State of Practice of Seismic Hazard Analysis: From the Good to the Bad

1
State of Practice of Seismic Hazard Analysis
From the Good to the Bad

• Norm Abrahamson, Seismologist

Pacific Gas Electric Company
2
Seismic Hazard Analysis

• Approaches to design ground motion
• Deterministic
• Probabilistic (PSHA)
• Continuing debate in the literature about PSHA
• Time Histories
• Scaling
• Spectrum compatible

3
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

4
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

5
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?

6
2004 ParkfieldNear Fault PGA Values
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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.

8
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

9
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

10
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

11
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

12
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!

13
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

14
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

15
Terminology

• Aleatory Variability (random)
• Randomness in M, location, ground motion (e)
• 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

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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

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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)

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Unknown Die Example
Roll Model 1 Global Analog Model 2 Region Specific Model 3 Region Specific
1 1/6 0 0.05
2 1/6 0 0.09
3 1/6 0.25 0.18
4 1/6 0.50 0.36
5 1/6 0.25 0.18
6 1/6 0 0.09
7 0 0 0.05
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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

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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

21
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

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Overestimate of Epistemic Uncertainty

• Rate
• Constrained by paleo
• earthquake recurrence
• 600 Yrs for full rupture
• Mean char mag9.0
• Alternative mag distributions considered as
  epistemic uncertainty
• exponential model brought along with low weight,
  but leads to over-estimation of uncertainty

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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

24
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

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Problems with Current Practice

• Major problems have been related to the ground
  motion variability
• Ignoring the ground motion variability
• Assumes s0 for ground motion
• Considers including ground motion s as a
  conservative option
• This is simply wrong.
• Applying severe truncation to the ground motion
  distribution
• e.g. Distribution truncated at 1s
• Ground motions above 1s are considered
  unreasonable
• No empirical basis for truncation at less than
  3s.
• Physical limits of material will truncate the
  distribution

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Example of GM Variability

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GM Variability Example

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GM Truncation Effects (Bay Bridge)

29
2004 Parkfield


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Ergodic Assumption

• Trade space for time

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Mixing epistemic and aleatory(in Aleatory)
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Standard Deviations for LN PGA
Region Total Single Site
ChenTsai (2002) Taiwan 0.73 0.63
Atkinson (2006) Southern CA 0.71 0.62
Morikawa et al (2008) Japan 0.78
Lin et al (2009) Taiwan 0.73 0.62
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Single Ray Path
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Standard Deviations for LN PGA
Region Total Single Site Single Path and site
ChenTsai (2002) Taiwan 0.73 0.63
Atkinson (2006) Southern CA 0.71 0.62 0.41
Morikawa et al (2008) Japan 0.78 0.36
Lin et al (2009) Taiwan 0.73 0.62 0.37
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Removing the Ergodic Assumption

• Significant reduction in the aleatory variability
  of ground motion
• 40-50 reduction for single path - single site

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Hazard Example

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Die combine rolls (ergodic)
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Non-Ergodic Reduced Aleatory
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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

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Non-Ergodic Increased Epistemic
41
Standard Deviations for Surface Fault Rupture
Std Dev (log10)
Global Model (ave D) 0.28
Global Model Variability Along Strike 0.27
Total Global 0.39
Single Site 0.17
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Removing the Ergodic Assumption

• Single site aleatory variability
• Much smaller than global variability
• Value of even small number of site-specific
  observations

N Epistemic Std Dev In Median (log10)
0 0.35
1 0.17
2 0.12
3 0.10
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Large Impacts on Hazard
44
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

45
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)

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Crane Valley Dam Example

• Controlling Scenarios from deaggregation
• For return period 1500 years
• SA(T0.2) M5.5-6.0, R20-30 km
• Sa(T2) M7.5-8.0, R170 km

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Scenario Ground Motions
(Baker and Cornell Approach Conditional Mean
Spectra)
Find number of standard deviations needed to
reach UHS Next, Construct the rest of the
spectrum
48
Correlation of Epsilons
T1.5
T0.3
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Correlation of Variability

• Correlation decreases away from reference period
• Increase at short period results from nature of
  Sa

slope
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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

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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.

52
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

53
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

54
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)

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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)

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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 (Rlt50 km)
• In most cases, too much smoothing is applied
• Most PSHAs do not check amount of smoothing
• Is it consistent with observations?

57
ExampleCrane Vly Dam
San Andreas Flt
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Site-Specific Checks of Smoothing

• Assume Poisson with uniform rate within Sierra
  Nevada zone
• Mgt3, Rlt50, 24 years expect 20 eqk
• Observation
• Mgt3, Rlt50 km 40 earthquakes
• Mgt3, Rlt17 km 0 earthquakes
• Simple Tests
• If Poisson, what is the chance of gt40 eqk
• P lt 0.0001
• For Rlt50 km region, Rate is too low
• Too much smoothing

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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 0.007
• Indicates rate is not uniform within 50 km radius
• Too much smoothing
• Alternative method to set rate for Rlt17 km region
• No eqk observed
• What rate would lead to reasonable probability of
  producing the observation (no earthquakes)
• P0.5 , rate 0.3 ave zone rate
• P0.1 , rate 1.0 ave zone rate

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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

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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

62
Standard Deviation by VS30
63
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

64
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

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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