E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S State of Practice of Seismic Hazard Analysis: From the Good to the Bad Norm Abrahamson, Seismologist Pacific Gas & Electric Company

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Seismic Hazard Analysis Approaches to design ground motion –Deterministic –Probabilistic (PSHA) –Continuing debate in the literature about PSHA Time Histories –Scaling –Spectrum compatible

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Seismic Hazard Approaches Deterministic approach –Rare earthquake selected –Median or 84th percentile ground motion Probabilistic approach –Probability of ground motion selected Return period defines rare Performance approach –Probability of damage states of structure Structural fragility needed Risk approach –Probability of consequence Loss of life Dollars

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Deterministic vs Probabilistic Deterministic –Consider of small number of scenarios (Mag, dist, number of standard deviation of ground motion) –Choose the largest ground motion from cases considered Probabilistic –Consider all possible scenarios (all mag, dist, and number of std dev) –Compute the rate of each scenario –Combine the rates of scenarios with ground motion above a threshold to determine probability of “exceedance”

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Deterministic Approach Select a specific magnitude and distance (location) –For dams, typically the “worst-case” earthquake –(MCE) Design for ground motion, not earthquakes –Ground motion has large variability for a given magnitude, distance, and site condition –Key issue: What ground motion level do we select?

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Parkfield Near Fault PGA Values

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Worst-Case Ground Motion is Not Selected in Deterministic Approach Combing largest earthquake with the worst- case ground motion is too unlikely a case –The occurrence of the maximum earthquake is rare, so it is not “reasonable” to use a worst-case ground motion for this earthquake –Chose something smaller than the worst-case ground motion that is “reasonable”.

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S What is “Reasonable” The same number of standard deviation of ground motion may not be “reasonable” for all sources –Median may be reasonable for low activity sources, but higher value may be needed for high activity sources Need to consider both the rate of the earthquake and the chance of the ground motion

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Components of PSHA Source Characterization –Size, location, mechanism, and rates of earthquakes Ground motion characterization –Ground motion for a given earthquake Site Response –Amplification of ground motion at a site Hazard Analysis –Hazard calculation –Select representative scenarios Earthquake scenario and ground motion

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Selected Issues in Current Practice (Less) Common Problems with current Practice Max magnitude VS30 Spatial smoothing of seismicity Double counting some aspects of ground motion variability Epistemic uncertainties –Mixing of epistemic and aleatory on the logic tree –Underestimation of epistemic uncertainties –Over-estimation of epistemic uncertainties Hazard reports / hand off of information –UHS and Scenario Spectra

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Common Misunderstandings Distance Measures –Different distance metrics for ground motion models often used interchangeably Rupture distance JB distance Rx (new for NGA models) Hypocentral distance Epicentral distance Return Period and Recurrence Interval used interchangeably –Recurrence interval used for earthquakes –Return period for ground motion at a site

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Common Misunderstandings Standard ground motion models thought to give the larger component –Most ground motion models give the average horizontal component Average is more robust for regression Scale factors have been available to compute the larger component –Different definitions of what is the larger component Larger for a random orientation Larger for all orientations Sa(T) corresponding to the larger PGA –Can be lower than the average!

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Use and Misuse of VS30 VS30 –Not the fundamental physical parameter –For typical sites, VS30 correlated with deeper Vs profile Most soil sites are in alluvial basins (deep soils) CA empirical based models not applicable to shallow soil sites Proper Use –Clear hand-off between ground motion and site response Consistent definition of “rock” –Use for deep soil sites that have typical profiles Misuse –Replace site-specific analysis for any profile (not typical as contained in GM data base) –Use ground motion with VS30 for shallow soil sites (CA models) Need to select a deeper layer and conduct site response study Or use models with soil depth and VS30

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Sloppy Use of Terms: Mmax Most hazard reports list a maximum magnitude for each source –Has different meanings for different types of sources Zones –Maximum magnitude, usually applied to exponential model Faults –Mean magnitude for full rupture, usually applied to characteristic type models –Allows for earthquake larger than Mmax –Called mean characteristic earthquake Issue –Some analyses use exp model for faults or characteristic models for regions –Not clear how to interpret Mmax Improve practice –Define both Mmax and Mchar in hazard reports

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Terminology Aleatory Variability (random) –Randomness in M, location, ground motion (  ) –Incorporated in hazard calculation directly –Refined as knowledge improves Epistemic Uncertainty (scientific) –Due to lack of information –Incorporated in PSHA using logic trees (leads to alternative hazard curves) –Reduced as knowledge improves

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Aleatory and Epistemic For mean hazard, not important to keep separate Good practice –Keep aleatory and epistemic separate Not always easy –Allows identification of key uncertainties, guides additional studies, future research Source characterization –Common to see some aleatory variability in logic tree (treated as epistemic uncertanity) Rupture behavior (segmentation, clustering) Ground motion characterization –Standard practice uses ergodic assumption Some epistemic uncertainty is treated as aleatory variability

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Example: Unknown Die Observed outcome of four rolls of a die –3, 4, 4, 5 What is the model of the die? – Probabilities for future rolls (aleatory) How well do we know the model of the die? –Develop alternative models (epistemic)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Unknown Die Example RollModel 1 Global Analog Model 2 Region Specific Model 3 Region Specific 11/ / / / / /

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Epistemic Uncertainty Less data/knowledge implies greater epistemic uncertainty In practice, this is often not the case –Tend to consider only available (e.g. published) models –More data/studies leads to more available models –Greater epistemic uncertainty included in PSHA

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Characterization of Epistemic Uncertainty Regions with little data –Tendency to underestimate epistemic With little data, use simple models –Often assume that the simple model is correct with no uncertainty Regions with more data –Broader set of models –More complete characterization of epistemic –Sometimes overestimates epistemic

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Underestimation of Epistemic Uncertainty Standard Practice: If no data on time of last eqk, assume Poisson only Good Practice: Scale the Poisson rates to capture the range from the renewal model

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Overestimate of Epistemic Uncertainty Rate: Constrained by paleo earthquake recurrence 600 Yrs for full rupture Mean char mag=9.0 Alternative mag distributions considered as epistemic uncertainty exponential model brought along with low weight, but leads to over- estimation of uncertainty

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Epistemic Uncertainty Good Practice –Consider alternative credible models Use minimum uncertainty for regions with few available models –Check that observations are not inconsistent with each alternative model Poor Practice –Models included because they were used in the past –Trouble comes from applying models in ways not consistent with their original development E.g. exponential model intended to fit observed rates of earthquakes, not to be scaled to fit paleo-seismic recurrence intervals

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Ground Motion Models Aleatory –Standard practice to use published standard deviations Ergodic assumption - GM median and variability is the same for all data used in GM model –Standard deviation applies to a single site / single path Epistemic –Standard practice to use alternative available models (median and standard deviation) –Do the available models cover the epistemic uncertainty Issue with use of NGA models

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Problems with Current Practice Major problems have been related to the ground motion variability –Ignoring the ground motion variability Assumes  =0 for ground motion Considers including ground motion  as a conservative option This is simply wrong. –Applying severe truncation to the ground motion distribution e.g. Distribution truncated at +1  –Ground motions above 1  are considered unreasonable No empirical basis for truncation at less than 3 . Physical limits of material will truncate the distribution

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Example of GM Variability

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S GM Variability Example

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S GM Truncation Effects (Bay Bridge)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Parkfield

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Ergodic Assumption Trade space for time

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Mixing epistemic and aleatory (in Aleatory)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Standard Deviations for LN PGA RegionTotalSingle Site Chen&Tsai (2002) Taiwan Atkinson (2006) Southern CA Morikawa et al (2008) Japan0.78 Lin et al (2009) Taiwan

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Single Ray Path

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Standard Deviations for LN PGA RegionTotalSingle Site Single Path and site Chen&Ts ai (2002) Taiwan Atkinson (2006) Southern CA Morikawa et al (2008) Japan Lin et al (2009) Taiwan

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Removing the Ergodic Assumption Significant reduction in the aleatory variability of ground motion –40-50% reduction for single path - single site

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Hazard Example

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Die: combine rolls (ergodic)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Non-Ergodic: Reduced Aleatory

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Removing the Ergodic Assumption Penalty: must include increased epistemic uncertainty –Requries model for the median ground motion for a specific path and site –Benefits come with constraints on the median Data Numerical simulations Current State of Practice –Most studies use ergodic assumption Mean hazard is OK, given no site/path specific information –Some use of reduced standard deviations (reduced aleatory), but without the increased epistemic Underestimates the mean hazard Bad practice

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Non-Ergodic: Increased Epistemic

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Standard Deviations for Surface Fault Rupture Std Dev (log10) Global Model (ave D) 0.28 Global Model Variability Along Strike 0.27 Total Global0.39 Single Site0.17

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Removing the Ergodic Assumption Single site aleatory variability –Much smaller than global variability Value of even small number of site- specific observations NEpistemic Std Dev In Median (log10)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Large Impacts on Hazard

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Keeping Track of Epistemic and Aleatory If no new data –Broader fractiles –No impact on mean hazard Provides a framework for incorporation of new data as it becomes available –Identifies key sources of uncertainty Candidates for additional studies –Shows clear benefits of collecting new data

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Hazard Reports Uniform Hazard Spectra –The UHS is an envelope of the spectra from a suite of earthquakes Standard practice hazard report includes: –UHS at a range of return periods gives the level of the ground motion –Deaggregation at several spectral periods for each return period identifies the controlling M,R Good practice hazard report includes: –UHS –Deaggregation –Representative scenario spectra that make up the UHS. Conditional Mean Spectra (CMS)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Crane Valley Dam Example Controlling Scenarios from deaggregation For return period = 1500 years: –SA(T=0.2):M= , R=20-30 km –Sa(T=2):M= , R=170 km

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Scenario Ground Motions Find number of standard deviations needed to reach UHS Next, Construct the rest of the spectrum (Baker and Cornell Approach: Conditional Mean Spectra)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Correlation of Epsilons T=1.5T=0.3

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Correlation of Variability Correlation decreases away from reference period Increase at short period results from nature of Sa slope

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Scenario Spectra for UHS Develop a suite of deterministic scenarios that comprise the UHS Time histories should be matched to the scenarios individually, not to the entire UHS

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Improvements to PHSA Practice At the seismology/engineering interface, we need to pass spectra for realistic scenarios that correspond the hazard level –This will require suites of scenarios, even if there is a single controlling earthquake The decision to envelope the scenarios to reduce the number of engineering analyses required should be made on the structural analysis side based on the structure, not on the hazard analysis side.

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Time Histories Non-linear response is sensitive to the selection of the time histories –Large variability from the recordings with similar M,R Best approach for selecting and modifying time histories depends on what we want to get out of the analyses –Average response –Variability of response Strongly held opposing opinions on different approaches and objectives

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Selection Approaches Seismological Properties –Similar Mag, Dist, Mech –Goal: capture key unknown characteristics of ground motion that are important to the structural response Recording Properties –Wider Mag, dist, mech –Identify key characteristics of ground motion that are important to the structural response E.g. spectral shape, pulses, duration, … –Select recordings that sample the key characteristics

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Modification Approaches Scaling –multiply Acc(t) by (smallest) factor to meet code requirements Same factor for two horizontal components Spectrum compatible –Scale and also adjust the frequency content to be consistent with the design spectrum (meet code requirements)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Time Histories Summary No clear objective method for selecting/modifying time histories Problem is getting worse as data sets expand –More choices –Selecting a small subset (e.g. 3 or 7)

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Spatial Smoothing of Seismicity Zone boundaries –Based on tectonic regions –Based on seismicity rates Activity rate –Usually from observed seismicity Smoothing Approaches –Uniform within a zone –Zoneless, based on a smoothing distance Key Issue –Smoothing for the Host zone (R<50 km) –In most cases, too much smoothing is applied Most PSHAs do not check amount of smoothing –Is it consistent with observations?

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Example: Crane Vly Dam San Andreas Flt

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Site-Specific Checks of Smoothing Assume Poisson with uniform rate within Sierra Nevada zone –M>3, R<50, 24 years: expect 20 eqk Observation –M>3, R<50 km: 40 earthquakes –M>3, R<17 km: 0 earthquakes Simple Tests –If Poisson, what is the chance of >=40 eqk P= < For R<50 km region, Rate is too low –Too much smoothing

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Check Smoothing Near Site Simple Tests –If uniform rate within 50 km, what is chance of observing 0 out of 40 earthquakes within 17 km? Prob = Indicates rate is not uniform within 50 km radius –Too much smoothing Alternative method to set rate for R<17 km region –No eqk observed –What rate would lead to reasonable probability of producing the observation (no earthquakes) P=0.5, rate = 0.3 ave zone rate P=0.1, rate = 1.0 ave zone rate

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S General Testing of Smoothing Start with broad smoothing Compare the statistics of the observed spatial distribution with the spatial distribution from multiple realizations of te model –Nearest neighbor pdf –Separation distance pdf If rejected with high confidence (e.g. 95% or 99%) then reduce the smoothing and repeat In general, US practice leads to too much smoothing. –Standard practice does not apply checks of the smoothing –Beginning to see checks in some PSHA studies

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Double Counting of Ground Motion Variability Site-specific site response –Compute soil amplification Median amplification Variability of amplification Double Counting Issue –Site response variability is already in the ground motion standard deviation for empirical model

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Standard Deviation by VS30

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Approaches to Site Response Variability Common Practice –Use the variability of the amplification and live with the over-estimation of the total variability –Use only the median amplification and assume that the standard deviation used for the input rock motion is applicable to the soil Changes to practice –Reduce the variability of the rock ground motion Remove average variability for linear response –About 0.3 ln units Use downhole observation (e.g. Japanese data) to estimate reduction –About 0.35 ln units

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Double Counting of Ground Motion Variability Time Histories –Scaled recordings include peak-to-trough variability Double Counting Issue –Peak-to-trough variability is already in the ground motion standard deviation for empirical model –Variability effects are in the UHS –Use of spectrum compatible avoids the double counting

E E R I D I S T I N G U I S H E D L E C T U R E S E R I E S Summary Large variation in the state of practice of seismic hazard analysis around the world –Poor to very good –Significant misunderstandings of hazard basics remain Testing of models for consistency with available data is beginning for source characterization Common mixing of aleatory variability and epistemic uncertainty make it difficult to assess the actual epistemic part –For sources, avoid modeling aleatory variability as branches on logic tree –Move toward removing ergodic assumption for ground motion –Good practice currently removes ergodic for fault rupture Improved handoff of hazard information is beginning –Scenario spectra in addition to UHS