment of the frequency of exceedance by 44% ( due to the use of zonation ZS4 instead from ZS9 in Benevento (29% for Vibo Valentia). If we compared another set of frequencies of exceedance the result would be different. Still, this value is more or less an average value of increase for the whole hazard curve. This amplification is quite high. Thus, the choice between the two available zonations could lead to completely different outcomes, as we have seen both from the hazard curves and the hazard spectra. This average value though, is in any case much higher than the respective levels of increase that was introduced at the hazard spectra and was cited in the previous page. As we will also see later on, the effect of all the different parameters that will be used in this study is much higher on the hazard curves than it is on the hazard spectra. In the figures that follow, the two selected sites and the seismic zones around them with the two different zonations have been represented. In Figure 4.5 Benevento is shown with zones 59, 62, 63 and 64 from zonation ZS4 around it. In Figure 4.6, the same site is shown but now the new zonation ZS9 has been selected. We can see that the previous four zones have been merged into one, wholly or in part. The same happens for Vibo Valentia, which can be seen in Figures 4.7 and 4.8. The zones 65, 66, 68, 69, 70 and 71 from the old zonation ZS4 have givven their place to just one zone with the number 927 at the newer zoning system ZS9. The results that have been previously presented are due to the fact that in PSHA calculations the spatial integration and therefore the seismic zone dimensions play a very important role. If one looks at Figures 4.5 to 4.8, it is easy to see that zonation ZS9 uses much larger seismic zones than zonation ZS4 does. This has as an effect the decrease of the seismic rate per square kilometre! Therefore, the introduction of the new and larger seismic zones introduced by ZS9, led to zones with lower seismicity levels. 44

59 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra N N BENEVENTO BENEVENTO Sites ZS4 Sites ZS9 Figure 4.5: Seismic zones around Benevento with zonation ZS4 Figure 4.6: Seismic zones around Benevento with zonation ZS9 N N VIBO VALENTIA Sites ZS VIBO VALENTIA Sites ZS9 929 Figure 4.7: Seismic zones around Vibo Valentia with zonations ZS4 Figure 4.8: Seismic zones around Vibo Valentia with zonations ZS9 On the other hand though, if one compares the Gutenberg-Richter regressions that result from the use of ZS4 seismic zonation and CPTI04 seismic catalogue for zones 59, 62, 63 and 64 to the Gutenberg-Richter regression that results from the use of ZS9 zoning system and CPTI04 earthquake catalogue for zone 927, will see that the Gutenberg-Richter regression for whose computation ZS9 has been used lies above all of the regressions which have been computed using zonation ZS4, which means a higher value of a and a lower value of b. 45

60 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra As it has been mentioned in Chapter 2 though, parameters a and b are representative of the seismicity of an area. Thus, a higher value of a and a lower value of b, would theoretically result to higher seismic computations, whereas we see that the use of ZS9 instead of ZS4 has had the opposite effect. What is actually happening is that the importance of the Gutenberg- Richter regression is less than the importance of the spatial integration for the PSHA calculations and therefore overtaken by the latter. 4.2 Seismic Catalogue After changing the seismic zonation we will explore the effect of the seismic catalogue in the hazard calculations. All the parameters will be the same between the two compared curves except from the catalogue, which will once be the NT4 and the other time the CPTI04. As it can be seen from Figures 4.9 and 4.10, where the hazard curves for Benevento and Vibo Valentia are respectively shown, the use of NT4 seismic catalogue will increase the annual frequency of exceedance of a particular value of acceleration in comparison to the frequency of exceedance that would result from the use of the CPTI04 seismic catalogue for the same value of acceleration. ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE NT4-ZS9 - T=0sec CPTI04-ZS9 - T=0sec NT4-ZS9 - T=2sec CPTI04-ZS9 - T=2sec ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE NT4-ZS9 - Ts=0sec CPTI04-ZS9 - Ts=0sec NT4-ZS9 - Ts=2sec CPTI04-ZS9 - Ts=2sec 1.0E ACCELERATION (g) Figure 4.9: Hazard curves for Benevento for two spectral periods and for catalogues NT4 and CPTI04 1.0E ACCELERATION (g) Figure 4.10: Hazard curves for Vibo Valentia for two spectral periods for catalogues NT4 and CPTI04 If we follow the procedure described in the previous paragraph, and compare the exceedance frequencies for Benevento and for structural period equal to zero seconds, the calculation will show a decrease of the frequency of exceedance by -26.8% (for acceleration equal to 7.14x10-2 g) when NT4 earthquake catalogue is used instead of the CPTI04 for Benevento but an increase by 4.8% (for acceleration equal to 8.15x10-2 g) for Vibo Valentia. Consequently, the effect of the earthquake catalogue is not the same on all of the sites. This will become clearer when the hazard maps will be presented in the next chapter. 46

61 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ACCELERATION (g UNIFORM HAZARD SPECTRUM NT4-ZS9 - Tr=10,000 years CPTI04-ZS9 - Tr=10,000 years NT4-ZS9 - Tr=475 years CPTI04-ZS9 - Tr=475 years ACCELERATION (g UNIFORM HAZARD SPECTRUM NT4-ZS9 - Tr=10,000 years CPTI04-ZS9 - Tr=10,000 years NT4-ZS9 - Tr=475 years CPTI04-ZS9 - Tr=475 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.11: Hazard spectra for Benevento for two return periods and for catalogues NT4 and CPTI04 Figure 4.12: Hazard spectra for Vibo Valentia for two return periods and for catalogues NT4 and CPTI04 In Figures 4.11 and 4.12, the uniform hazard spectra for Benevento and Vibo Valentia are presented respectively. The different choice of seismic catalogue, either NT4 or CPTI04, affects the spectra in the same way it previously affected the hazard curves. The result is that the choice of CPTI04 catalogue instead of NT4 lowers the seismicity of the selected sites in terms of ground acceleration only for one of the two sites. If we compare again the maximum values of the hazard spectra, the decrease that results from the use of NT4 catalogue is equal to 6.4% for T r =10,000 and 13.2% for T r =475 for Benevento. On the other hand, the increase for Vibo Valentia is equal to 8.9% for T r =10,000 and 7.7% for T r =475 years. 0.0 GUTENBERG-RICHTER REGRESSIONS COMPARISON log fc -1.5 y = x y = x CPTI NT4 Figure 4.13: Gutenberg-Richter regression relations for Benevento with both old and new catalogue 47

62 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra 0.0 GUTENBERG-RICHTER REGRESSIONS COMPARISON log fc -1.5 y = x y = x CPTI NT4 Figure 4.14: Gutenberg-Richter regression relations for Vibo Valentia with both old and new catalogue The two diagrams above present the Gutenberg-Richter relations for Benevento (Figure 4.13) and Vibo Valentia respectively (Figure 4.14), which have been carved using both earthquake catalogues, NT4 and CPTI04. When the old catalogue is being used, the Gutenberg-Richter that results may have a smaller a value but has a larger b value (smaller by absolute value). The parameter a represents the seismic activity and as its value increases so does the seismicity of the region, while as the b value increases, the number of larger magnitude earthquakes also increases compared to those of smaller magnitude. The fact that not both of the Gutenberg-Richter parameters are influenced in such a way to provoke an increase to the seismic hazard calculations, has as a result that only in some of the selected sites, the seismicity is increased form the use of the CPTI04 Earthquake Catalogue while in others the seismicity is decreased. 4.3 Catalogue Completeness The next comparison will involve two different methodologies to assess the completeness of the seismic catalogue CPTI04. The two different methodologies that we will consider are those referring to the historical and the statistical evaluation of completeness, as these were presented in paragraph 3 of the previous chapter. Looking at the hazard curves shown in Figures 4.15 and 4.16, where we alternate between the two completenesses, the small influence of the change of this parameter on the hazard curves is evident. The two curves that are compared almost coincide with one another for both completenesses, both structural periods and both sites. The sites, on which the hazard calculations were done upon, are Pavia and Vibo Valentia. The two selected sites, experience completely different levels of seismicity, according to recent hazard maps. Pavia is on the lower scale of seismicity, while Vibo Valentia on the higher one. 48

63 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra From these analyses and from all the others that were conducted but not presented here, we can conclude that for low seismicity areas such as Pavia, the curve that results from the use of the statistical completeness is above the respective one that results from the use of historical completeness. The opposite happens on high seismicity areas, such as Vibo Valentia. ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE Historical - Ts=0sec (PGA) Statistical - Ts=0sec (PGA) Historical - Ts=4sec Statistical - Ts=4sec ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E-04 HAZARD CURVE Historical - Ts=0sec (PGA) Statistical - Ts=0sec (PGA) Historical - Ts=4sec Statistical - Ts=4sec 1.0E ACCELERATION (g) Figure 4.15: Hazard curves for Pavia for two spectral periods and for completenesses historical and statistical 1.0E ACCELERATION (g) Figure 4.16: Hazard curves for Vibo Valentia for two spectral periods and for completenesses historical and statistical If we compare one of the arithmetical values of the hazard curves of the above figures, we will see that the use of the statistical completeness causes an increase of the probability of exceedance of the respective acceleration level by 17% (for acceleration equal to 3.06x10-2 g) in the case of Pavia (for T S =0sec) but a decrease of 14% in the case of Vibo Valentia (again for acceleration equal to 3.06x10-2 g). In comparison to the levels of 44% that occurred from the use of ZS4 instead of ZS9, we can say that the effect of completeness is rather small. These results confirm the fact that the completeness period, as well as the seismic catalogue, does not always act in the same direction, as zonation does. On the two following figures, 4.17 and 4.18, the hazard spectra that result from the use of the two different completeness periods are illustrated. When the parameter to be modified is the completeness period, either statistical or historical, the influence on the uniform hazard spectra curves is small. The two curves in most of the cases that we have explored have very small differences, for both return periods and for both sites. As it also happened in the case of the hazard curves (Figure 4.15 and 4.16), for low seismicity areas such as Pavia, the spectrum that resulted from the analyses using the statistical completeness is above the spectrum that results from the use of historical completeness. The opposite happens on high seismicity areas, such as Vibo Valentia. In particular, the numerical comparison of the maximum values between the respective hazard spectra will show an increase by 7% for Pavia and a decrease by 6% for Vibo Valentia when statistical completeness is being considered instead of the historical one. 49

64 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ACCELERATION (g UNIFORM HAZARD SPECTRUM Historical - Tr=10,000 years Statistical - Tr=10,000 years Historical - Tr=475 years Statistical - Tr=475 years ACCELERATION (g UNIFORM HAZARD SPECTRUM Historical - Tr=10,000 years Statistical - Tr=10,000 years Historical - Tr=475 years Statistical - Tr=475 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.17: Hazard spectra for Pavia for two return periods and for completenesses historical and statistical Figure 4.18: Hazard spectra for Vibo Valentia for two return periods and for completenesses historical and statistical The reason of the small influence of the completeness parameter can be easily comprehended with the help of the next table. Since the period of time for which the catalogue is considered to be historical complete is longer that the period of statistical completeness, the number of total events taken into account if we consider the historical completeness is also larger. Therefore, as it can be seen from the Table 4.2 (in this table the number of events is the total number of events that occur within the zone and the completeness is given for the smallest earthquake event), the number of events/year is more or less similar. Zone Table 4.2. Ratios of events over completeness, for both historical and statistical completeness Total number of events historical completeness Historical completeness of smallest event N events/ year Total number of events for statistical completeness Statistical completeness of smallest event N events/ year In the two diagrams that follow, the Gutenberg-Richter realations have been plotted for Pavia (Figure 4.19) and Vibo Valentia (Figure 4.20) and for both completenesses, historical and statistical. As we have already seen in the hazard curves and the hazard spectra of Figures 4.15 to 4.18, the effects from the use of either historical or statistical completeness are not standard. This is because the differences in b and f c values do not follow a standard pattern. In Figures 4.19 and 4.20 one can see that both statistical and historical completenesses can cause an increase to the a value and a decrease to the b value, but without them being severe. Also, from a number of other analyses that have been conducted but not presented here, it can be concluded that the effect of the completeness period on the seismic hazard calculations is rather small, if compared to the effect the selection of seismic zonation has. 50

65 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra 0.0 GUTENBERG-RICHTER REGRESSIONS COMPARISON log fc -1.5 y = x y = x Historical Completeness Statistical Completeness Figure 4.19: Gutenberg-Richter relations for Pavia with both completenesses 0.0 GUTENBERG-RICHTER REGRESSIONS COMPARISON -0.5 log fc y = x y = x Historical Completeness Statistical Completeness Figure 4.20: Gutenberg-Richter relations for Vibo Valentia with both completenesses 4.4 Magnitude Scale The next parameter that is going to be modified in order to investigate its effect on the seismic hazard calculations is the magnitude scale. For all the analyses that have been carried out so far, M SP magnitude scale of the CPTI04 seismic catalogue has been used, since Sabetta&Pugliese attenuation relation has been used. As has already been stated, the magnitude scale that is being used depends on the magnitude scale used in the attenuation relationships. Sabetta&Pugliese attenuation relation uses a double scale, where magnitude scale will be M S for M>5.5 and M L for M<

66 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra This double scale was selected in order to coincide with the M w scale which, as has been mentioned in Chapter 3, is the only one who does not saturate. Thus, for M<5.5 a conversion (included in the CPTI04 catalogue in the column Msp ) was used to transform M S to M L. In this paragraph we are going to use Ambraseys 1996 as attenuation relation and compare the hazard calculations which result from the use of both M SA and M W magnitude scale as they are reported in the seismic catalogue CPTI04. As we will see later on, the variation that occurs in the hazard results, is only coming from the different magnitude bins adopted by the two magnitude scales, and consequently from the different number of earthquake events falling in each bin. The attenuation relation has nothing to do with this since the magnitude adjustments for the attenuation are performed independently and simply the appropriate column from CPTI04 has to be selected (M SA for Ambraseys 96, M SP for Sabetta&Pugliese and M W for Ambraseys 2005). As it can be seen in Figures 4.21 and 4.22, the curves that have been calculated using the M w magnitude scale lie above the respective ones which have been calculated with the use of M SA. However, the difference between the two curves is negligible. In particular the differences have been calculated to be equal to 2.7% for Rome (for acceleration equal to 5.10x10-2 g) and 7.3% for Benevento (for acceleration equal to 1.33x10-1 g). ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E E-05 HAZARD CURVE Ms - Ts=0sec (PGA) Mw - Ts=0sec (PGA) Ms - Ts=2sec Mw - Ts=2sec ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E-04 HAZARD CURVE Ms - Ts=0sec (PGA) Mw - Ts=0sec (PGA) Ms - Ts=2sec Mw - Ts=2sec 1.0E ACCELERATION (g) Figure 4.21: Hazard curves for Rome for two spectral periods, attenuation Ambraseys et al and for magnitude scales M S and M w 1.0E ACCELERATION (g) Figure 4.22: Hazard curves for Benevento for two spectral periods, attenuation Ambraseys et al and for magnitude scales M S and M w Again, the effect of the different magnitude scales on the calculations of the hazard spectra will be investigated. After completing the hazard calculations with the two different magnitude scales and with Ambraseys et al as the attenuation relation, Figures 4.23 and 4.24 for Rome and Benevento result respectively. As it was the case for the hazard curves, when it comes to the Ambraseys et al attenuation relation, the use of M w magnitude scale instead of the M SA has a trivial effect. The two spectra have very small differences, for both return periods and for both sites. 52

67 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra The spectrum that resulted from the analyses using the M w magnitude scale is barely above the spectrum that results from the use of M SA. In particular, the numerical comparison of the maximum values between the respective hazard spectra shows an increase by 0.01% for Rome and by 1.9% for Benevento when M w magnitude scale is being considered instead of the M SA one. ACCELERATION (g UNIFORM HAZARD SPECTRUM Ms - Tr=10,000 years Mw - Tr=10,000 years Ms - Tr=475 years Mw - Tr=475 years ACCELERATION (g) UNIFORM HAZARD SPECTRUM Ms - Tr=10,000 years Mw - Tr=10,000 years Ms - Tr=475 years Mw - Tr=475 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.23: Hazard spectra for Rome for two return periods, attenuation Ambraseys et al and for magnitude scales M SA and M w Figure 4.24: Hazard spectra for Benevento for two return periods, attenuation Ambraseys et al and for magnitude scales M SA and M w When different magnitude scales are used, the variables of the Gutenberg-Richter relationship are altered and the final outcome will also be altered. In order to understand why the Gutenberg-Richter regression changes depending on the magnitude scale that is used, a number of tables will be apposed. In Tables 4.3 to 4.5, the number of events for each magnitude bin, for both magnitude scales and for three different sites are shown (Table 4.3: Rome, Table 4.4: Benevento and Table 4.5: Vibo Valentia). The tables are followed by the respective graphical representations of the Gutenberg-Richter relation for historical completeness for those three sites (Figure 4.25: Rome, Figure 4.26: Benevento and Figure 4.27: Vibo Valentia). As it can be seen from those tables, the magnitude bins between the two different scales are not equal. Following the methodology adopted by Stucchi et al. [2004] in the implementation the INGV map, to take into account the different magnitude ranges of M SA ( ) and M w ( ) reported in the CPTI04 catalogue, the corresponding intervals have been divided in 12 classes corresponding to bins of different width. The bin width is equal to 0.3 for M SA and 0.23 for M w. Also, since the scales are different, the values of magnitude for the respective bins are also different. That has, as a result, a different number of events falling in each bin. This fact causes a change in the slope of the Gutenberg-Richter regressions (b value) as well as a change of the point where the Gutenberg-Richter line crosses the vertical axis (α value). In all three Figures 4.25, 4.26 and 4.27 that follow, the Gutenberg-Richter trend lines that have been computed using M w as magnitude scale exhibit higher a values and lower b values (greater in absolute values). As a matter of fact, for all the zones of the ZS9 Seismic Zonation the b values derived using M SA magnitude scale, are larger (smaller in absolute values) than the respective ones derived using M W magnitude scale. 53

68 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Furthermore, the constant parameter α is also influenced from the use of different magnitude scales. When M W is used, theα values are always greater than those resulting from the use of M SA. The value of parameter α increases as the seismic activity of the area becomes higher. Table 4.3. Number of events for each magnitude and for both magnitude scales for Rome Zone 911: Rome Historical N of N of M SA M W Completeness earthquakes earthquakes ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± GUTENBERG-RICHTER REGRESSIONS COMPARISON -0.5 log fc y = x y = x Ms Magnitude Scale Mw Magnitude Scale Figure 4.25: Gutenberg-Richter relations for Rome (zone 922) with both magnitude scales 54

69 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Table 4.4. Number of events for each magnitude and for both magnitude scales for Benevento Zone 927: Benevento Historical N of N of M SA M W Completeness earthquakes earthquakes ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± GUTENBERG-RICHTER REGRESSIONS COMPARISON -0.6 y = x log fc y = x Ms Magnitude Scale Mw Magnitude Scale Figure 4.26: Gutenberg-Richter relations for Benevento (zone 927) with both magnitude scales 55

70 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Table 4.5. Number of events for each magnitude and for both magnitude scales for Vibo Valentia Zone 929: Vibo Valentia Historical N of N of M SA M W Completeness earthquakes earthquakes ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± GUTENBERG-RICHTER REGRESSIONS COMPARISON log fc y = x y = x Ms Magnitude Scale Mw Magnitude Scale Figure 4.27: Gutenberg-Richter relation for Vibo Valentia (zone 929) with both magnitude scales It is evident that the M w Gutenberg-Richter curve is above the M SA one, if not for the whole range of magnitudes, for the greater part of it. Only for the last part of G-R, which corresponds to large magnitudes, the M w regression will go beneath the M SA one, affecting mostly distant sites and for longer periods. Also, from the above figures, we can see that the difference of the two curves is greater for small magnitudes, than it is for larger ones Thus, we could say that the use of M W, results in general in higher seismic parameters which in turn result to higher hazard curves. This is an effect that takes place regardless of the attenuation relation adopted. The differences in the values of a, and b are shown for some zones in the following table. 56

71 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Table 4.6. Numerical differences in a and b Zone M W Stat. -b M S Stat. -b M W Stat. a M S Stat. a < > < > < > < > < > < > < > < > < > < > In Table 4.7 the total number of earthquake events occurring within some zones has been counted. As one can see, if M W magnitude scale is used instead of M SA, the total number of events is greater. Table 4.7. Ratios of events over completeness, for both historical and statistical completeness Zone M S /M w Historical completeness of smallest event / / / / / / Maximum Magnitude The next parameter that will be modified is the maximum magnitude M max that can occur within a seismic zone. The values of the maximum magnitudes are estimated as the maximum magnitude that has appeared within the zone, taking into consideration the completeness of the seismic catalogue. This is going to be one set of maximum magnitudes. The other set of magnitudes is going to be taken from the INGV report [Stucchi et al. 2004]. In this set, only a number of magnitudes are altered from their original value which results from the Gutenberg-Richter procedure. The cases where the value of M max was changed were not many, since from the 36 zones of the ZS9 seismic zonation only twelve were assigned with a new higher M max in the INGV report. This change resulted always to grater values of magnitude. All of the seismic zones where the INGV report has assigned a different maximum magnitude than the originally one calculated from the Gutenberg-Richter relation, are shown in the following table. In most of the cases the increase of the maximum magnitude was equal to just one class. 57

72 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Table 4.8. M max Values from G-R and from INGV Zone M max from G-R M max from INGV Still, this selective increase of the maximum magnitude to some of the zones had practically no effect to the seismic calculations, both hazard curves and uniform hazard spectra. As it can be seen from the Figures 4.28 to 4.31 that follow, the compared curves almost lie on one another and this happens for all the sites, for both structural periods and for both return periods. In these curves both maximum magnitudes have been used and the resultant curves are compared with each other. Numerically, the increase in the hazard calculations that is caused from the use of the INGV report s maximum magnitude instead of the original maximum magnitude is equal to 0.5% (for acceleration equal to 1.02x10-2 ) for the hazard curves of Nocera Umbra and 1.1% (for acceleration equal to 1.24x10-1 ) for the hazard curves of Venzone. When the maximum values of the spectra are compared, the differences are found equal to 0.16% for Nocera Umbra and 0.02% for Venzone. ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E E E-06 HAZARD CURVE Msmax from GR - Ts=0sec (PGA) Msmax from INGV - Ts=0sec (PGA) Msmax from GR - Ts=4sec Msmax from INGV - Ts=4sec ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE Msmax from GR - Ts=0sec (PGA) Msmax from INGV - Ts=0sec (PGA) Msmax from GR - Ts=4sec Msmax from INGV - Ts=4sec 1.0E ACCELERATION (g) Figure 4.28: Hazard curves for Nocera Umbra for two spectral periods and for maximum magnitude from G-R and from INGV 1.0E ACCELERATION (g) Figure 4.29: Hazard curves for Venzone for two spectral periods and for maximum magnitude from G-R and from INGV 58

73 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ACCELERATION (g UNIFORM HAZARD SPECTRUM Msmax from GR - Tr=10,000 years Msmax from INGV - Tr=10,000 years Msmax from GR - Tr=475 years Msmax from INGV - Tr=475 years ACCELERATION (g UNIFORM HAZARD SPECTRUM Msmax from GR - Tr=10,000 years Msmax from INGV - Tr=10,000 years Msmax from GR - Tr=475 years Msmax from INGV - Tr=475 years TSTRUCTURAL (sec) Figure 4.30: Hazard spectra for Nocera Umbra for two return periods and for maximum magnitude from GR and from INGV TSTRUCTURAL (sec) Figure 4.31: Hazard spectra for Venzone for two return periods and for maximum magnitude from GR and from INGV In order to explore more thoroughly the effect of the increase of M max on the hazard curves and the uniform hazard spectra one site will be selected, where the M max is going to be inchmeal increased by one, two and finally three classes. The original M max of the seismic zone Nocera Umbra belongs to is 6.37 units. The selected site is going to be Nocera Umbra. The seismic zones whose contribution will be taken into consideration for Nocera Umbra are 914, 915, 916, 917, 918, 919, 920, 921 and 923. The M max of these zones will be increased by one, two and three classes. Using Crisis software, the hazard curves and the uniform hazard spectra are produced for Nocera Umbra. We begin with the hazard curves. In Figure 4.32 the four hazard curves have been plotted together. These curves result from the original M max and from the increased values of M max by one, two and three classes for structural period equal to zero (PGA). In Figure 4.33 the same four curves are plotted but this time for structural period equal to 4 seconds. For both structural periods, the difference is augmented as the acceleration becomes higher. This is because M max influences mostly the higher accelerations at longer return periods. For the PGA curve (T s =0sec), when M max is increased only by one class, the influence is negligible. A slight difference is evoked from the increase of M max by two classes and even after increasing by three classes the M max, the difference in the PGA curves remains relatively small. The amplification of the annual frequency of exceedance is calculated as equal to 6.0%, 9.2% and 11.5% for the increase of M max by one, two and three classes, for structural period equal to zero and for accelerations equal to 1.22x10-2 g, 1.28x10-2 g and 1.22x10-2 g respectively. The differences in the T=4sec PSA curve, are more evident even from the first increase. After the second increase, the difference is already substantial and when the M max is increase by three classes, the differences from the original curve reach higher levels. For this structural period, the increases of the annual frequency of exceedance are 13.3%, 25.4% and 35.8% for a respective increase of the maximum magnitude by one, two and three classes and for levels of acceleration equal to 5.10x10-3 g. The difference between Figures 4.28 and 4.32 is that for the latter, we have increased simultaneously the M max of all the zones that affect our site. 59

74 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE Mmax from GR Mmax 1 class above Mmax from GR Mmax 2 classes above Mmax from GR Mmax 3 classes above Mmax from GR ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE Mmax from GR Mmax 1 class above Mmax from GR Mmax 2 classes above Mmax from GR Mmax 3 classes above Mmax from GR 1.0E ACCELERATION (g) Figure 4.32: Hazard curves for Nocera Umbra, structural period T S =0 and M max from GR and one, two and three classes above it 1.0E ACCELERATION (g) Figure 4.33: Hazard curves for Nocera Umbra, structural period T S =4 and M max from GR and one, two and three classes above it The same course of calculations is repeated for the computations of the hazard spectra. Again, the M max of all the zones that affect seismically Nocera Umbra will be increased by one, two and three classes in order to investigate the effect this increase has on the uniform hazard spectra. From the diagrams in Figures 4.34 and 4.35, one can see that, as expected, M max mainly acts on long return periods and long spectral periods: if the maximum values of each spectrum are compared, one can see that the difference between the uniform hazard spectra is greater at the curves with return period 10,000 years than the respective ones with 475 years. For the 475 years spectra, the first increase of the maximum magnitude results to almost no effect. The same also happens after the second increase of the value of M max. The values of the increased M max spectra are higher than the values of the spectra of the initial M max, in a range of accelerations which extends slightly after the peak of the hazard and until periods of two seconds, where the four curves merge again. Even after the increase of three classes to the M max, the amplification of the maximum value of the acceleration, compared to the original value is equal to 4.3%. ACCELERATION (g UNIFORM HAZARD SPECTRUM Mmax from GR Mmax 1 class above Mmax from GR Mmax 2 classes above Mmax from GR Mmax 3 classes above Mmax from GR ACCELERATION (g UNIFORM HAZARD SPECTRUM Mmax from GR Mmax 1 class above Mmax from GR Mmax 2 classes above Mmax from GR Mmax 3 classes above Mmax from GR TSTRUCTURAL (sec) Figure 4.34: Hazard spectra for Nocera Umbra, return period T r =475y and M max from GR and one, two and three classes above it TSTRUCTURAL (sec) Figure 4.35: Hazard spectra for Nocera Umbra, return period T r =10,000y and M max from GR and one, two and three classes above it 60

75 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra The differences between the increased spectra with return period 10,000 years and the initial one are more evident even from the first change. Again the differences begin to appear only right before the peak of the spectra and as we further increase the values of M max, the range of differences widens. Also, the maximum difference between the curves is shifted towards longer periods (at T=0.50sec for one class above the initial, at T=0.75sec for two classes above the initial and at T=1.00sec for three classes above the initial). The increase of the maximum acceleration for the return period of 10,000 years is 5.2%, 10.2% and 14.6% respectively for the increase of one, two and three classes of the maximum magnitude. Of course, if one wanted to increase the M max in order to take into account the uncertainty of such a prediction, it would never be by three classes. Such an increase is excessive and was merely done here in order to investigate the influence of M max on the uniform hazard spectra and on hazard curves. Therefore, we can say that an increase of M max by reasonable amounts (one class) would have almost no effect on both a hazard curve and a hazard spectrum. 4.6 Attenuation Relation The final parameter, whose effect on the seismic hazard calculations will be investigated, is the attenuation relation. The three attenuation relations that will be used are those already mentioned in Chapter 3. In order for the results from the use of the different attenuations to be comparable, two analyses have been carried out: one where the M S data from CPTI04 have been used and a second, where a conversion was made in the magnitude scale from M S to M w and as such entered into the attenuation relations and combined with the M w data from CPTI04. ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E-05 HAZARD CURVE Sabetta&Pugliese Ts=0sec (PGA) Ambraseys et al Ts=0sec (PGA) Ambraseys et al Ts=0sec (PGA) ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E-05 HAZARD CURVE Sabetta&Pugliese Ts=2sec Ambraseys et al Ts=2sec Ambraseys et al Ts=2sec 1.0E ACCELERATION (g) 1.0E ACCELERATION (g) Figure 4.36: Hazard curves for Rome for Figure 4.37: Hazard curves for Rome for spectral period T S =0sec and for spectral period T S =2sec and for attenuations Sabetta&Pugliese, attenuations Sabetta&Pugliese, Ambraseys et al and 2004 Ambraseys et al and

76 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E-04 HAZARD CURVE Sabetta&Pugliese Ts=0sec (PGA) Ambraseys et al Ts=0sec (PGA) Ambraseys et al Ts=0sec (PGA) ANNUAL FREQUENCY O EXCEEDANCE 1.0E E E E E-05 HAZARD CURVE Sabetta&Pugliese Ts=2sec Ambraseys et al Ts=2sec Ambraseys et al Ts=2sec 1.0E ACCELERATION (g) 1.0E ACCELERATION (g) Figure 4.38: Hazard curves for Venzone for Figure 4.39: Hazard curves for Venzone for spectral period T S =0sec and for spectral period T S =2sec and for attenuations Sabetta&Pugliese, attenuations Sabetta&Pugliese, Ambraseys et al and 2004 Ambraseys et al and 2004 The hazard curves for Rome (Figures 4.36 and 4.37) and Venzone (Figures 4.38 and 4.39) have been plotted for all three attenuation relations and for spectral periods zero and two seconds. The differences are significant: Sabetta&Pugliese 1996 and Ambraseys et al do not appear that dissimilar with each other. The main difference is between Ambraseys et al and the other two attenuations, in case of the PGA hazard curves. For T S =0sec the Ambraseys et al gives a far more severe hazard curve but for T S =2sec the most harsh outcomes are given from the Sabetta&Pugliese 1996 attenuation relation. The hazard spectra for Rome (Figures 4.40 and 4.41) and Venzone (Figures 4.42 and 4.43) have been plotted again for the three attenuation relations and for return periods four hundred and seventy five years and ten thousand years. The effect of the attenuations on the hazard spectra is similar to the one the attenuations had on the hazard curves. For periods shorter than 0.65 seconds the Ambraseys et al spectrum provides values much greater than the respective accelerations given by the other two spectra. This happens for both sites and for both return periods. For longer periods, the three spectra exhibit evidently smaller differences. ACCELERATION (g) UNIFORM HAZARD SPECTRUM Sabetta&Pugliese Tr=475 years Ambraseys et al Tr=475 years Ambraseys et al Tr=475 years ACCELERATION (g) UNIFORM HAZARD SPECTRUM Sabetta&Pugliese Tr=10,000 years Ambraseys et al Tr=10,000 years Ambraseys et al Tr=10,000 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.40: Hazard spectra for Rome for Figure 4.41: Hazard spectra for Rome for return period T r =475y and for return period T r =10,000y and for attenuations Sabetta&Pugliese, attenuations Sabetta&Pugliese, Ambraseys et al and 2004 Ambraseys et al and

77 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra ACCELERATION (g) UNIFORM HAZARD SPECTRUM Sabetta&Pugliese Tr=475 years Ambraseys et al Tr=475 years Ambraseys et al Tr=475 years ACCELERATION (g) UNIFORM HAZARD SPECTRUM Sabetta&Pugliese Tr=10,000 years Ambraseys et al Tr=10,000 years Ambraseys et al Tr=10,000 years TSTRUCTURAL (sec) TSTRUCTURAL (sec) Figure 4.42: Hazard spectra for Venzone for Figure 4.43: Hazard spectra for Venzone for return period T r =475y and for return period T r =10,000y and for attenuations Sabetta&Pugliese, attenuations Sabetta&Pugliese, Ambraseys et al and 2004 Ambraseys et al and 2004 Figures show how PSHA in Italy is controlled by small magnitude earthquakes at very short distances. This becomes evident if we recall Figures of Chapter 3 where the response spectra derived from the different attenuations are compared. Ambraseys et al is an attenuation relation, which includes a magnitude dependence in the geometric decay with distance, and provides much higher values if compared to Sabetta&Pugliese 1996 and Ambraseys et al but only for short periods (less than 0.5sec), small magnitudes (less than 6) and short distances (less than 20 km). In fact figures of uniform hazard spectra for sites of medium and high seismicity as Rome and Venzone, are very similar to Figure 3.10 showing the comparison of the attenuations in case of M=5 and D=3 km. The higher values provided by Ambraseys et al lead to a rapid decrease as magnitude and distance are increased (Figures 3.11 and 3.12). Another aspect to be taken into consideration in order to understand the difference between the considered attenuations is the effect of the random uncertainty σ incorporated in each relation. In Figure 4.44 an example taken from Reiter [1990], is shown for the city of San Francisco. The hazard curves have been calculated using three different attenuation relations with and without random uncertainty σ. From this figure, it is obvious that the effect of including the standard deviation increases as the probability of exceedance decreases. At high ground motion levels the hazard, without uncertainty, may be dominated by the likely, high ground motion from the occurrence of unlikely but large and/or nearby earthquakes. When uncertainty is included the effect of low likelihood high ground motion from high likelihood smaller and/or more distant earthquakes may be also taken into account. The relative contribution of these events can become more important [Reiter; 1990]. The standard deviation is constant with magnitude for Sabetta&Pugliese and Ambraseys et al attenuation relations, but in the case of Ambraseys et al. 2004, it varies with magnitude, increasing as magnitude decreases. In any case, sigma takes greater values in Ambraseys et al than it does in the other two attenuations. As a result, at low probabilities of exceedance, where the effect of including the standard deviation increases, Ambraseys et al draws away from the other two curves, leading to much greater acceleration levels for the same probability of exceedance. 63

78 Chapter 4: Sensitivity Analysis on Hazard Curves and Uniform Hazard Spectra Figure 4.44: Hazard estimates for San Francisco using three different ground-motion models with and without random uncertainty σ [Reiter; 1990] With the attenuation relationship, the sensitivity analysis on the hazard curves and the uniform hazard spectra is completed. A number of parameters were modified in order to examine their effect on the seismic hazard calculations for the selected sites. These effects may quantitatively differ from site to site. Since the desired outcome of this thesis is to acquire the global role of each parameter in a seismic hazard calculation, rather than the local one, in Chapter 5 the same calculations will be repeated, but this time the results will be presented in terms of hazard maps. 64

79 Chapter 5: Sensitivity Analysis on Hazard Maps 5. SENSITIVITY ANALYSIS ON HAZARD MAPS In Chapter 4 all the results from the sensitivity analysis were presented in terms of hazard curves and uniform hazard spectra. In the current Chapter the results will be presented in the form of hazard maps. All the parameters that were modified in Chapter 4 will be considered once again and the respective comparisons will be presented, so that the effect of each parameter can be clearly and utterly appreciated. It should be noted that all the hazard maps have been calculated for rock-stiff soil conditions. 5.1 Seismic Zonation The first parameter that was modified in the previous chapter was the seismic zonation. Two seismic zonations were used, while all the other parameters remained the same, and these were the ZS4 older zonation and the more recent one ZS9. In Figures 5.1a and 5.1b, the two hazard maps as they result from the use of the two different zonations are presented. PV VZ N PV VZ N N U N U RM BN RM BN V V V V ZS a ZS b Figure 5.1: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the ZS4 (Figure 5.1a) and ZS9 seismic zonation (Figure 5.1b) 65

80 Chapter 5: Sensitivity Analysis on Hazard Maps The PGA values that result from the use of ZS4 seismic zonations are higher in comparison to the PGA values that result from the ZS9 seismic zonation nearly throughout the entire Italian peninsula. Using Figures 5.1a and 5.1b and in particular, subtracting the latter from the former, the hazard map of Figure 5.2 has been realized. The difference in the PGA values is a more representative way for displaying the results since it can easily be seen where the differences (positive or negative) are concentrated. PV VZ N N U RM BN ZS4 - ZS V V Figure 5.2: Difference between the PGA values (in g) obtained by the ZS4 and the ZS9 seismic zonation As shown in Figure 5.2, regardless of the seismicity of the area, if zonation ZS4 is used, an increase of the PGA will be seen in the hazard map. This increase reaches levels of around 0.120g in the southern Italy, near the Vibo Valentia site. This area in general presents one of the higher seismicity levels in Italy. By changing the seismic zonation, the effect on the hazard map is strong as we have already seen in happening to the hazard curves and hazard spectra presented in the previous chapter. 66

81 Chapter 5: Sensitivity Analysis on Hazard Maps Among the six selected sites, the one that experiences the higher increase of the PGA values is Vibo Valentia and this increase is equal to 30.4% when ZS4 is used instead of the ZS9 Zonation. Still, the maximum percentage increase of the PGA values is located in a low seismicity area in the northern Italy, west of Venzone and has been calculated to be 251%! 5.2 Seismic Catalogue As discussed in Chapter3, two seismic catalogues have been considered: NT4 and CPTI04. The hazard maps realized using both these catalogues can be seen in Figures 5.3a and 5,3b. As we can see, the PGA values of Figure 5.3b, which have been calculated using the CPTI04 earthquake catalogue, are lower than the respective PGA values of Figure 5.3a, which have been calculated using the NT4 catalogue, only in some parts of the country. In others, the PGAs coming from CPTI04 are higher than in Figure 5.3a. Only in central Italy and in the foot of the Italian peninsula, the CPTI04 provides higher PGA values than the NT4. This is clearer in the comparative hazard map of Figure 5.4, where the values of 5.3b map are deducted from the respective values of the 5.3a hazard map. PV VZ N PV VZ N N U N U RM BN RM BN V V V V NT a CPTI b Figure 5.3: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by NT4 (Figure 5.3a) and CPTI04 earthquake catalogue (Figure 5.3b) Figure 5.4 signifies what has already been presented in paragraph 4.2 of the previous Chapter, and that is that the use of NT4 earthquake catalogue instead of the CPTI04 does not have the same effect on all of the extents of the Italian country. The seismicity of some areas has been amplified, while in other areas the PGA values have been impoverished. This is a result of the fact that in the old earthquake catalogue NT4, the number of larger magnitude earthquakes for some of the seismic zones is greater. Thereby, when NT4 earthquake catalogue is used, the seismicity of Benevento reduces, while the seismicity of Vibo Valentia increases. This is also in accordance to the results that were presented in the second paragraph of the previous chapter, where the hazard curves and the hazard spectra for these sites where shown. 67

82 Chapter 5: Sensitivity Analysis on Hazard Maps In any case, the maximum increase in the PGA values of the hazard map of Figure 5.3b is equal to 0.064g and appears in Eastern Sicily. In the same area the maximum percentage increase is located and is equal to 42%. Thus, effect of the earthquake catalogue should not be considered trivial, but certainly is not of the same importance as seismic zonation. PV VZ N N U RM BN NT4 - CPTI V V Figure 5.4: Difference between the PGA values (in g) obtained by the NT4 and the CPTI04 earthquake catalogue 5.3 Catalogue Completeness Thereinafter, the influence of the earthquake catalogue completeness on the hazard maps is going to be examined. The hazard map of Figure 5.5a has been computed using the statistical completeness of the CPTI04 earthquake catalogue, while 5.5b hazard map has been calculated with the historical completeness of the same catalogue. The rest of the required parameters for the hazard analysis are those apposed in paragraph 3.6 of the Chapter 3. 68

83 Chapter 5: Sensitivity Analysis on Hazard Maps VZ VZ PV N PV N N U N U RM BN RM BN V V V V Statistical Completeness a Historical Completeness b Figure 5.5: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the statistical (Figure 5.5a) and historical completeness (Figure 5.5b) As it has previously been discussed, when we alternate between the two completenesses, the influence of the change of this parameter is rather small. In order for this to become more understandable the difference between the two hazard maps of Figure 5.5 has been calculated and presented in Figure 5.6. Once again, the effect of the completeness period of the earthquake catalogue is not uniform among the Italian region. As it can be seen from the following map, in some regions, (e.g. Emilia Romagna and Puglia) the use of the statistical completeness causes higher PGA values than the use of the historical completeness. The opposite effect is observed in other regions (e.g. Abruzzo and Calabria). The reason for this trend has been explained through Table 4.2, in Chapter 4. The data given in this table are the total number of events that occur for the zones where the selected sites are located, the completeness of the smallest earthquake event and the ratios of events over the respective completeness period. The different ratios for the historical and the statistical completeness are more or less similar. Still, for the three sites of Pavia, Venzone and Rome, the ratio that results from the statistical completeness is higher than the respective ratio that results from the use of the historical completeness. As it can be seen in Figure 5.6, these are the sites for which the hazard calculations with statistical completeness lead to more unfavorable values of PGA. Overall, the effect of the completeness period on the seismic hazard calculations is rather small. The higher difference in the PGA values between the hazard maps shown in Figures 5.5a and 5.5b is equal to 0.030g and appears east of Benevento. The maximum percentage difference is located somewhat north of the area where the maximum difference is located and is equal to 23%. 69

84 Chapter 5: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN Statistical Comp. - Historical Comp V V Figure 5.6: Difference between the PGA values (in g) obtained by the statistical and the historical completeness 5.4 Magnitude Scale The next parameter that is going to be modified in order to investigate its effect on the seismic hazard calculations is the magnitude scale. So far, the magnitude scale that has been used has been the M S one. In this paragraph, the results form the M S magnitude scale will be compared to the results from the use of M w magnitude scale. As was also done in the previous chapter, Ambraseys et al will be used. In order to carry out this comparison, the following two hazard maps have been drawn. 70

85 Chapter 5: Sensitivity Analysis on Hazard Maps VZ VZ PV N PV N N U N U RM BN RM BN V V V V Mw (Ambraseys 1996) a Ms (Ambraseys 1996) b Figure 5.7: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the M w (Figure 5.7a) and M S (Figure 5.7b) magnitude scale using Ambraseys et al attenuation relation In the first map of Figure 5.7, the M w magnitude scale has been used, while in the second one, M S was used. Ambraseys et al attenuation relation has been used, in order to explore the effect of M w in other attenuation laws. As mentioned above, the Ambraseys et al attenuation relation requires M S as input magnitude scale, in comparison to the Sabetta&Pugliese 1996 which requires the double scale previously mentioned, that is almost equivalent to the M w magnitude scale. The comparison of the two previous hazard maps can be done through Figure 5.8, where the hazard map of Figure 5.7b has been ablated from that of Figure 5.7.a. As it can be seen in these figures, some of the PGA values with return period equal to four hundred and seventy five years that have been calculated using the M w magnitude are increased in comparison to the respective ones which have been calculated with the use of M S. However, the differences between the two hazard maps are negligible. In the case of the Ambraseys et al attenuation relationship, the comparison of the two resultant hazard maps, which has been done in Figure 5.8, shows an increase in the PGA values that does not exceed 0.035g and an almost equal decrease in other areas. Again, if the comparison is done in percentage terms, the increase and the decrease, which in the case of the magnitude scale fluctuate in the same levels, is estimated around 23%. In other words, the Ambraseys et al relation, proved to be rather insensitive in the alteration of the magnitude scale. 71

86 Chapter 5: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN Mw - Ms (Ambraseys et al. 1996) V V Figure 5.8: Difference between the PGA values (in g) obtained by the M w and the M S magnitude scale using Ambraseys et al attenuation relation 5.5 Maximum Magnitude The next parameter to be modified is the maximum magnitude M max that can occur within a seismic zone. The two maximum magnitude sets that will be used are one that results as the maximum magnitude that has appeared within the zone, taking into consideration the completeness of the seismic catalogue and the other set will be the values assigned as maximum magnitude in the INGV report [Stucchi et al. 2004]. In this set, a number of magnitudes have been increased from their original values and in twelve seismic zones a new higher M max has been assigned. In the two following Figures, 5.9a and 5.9b, the hazard maps as they result from the use of the two sets of maximum magnitudes previously mentioned are shown. As we have already seen in Chapter 4, the selective increase of the maximum magnitude in a small number of seismic zones has a limited effect on the seismic hazard calculations. 72

87 Chapter 5: Sensitivity Analysis on Hazard Maps PV VZ N PV VZ N N U N U RM BN RM BN V V V V INGV Mmax a GR Mmax b Figure 5.9: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the INGV M max (Figure 5.9a) and original M max (Figure 5.9b) PV VZ N N U RM BN V V INGV Mmax - GR Mmax Figure 5.10: Difference between the PGA values (in g) obtained by the M max given in the INGV report and the original M max 73

88 Chapter 5: Sensitivity Analysis on Hazard Maps After the two individual maps of Figure 5.9, the comparative map of Figure 5.10 has been presented. In this map, the PGA values of 5.9b hazard map are subtracted from the PGA values of 5.91a hazard map in order for the comparison to become clearer. As was expected the use of either the one or the other maximum magnitude set does not influences that much the hazard results. In fact, the maximum difference in the PGA values is equal to 0.012g and appears south-west of Vibo Valentia. The maximum percentage difference on the other hand is equal to only 14%. Since only a limited number of maximum magnitudes has been increased in the previous comparison, we will increase the maximum magnitudes of all the seismic zones by one and three classes in order to further investigate the effect of this parameter on the hazard calculations. By doing so, the two hazard maps of Figure 5.11 arise. In Figure 5.11a a maximum magnitude increased by one class has been used and in Figure 5.11b the maximum magnitude has been increased by three classes. The gradual amplification of the PGA values is evident. The seismicity of the Italian peninsula is increased throughout the country but mainly in the areas where the seismicity was already high. It shows that the increase of a high maximum magnitude is more unfavorable than the increase of a lower magnitude since the former leads to particularly high seismic levels. Of course, the increase by three magnitude classes is rather excessive but clarifies the effect of the maximum magnitude in the hazard calculations. VZ VZ PV N PV N N U N U RM BN RM BN V V V V GR+1 Mmax a GR+3 Mmax b Figure 5.11: Values of PGA (in g) with a probability of exceedance 10% in 50 years (Return Period 475 years) obtained by the M max plus one magnitude class (Figure 5.11a) and M max plus three magnitude classes (Figure 5.11b) 74

89 Chapter 5: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN GR+1 Mmax - GR Mmax V V Figure 5.12: Difference between the PGA values (in g) obtained by the M max plus one magnitude class and the original M max Two new hazard maps result in this way, these of Figures 5.12 and From these comparative maps, some numerical conclusions can be drawn. In particular, from Figure 5.12, where the maximum magnitude has been increased by one class, the maximum difference in the PGA values is equal to 0.022g and the percentage difference 18%. Using Figure 5.13, the maximum PGA difference is 0.07g and the maximum percentage difference results to 46%. From these numbers it is clear that the maximum magnitude does not play a leading role in the hazard calculations. 75

90 Chapter 5: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN GR+3 Mmax - GR Mmax V V Figure 5.13: Difference between the PGA values (in g) obtained by the M max plus three magnitude class and the original M max 5.6 Attenuation Relation The final parameter whose effect on the hazard maps will be investigated is the attenuation relation. The three attenuation relations that have already been used when the hazard spectra and the hazard curves were presented in the previous Chapter are the Sabetta&Pugliese 1996, the Ambraseys et al and the Ambraseys et al It is a common PSHA practice to combine a number of relations in a logic tree, even if there are one or more models that have been derived specifically for the region in question. The differences among the different attenuation relations have already proved to be significant, from the previous chapter. In this paragraph, the total effect on the hazard map will be studied. 76

91 Chapter 5: Sensitivity Analysis on Hazard Maps In the two Figures that follow, Figure 5.14a and 5.14b, Sabetta&Pugliese 1996 and Ambraseys et al have been used to produce the two respective hazard maps. These two maps will be compared to each other by subtracting the PGA values of 5.14b by the PGA values of 5.14a. The hazard map that results can be seen in Figure VZ VZ PV N PV N N U N U RM BN RM BN V V V V Sabetta&Pugliese a Ambraseys et al b Figure 5.14: Values of PGA (in g) with a probability of exceedance 10% in 50 years (return period 475 years) obtained by the Sabetta&Pugliese (Figure 5.14a) and the Ambraseys et al attenuation relation (Figure 5.14b) When observing Figure 5.15, two trends appear; negative values are encountered in central Italy and positive values in the southernmost part of peninsular Italy. That is in agreement with the fact that Ambraseys et al gives higher weights to small-medium magnitudes (central Italy) while Sabetta&Pugliese 1996 gives higher weights to large magnitudes (southern Italy). The maximum positive differences are about 0.021g inside the most seismic areas such as Sicily and much lower elsewhere. This is due to the fact that in the Sicilian volcanic area of Etna (seismic zone N 936 and yellow spot in Fig 5.15), the earthquakes are of low magnitude but very shallow and thus, attenuate much faster. In the Etna area a specific volcanic attenuation should have been used as has been done in the INGV report. This exceeded the scope of this thesis and therefore the same attenuation was used for the whole Italian peninsula. Therefore, the differences relative to Etna area will not be considered. The next maximum positive difference which appears south-east of Benevento is equal to 0.018g. The maximum negative differences are around 0.024g. In percentage terms the positive differences are equal to 8% while the negative are estimated around 26%. Thus, the influence of the attenuation relation seems relevant only in specific areas. 77

92 Chapter 4: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN Sabetta&Pugliese - Ambraseys V V Figure 5.15: Difference between the PGA values (in g) obtained by the Sabetta&Pugliese 1996 and Ambraseys et al attenuation relation The next and final comparison will be made between the most recent attenuation relation of Ambraseys et al and the Sabetta&Pugliese Using the Ambraseys et al the hazard map of Figure 5.16a is obtained. If the PGA values of the hazard map of Figure 5.16a are subtracted from Figure 5.16a, the map of Figure 5.17 is resulting. 78

93 Chapter 4: Sensitivity Analysis on Hazard Maps VZ VZ PV N PV N N U N U RM BN RM BN V V V V Sabetta&Pugliese a Ambraseys et al b Figure 5.16: Values of PGA (in g) obtained by the Sabetta&Pugliese 1996 (Figure 5.16a) and the Ambraseys et al attenuation relation (Figure 5.16b) The PGA values that result from the use of the Ambraseys et al attenuation relation are particularly increased in comparison to the PGA values that result from the use of either one of the other two attenuation relations. Ambraseys et al is an attenuation relation which includes a magnitude dependence in the geometric decay with distance and thus, provides much higher values with respect to Sabetta&Pugliese 1996 and Ambraseys et al but only for short periods (less than 0.5sec), small magnitudes (less than 6) and short distances (less than 20 km). As a consequence the PGA values obtained using this attenuation are particularly high in central Italy where medium-low magnitudes prevail. In figure 5.17 the highest difference is in fact obtained in the eastern part of Sicily but this is due to the volcanic area of Etna where earthquakes are shallow and of low magnitude and require a specific volcanic attenuation, as mentioned above. The maximum difference in the PGA values (apart from the area of Etna) is equal to -0.30g and appears very close to Rome, in the south-east of the capital. In percent terms this corresponds to a decrease by 293%! Thus, the effect of the attenuation relation on the results of the hazard calculations has so far been the strongest among all the other parameters that have been used and modified in this study. Something else that is worth mentioning is the fact that the use of these two attenuation relations, locates the maximum seismicity in different areas. Ambraseys et al showed that the maximum PGA appears eastern of Rome, whereas Sabetta&Pugliese 1996 located the maximum PGA south-east of Benevento. 79

94 Chapter 4: Sensitivity Analysis on Hazard Maps PV VZ N N U RM BN Sabetta&Pugliese - Ambraseys V V Figure 5.17: Difference between the PGA values (in g) obtained by the Sabetta&Pugliese 1996 and the Ambraseys et al attenuation relation Still, this situation would not be the same if the hazard map was done for another spectral period longer than 0.5 seconds. As has already been mentioned Ambraseys et al provides very high values only for PGA and short spectral periods. Thus, if Ambraseys et al and Sabetta&Pugliese were used once again for the hazard calculations but this time hazard maps with values of PSA for T S =1sec were to be generated, the icon would be the one shown in Figures 5.18a and 5.18b. The situation has now been inverted. While the acceleration values from the use of Sabetta&Pugliese have increased compared to the accelerations that correspond to PGA, the acceleration values that result from the use of Ambraseys et al have decreased and are now lower than the values of Figure 5.18b. Using the following figures, the comparative map of Figure 5.19 is drawn. 80

95 Chapter 4: Sensitivity Analysis on Hazard Maps VZ VZ PV N PV N N U N U RM BN RM BN Sabetta&Pugliese - PSA=1sec V V a Ambraseys PSA=1sec V V b Figure 5.18: Values of PSA for T S =1sec (in g) obtained by the Sabetta&Pugliese 1996 (Figure 5.18a) and the Ambraseys et al. 2004attenuation relation (Figure 5.18b) PV VZ N N U RM BN V V Sabetta&Pugliese - Ambraseys 2004 (PSA=1sec) Figure 5.19: Difference between the PSA for T S =1sec values (in g) obtained by the Sabetta&Pugliese 1996 and the Ambraseys et al attenuation relation 81