Abrahamson

8/12/2019 Abrahamson

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EERI DISTINGUISHED LECTURE SERIES 2009

State of Practice of SeismicHazard Analysis:

From the Good to the Bad

Norm Abrahamson, Seismologist

Pacific Gas & Electric Company


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Seismic Hazard Analysis

Approaches to design ground motion Deterministic

Probabilistic (PSHA)

Continuing debate in the literature about PSHA

Time Histories

Scaling Spectrum compatible


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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


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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 athreshold to determine probability of exceedance


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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 weselect?


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2004 Parkfield

Near Fault PGA Values

QuickTime and a

Photo - JPEG decompressorare needed to see this picture.

0.21

0.10

0.33

0.55

0.17

0.30

0.37

>1

0.230.16 0.22 0.13 0.16

1.31

0.31

1.130.63

0.21

0.28

0.85

0.43

0.25

0.11 0.08

0.39

0.25

0.30

0.580.58

0.63

0.450.85

0.51

0.82

0.84

0.20

0.23

0.23

0.17

30.490.25


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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-caseground motion for this earthquake

Chose something smaller than the worst-case

ground motion that is reasonable.


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What is Reasonable

The same number of standard deviation ofground motion may not be reasonable forall sources

Median may be reasonable for low activitysources, but higher value may be needed forhigh activity sources

Need to consider both the rate of theearthquake and the chance of the ground

motion


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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


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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


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C Mi d t di


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Common Misunderstandings

Standard ground motion models thought to givethe 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!

U d Mi f VS30


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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

Sl U f T M


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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

T i l


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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 toalternative hazard curves)

Reduced as knowledge improves

Al t d E i t i


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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 additionalstudies, 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 ample Unkno n Die


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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)

Unknown Die Example


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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 0.184 1/6 0.50 0.36

5 1/6 0.25 0.18

6 1/6 0 0.09

7 0 0 0.05

Epistemic Uncertainty


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Less data/knowledge implies greaterepistemic 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

Characterization of Epistemic Uncertainty


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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

U d ti ti f E i t i U t i t


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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

Overestimate of Epistemic Uncertainty


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Overestimate of Epistemic Uncertainty

Rate:

Constrained by paleo

earthquake recurrence

600 Yrs for full rupture

Mean char mag=9.0

Alternative mag distributionsconsidered as epistemicuncertainty

exponential modelbrought along with lowweight, but leads to over-estimation of uncertainty



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Good Practice Consider alternative credible models

Use minimum uncertainty for regions with few availablemodels

Check that observations are not inconsistent witheach alternative model

Poor Practice Models included because they were used in the past

Trouble comes from applying models in ways notconsistent with their original development

E.g. exponential model intended to fit observed rates ofearthquakes, not to be scaled to fit paleo-seismic recurrenceintervals

Ground Motion Models


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Ground Motion Models

Aleatory Standard practice to use published standard

deviations

Ergodic assumption - GM median and variability is the samefor 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 epistemicuncertainty

Issue with use of NGA models

Problems with Current Practice


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Problems with Current Practice

Major problems have been related to the ground motionvariability 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

Example of GM Variability


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Example of GM Variability

GM Variability Example


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GM Variability Example


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Bridge)

2004 Parkfield


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2004 Parkfield

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PeakAcceleratio

n(g)-AveHorizontalComp

Rupture Distance (km)

Median (Vs=380)

16th Percentile - intra-event

84th Percentile intra-event

H SHAKEMAP Stations

2 NSMP Stations

F CSMIP Stations

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PeakAcceleratio

n(g)-AveHorizontalComp

Rupture Distance (km)

Median (Vs=380)

16th Percentile - intra-event

84th Percentile intra-event

H SHAKEMAP Stations

2 NSMP Stations

F CSMIP Stations

Ergodic Assumption


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Ergodic Assumption

Trade space for time


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Mixingepistemic

and aleatory

(in Aleatory)

Standard Deviations for LN PGA


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Region Total Single Site

Chen&Tsai

(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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Region Total Single

Site

Single

Path and

site

Chen&Ts

ai (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

Removing the Ergodic Assumption


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g g p

Significant reduction in the aleatory variability of groundmotion 40-50% reduction for single path - single site

Hazard Example


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p

Die: combine rolls (ergodic)


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( g )

Non-Ergodic: Reduced Aleatory


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g y



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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

Non-Ergodic: Increased Epistemic


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Standard Deviations for Surface Fault Rupture


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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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Single site aleatory variability Much smaller than global variability

Value of even small number of site-specific observations

N Epistemic Std DevIn Median (log10)

0 0.35

1 0.172 0.12

3 0.10

Large Impacts on Hazard


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Keeping Track of Epistemic and Aleatory


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If no new data Broader fractiles No impact on mean hazard

Provides a framework for incorporation ofnew data as it becomes available

Identifies key sources of uncertainty Candidates for additional studies

Shows clear benefits of collecting new data

Hazard Reports


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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 periodidentifies the controlling M,R

Good practice hazard report includes: UHS

Deaggregation Representative scenario spectra that make up the UHS.

Conditional Mean Spectra (CMS)

Crane Valley Dam Example


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Controlling Scenarios from deaggregation For return period = 1500 years:

SA(T=0.2): M=5.5-6.0, R=20-30 km

Sa(T=2): M=7.5-8.0, R=170 km

Scenario Ground Motions


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(Baker and Cornell Approach: Conditional Mean Spectra)

Find number of

standard deviations

needed to reachUHS

Next,

Construct the rest

of the spectrum

Correlation of Epsilons


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T=1.5 T=0.3

Correlation of Variability


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Correlation

decreasesaway fromreference

period Increase at

short period

results fromnature of Sa

slo

pe


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Scenario Spectra for UHS Develop a suite of

deterministic scenariosthat comprise the UHS

Time histories shouldbe matched to thescenarios individually,not to the entire UHS

Improvements to PHSA Practice


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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 thestructure, not on the hazard analysis side.


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E l


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Example:

Crane Vly

Dam

San Andreas Flt

Site-Specific Checks of Smoothing


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Assume Poisson with uniform rate within SierraNevada zone M>3, R3, R3, R=40 eqk

P= < 0.0001

For R


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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 R


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Start with broad smoothing

Compare the statistics of the observed spatialdistribution with the spatial distribution from multiplerealizations of te model

Nearest neighbor pdf Separation distance pdf

If rejected with high confidence (e.g. 95% or 99%) thenreduce 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

Double Counting of Ground Motion Variability


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Site-specific site response Compute soil amplification

Median amplification

Variability of amplification

Double Counting Issue

Site response variability is already in theground motion standard deviation for

empirical model

Standard Deviation by VS30


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100 1000 2000VS30 (m/s)

T=0.2 sec

T=1.0 sec

Approaches to Site Response Variability


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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 motionis 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 estimatereduction

About 0.35 ln units

Double Counting of Ground Motion Variability


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Time Histories Scaled recordings include peak-to-trough

variability

Double Counting Issue

Peak-to-trough variability is already in the

ground motion standard deviation forempirical model

Variability effects are in the UHS

Use of spectrum compatible avoids the

double counting

Summary Large variation in the state of practice of seismic hazard


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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 isbeginning for source characterization

Common mixing of aleatory variability and epistemicuncertainty 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

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