lecture17-PSHA-part2

Slide 1

1Probabilistic Seismic Hazard Analysis (PSHA) Part IILecture-17Temporal uncertaintyPoisson process- describes number of occurrences of an event during a given time interval or spatial region.1.The number of occurrences in one time interval are independent of the number that occur in any other time interval.2.Probability of occurrence in a very short time interval is proportional to length of interval.3.Probability of more than one occurrence in a very short time interval is negligible.

2Probabilistic Seismic Hazard Analysis2Temporal uncertaintyPoisson process

where n is the number of occurrences and is the average number of occurrences in the time interval of interest.

3Probabilistic Seismic Hazard Analysis

Temporal uncertaintyPoisson processLetting = t

=1- P[N=0] =1- e-t


4Temporal uncertaintyPoisson processP = 1 e-t Consider a event that occurs, on average, every 1,000 yrs. What is the probability it will occur at least once in a 100yr period?

=1/1000 = 0.001P = 1-exp[-(0.001)(100)] = 0.09525Probabilistic Seismic Hazard AnalysisTemporal uncertaintyWhat is the probability it will occur at least once in a 1,000 yr period?

P = 1 exp[-(0.001)(1000)] = 0.632

Solving for ,


7Temporal uncertaintyThen, the annual rate of exceedance for an event with a 10% probability of exceedance in 50 yrs is

The corresponding return period is TR= 1/ = 475 yrs.For 2% in 50 yrs, = 0.000404/yr TR = 2475 yrs.Probabilistic Seismic Hazard Analysis

8Summary of uncertainties

Location fR(r)

Size fM(m)

Effects P[Y>Y* l M=M*, R=R*]

Timing P=1-e-t Probabilistic Seismic Hazard AnalysisSource-site distance pdfMagnitude pdfAttenuation relationship including standard errorPoisson modelCombining uncertainties probability computations

P[A] = P[AB1] + P[A B2] +.+ P[A BN]

P[A] = P[A|B1]P[B1] + P[A|B2] P[B2] +.+ P[A|BN] P[BN]

9Probabilistic Seismic Hazard AnalysisBBB1B2B3B4B5ATotal Probability TheoremCombining uncertainties probability computationsApplying total probability theorem,

P[Y > y*] = P[Y > y*| X] P[X] = P [Y >y*|X] fx (X)dxwhere X is a vector of parameters.

We assume that M and R are the most important parameters and that they are independent. Then,

P[Y > y*] = P [Y >y*|m, r] fM (m)fR (r)dmdr

10Probabilistic Seismic Hazard AnalysisCombining uncertainties-probability computationsP[Y > y*] = P [Y >y*|m, r] fM (m)fR (r)dmdr

Above equation gives the probability that y* will be exceeded if an earthquake occurs. Can convert probability to annual rate of exceedance by multiplying probability by annual rate of occurrence of earthquakes.

y* =v P [Y >y*|m, r] fM (m)fR (r)dmdrwhere v = exp[- m0]

11Probabilistic Seismic Hazard Analysis12Combining uncertainties-probability computations

If the site of interest is subjected to shaking from more than one site (say Ns sites), then

For realistic cases, pdfs for M and Rare too complicated to integrate analytically. Therefore, we do it numerically.Probabilistic Seismic Hazard Analysis

13Combining uncertainties-probability computations

Dividing the range of possible magnitudes and distances into NM and NR increments, respectively

This expression can be written, equivalently as

Probabilistic Seismic Hazard Analysis

Combining uncertainties-probability computationsWhat does it mean?


All possible distances are considered- contribution of each is weighted by its probability of occurrenceAll sites are consideredAll possible effects are considered- each weighted by its conditional probability of occurrenceAll possible magnitudes are considered- contribution of each is weighted by its probability of occurrenceProbabilistic Seismic Hazard Analysis

Combining uncertainties-probability computationsCompute conditional probability for each element on gridEnter in matrix (spreadsheet cell)15ln Yln Ylog Rr1r2r3rNY = Y*P[Y>Y*| M=m2, R=r1]P[Y>Y*| M=m2, R=r2]P[Y>Y*| M=m2, R=r3]Combining uncertainties-probability computationsSeismic hazard curve shows the mean annual rate of exceedance of a particular ground motion parameter. A seismic hazard curve is the ultimate result of a PSHA.16Probabilistic Seismic Hazard Analysis

log amax

log TR

amax

Using seismic hazard curvesCombining uncertainties-probability computationsContribution of sourcesCan break values down into contributions from each source.Plot seismic hazard curves for each source and total seismic hazard curve (equal to sum of source curves)Curves may not be parallel, may crossShows which source(s) most important.

17Probabilistic Seismic Hazard Analysislog amax

log TR

amax 2

Total

3

1Using seismic hazard curvesCombining uncertainties-probability computationsContribution of sourcesCan develop seismic hazard curves for different ground motion parametersPeak accelerationSpecial accelerationsOtherChoose desired value Read corresponding parameter values from seismic hazard curves


log TR

amax, Sa Total

Using seismic hazard curvesContribution of sourcesCan develop seismic hazard curves for different ground motion parametersPeak accelerationSpecial accelerationsOtherChoose desired value Read corresponding parameter values from seismic hazard curves


log TR

amax, Sa Probabilistic Seismic Hazard Analysis Disaggregation (De-aggregation) Common question:What magnitude & distance does that amax value correspond to?

5.05.56.06.57.07.58.08.525km0.010.010.020.03

0.030.02

0.01

0.01

50km

0.020.030.040.040.050.04

0.030.02

75km

0.030.030.050.060.090.060.050.02

100km

0.030.030.050.050.080.050.050.02125km

0.020.020.03

0.040.050.030.020.01

150km0.010.010.020.030.050.020.01

0.00175km0.000.000.01

0.01

0.030.01

0.010.00

200km0.000.00

0.00

0.00

0.01

0.00

0.00

0.00

Total hazard includes contributions from all combinations ofM & R20Probabilistic Seismic Hazard AnalysisDisaggregation (De-aggregation)Common question5.05.56.06.57.07.58.08.525km0.010.010.020.030.030.020.010.0150km0.020.030.040.040.050.040.030.0275km0.030.030.050.060.090.060.050.02100km0.030.030.050.050.080.050.050.02125km0.020.020.030.040.050.030.020.01150km0.010.010.020.030.050.020.010.00175km0.000.000.010.010.030.010.010.00200km0.000.000.000.000.010.000.000.00What magnitude & distance does that amax value correspond to?Total hazard includes contributions from all combinations of M & R.Break hazard down into contributions to see where hazard is coming from.M=7.0 at R=75km21Logic tree methodsNot all uncertainty can be described by probability distributions

Most appropriate model may not be clearAttenuation relationshipMagnitude distributionetcExperts may disagree on model parametersFault segmentationMaximum magnitudeetc22Probabilistic Seismic Hazard AnalysisLogic tree methodsm23Probabilistic Seismic Hazard AnalysisAttenuation ModelMagnitudeDistributionMmaxBJFA&SG-RCharG-RChar(0.5)(0.7)(0.5)(0.7)(0.3)(0.3)7.0 (0.2)7.5 (0.2)7.0 (0.2)7.0 (0.2)7.0 (0.2)7.5 (0.2)7.5 (0.2)7.5 (0.2)7.2 (0.6)7.2 (0.6)7.2 (0.6)7.2 (0.6)Logic tree methodsm24Probabilistic Seismic Hazard AnalysisAttenuation ModelMagnitudeDistributionMmaxBJFA&SG-RCharG-RChar(0.5)(0.7)(0.5)(0.7)(0.3)(0.3)7.0 (0.2)7.5 (0.2)7.0 (0.2)7.0 (0.2)7.0 (0.2)7.5 (0.2)7.5 (0.2)7.5 (0.2)7.2 (0.6)7.2 (0.6)7.2 (0.6)7.2 (0.6)Sum of weighing factors coming out of each node must equal 1.0Logic tree methodsm25Probabilistic Seismic Hazard AnalysisAttenuation ModelMagnitudeDistributionMmaxBJFA&SG-RCharG-RChar(0.5)(0.7)(0.5)(0.7)(0.3)(0.3)7.0 (0.2)7.5 (0.2)7.0 (0.2)7.0 (0.2)7.0 (0.2)7.5 (0.2)7.5 (0.2)7.5 (0.2)7.2 (0.6)7.2 (0.6)7.2 (0.6)7.2 (0.6)0.5x0.7x0.2 = 0.07Logic tree methodsm26Probabilistic Seismic Hazard AnalysisAttenuation ModelMagnitudeDistributionMmaxBJFA&SG-RCharG-RChar(0.5)(0.7)(0.5)(0.7)(0.3)(0.3)7.0 (0.2)7.5 (0.2)7.0 (0.2)7.0 (0.2)7.0 (0.2)7.5 (0.2)7.5 (0.2)7.5 (0.2)7.2 (0.6)7.2 (0.6)7.2 (0.6)7.2 (0.6)0.5x0.7x0.2 = 0.07Logic tree methodsm27Probabilistic Seismic Hazard AnalysisAttenuation ModelMagnitudeDistributionMmaxBJFA&SG-RCharG-RChar(0.5)(0.7)(0.5)(0.7)(0.3)(0.3)7.0 (0.2)7.5 (0.2)7.0 (0.2)7.0 (0.2)7.0 (0.2)7.5 (0.2)7.5 (0.2)7.5 (0.2)7.2 (0.6)7.2 (0.6)7.2 (0.6)7.2 (0.6)Final value of Y is obtained as weighted average of all values given by terminal branches of logic tree. 0.070.070.030.210.090.030.090.070.070.210.030.03W

Probabilistic Seismic Hazard AnalysisLogic tree methods

Recent PSHA logic tree included: Crustal areal source zones7 source zones2 attenuation relationships3 maximum magnitudes2 recurrence models3 source depths 252 terminal branches

Total PSHA required analysis of 612 combinations2829Reiter, L. (1990) Earthquake Hazard Analysis: Issues and insights, Columbia university press.Kramer (1996) Geotechnical Earthquake Engineering, Prentice Hall.Anderson, J.G. and J.N. Brune (1999). Probabilistic hazard analysis without the ergodic assumption, Seism. Res. Lett. 70, 19-23.Cornell, C.A. (1968). Engineering seismic risk analysis, Bull. Seism. Soc. Am., 58, 1583-1606.http://geo.cv.nctu.edu.tw/prob/download/SeismicHazardAnalysis.pdf (Accessed on 30 March 2012)http://www.nibs.org/client/.../Topic05a-SeismicHazardAnalysisNotes.pdf (Accessed on 30 March 2012) Recommended Reading

lecture17-PSHA-part2

Documents

Transcript of lecture17-PSHA-part2