Logic Tree Approach Used In Logic Tree Approach Used In PSHAPSHA

Presented ByPresented By

RAVINDRA K. GOLIYARAVINDRA K. GOLIYA

IntroductionIntroduction

Logic tree address uncertainty involved in SHA. Logic tree address uncertainty involved in SHA.

Uncertainties in SHA are dealt in sequential Uncertainties in SHA are dealt in sequential manner. manner.

Breaks a complex problem into smaller simple Breaks a complex problem into smaller simple problems.problems.

First introduced into probabilistic seismic hazard First introduced into probabilistic seismic hazard analysis (PSHA) by Kulkarni et al. (1984)analysis (PSHA) by Kulkarni et al. (1984)

Seismic Hazard AnalysisSeismic Hazard Analysis

Quantitative estimation of ground shaking hazards at a Quantitative estimation of ground shaking hazards at a particular site. particular site.

Deterministic Seismic Hazard Analysis (DSHA)Deterministic Seismic Hazard Analysis (DSHA)

Probabilistic Seismic Hazard Analysis (PSHA)Probabilistic Seismic Hazard Analysis (PSHA)

Steps involved in DSHASteps involved in DSHA

Identification and characterization of sourcesIdentification and characterization of sources

Selection of a source-to-site distance parameterSelection of a source-to-site distance parameter

Selection of the controlling earthquake.Selection of the controlling earthquake.

Hazard defined in terms of ground motion Hazard defined in terms of ground motion parameters.parameters.

Steps involved in PSHASteps involved in PSHA

Identification and characterization of source zone.Identification and characterization of source zone.

Seismicity of source zone is then characterized. Seismicity of source zone is then characterized.

Ground motion parameters are determined using Ground motion parameters are determined using predictive relationships. predictive relationships.

Probability of exceedence of ground motion Probability of exceedence of ground motion parameter during a particular time period is parameter during a particular time period is found.found.

Types of uncertainties involved in Types of uncertainties involved in SHASHA

There are two types of uncertainties that are There are two types of uncertainties that are dealt with in SHA :dealt with in SHA :

Aleatory uncertaintyAleatory uncertainty

Epistemic uncertaintyEpistemic uncertainty

Aleatory UncertaintyAleatory Uncertainty

Uncertainties that are related to an apparent Uncertainties that are related to an apparent

randomness in nature. randomness in nature.

It is easy to incorporate such variability directly It is easy to incorporate such variability directly

into the hazard calculations. into the hazard calculations.

Ground motion prediction equations are the Ground motion prediction equations are the

most important aleatory uncertainty in SHA.most important aleatory uncertainty in SHA.

Epistemic UncertaintyEpistemic Uncertainty

Uncertainties due to insufficient knowledge are Uncertainties due to insufficient knowledge are

known as epistemic uncertainties. known as epistemic uncertainties.

The main epistemic uncertainties involved in any The main epistemic uncertainties involved in any

SHA: SHA: Characteristics of the seismic source zones Characteristics of the seismic source zones The model for the recurrence relationship.The model for the recurrence relationship. The maximum earthquake magnitude. The maximum earthquake magnitude.

Logic TreeLogic Tree

Logic tree contains a series of nodes and Logic tree contains a series of nodes and branches. branches.

Each node represents an assessment of a state Each node represents an assessment of a state of nature or an input parameter. of nature or an input parameter.

Branch represents one possible discrete Branch represents one possible discrete alternative for the state of nature. alternative for the state of nature.

Branches are weighted suitably.Branches are weighted suitably.

A typical Logic Tree

Logic Tree contd…Logic Tree contd…

Logic Tree contd…Logic Tree contd…

It is advisable that a sufficient number of It is advisable that a sufficient number of

branches are placed at a given node to branches are placed at a given node to

adequately represent the uncertainty in the adequately represent the uncertainty in the

parameter estimation.parameter estimation.

Logic Tree WeightsLogic Tree Weights

Probabilities that represent the relative Probabilities that represent the relative likelihood or degree of belief that the branch likelihood or degree of belief that the branch represents are known as weights. represents are known as weights.

The weights are usually based on subjective The weights are usually based on subjective judgments.judgments.

Logic Tree Weights contd…Logic Tree Weights contd…

Vick (2002) defines :Vick (2002) defines :

Probability as a measure of stable Probability as a measure of stable frequency.frequency.

An expression of belief.An expression of belief.

Features of Logic Tree Weights based on Features of Logic Tree Weights based on frequency-based probabilitiesfrequency-based probabilities

1. Weights at a node must sum to unity.1. Weights at a node must sum to unity.

2. Events for which they are defined must be 2. Events for which they are defined must be exhaustive.exhaustive.

3. Events for which they are defined must be 3. Events for which they are defined must be mutually exclusive.mutually exclusive.

4. Must represent the relative rate at which 4. Must represent the relative rate at which alternative events are occurring.alternative events are occurring.

Features of logic-tree weights based on Features of logic-tree weights based on degree of beliefdegree of belief

1.1. Weights at a node should sum to unity.Weights at a node should sum to unity.

2.2. Branches do not include all of the possible Branches do not include all of the possible alternatives.alternatives.

3.3. Options on the branches of a logic tree will not Options on the branches of a logic tree will not be mutually exclusive.be mutually exclusive.

4.4. Weighted average of the hazard values does Weighted average of the hazard values does not give the expected value.not give the expected value.

How to assign weights?How to assign weights?

General considerationsGeneral considerations

Multiple set of relative weights applicable to the Multiple set of relative weights applicable to the selected equations should be adopted. selected equations should be adopted.

The degree of dependence between branches of The degree of dependence between branches of the logic tree should also be considered. the logic tree should also be considered.

Criteria for Grading Candidate EquationsCriteria for Grading Candidate Equations

Candidate equations should be grouped into two Candidate equations should be grouped into two categories – intrinsic and application specific.categories – intrinsic and application specific.

Intrinsic factors - confidence of the user in a Intrinsic factors - confidence of the user in a particular equation. particular equation.

The application-specific characteristics can be The application-specific characteristics can be divided into those divided into those

related to the conventions adopted for the hazard related to the conventions adopted for the hazard calculations.calculations.

related to the specific environment for which the SHA related to the specific environment for which the SHA is performed.is performed.

Ranking and Combining Criteria for Logic Ranking and Combining Criteria for Logic Tree WeightsTree Weights

a hierarchy for the influence of each factor on the a hierarchy for the influence of each factor on the final weighting.final weighting.

a transparent system for combining the grading a transparent system for combining the grading for the different factors into a single weight.for the different factors into a single weight.

Logic Tree for New Madrid Seismic Logic Tree for New Madrid Seismic Zone: A Case StudyZone: A Case Study

Source model alternatives for the

New Madrid seismic zone.

The area considered The area considered in the study is, as in the study is, as shown in the adjacent shown in the adjacent figure, between 35figure, between 35ooN N to 38to 38ooN latitude and N latitude and 8888ooW to 92W to 92ooW W longitude. Different longitude. Different faults and position of faults and position of past earthquakes are past earthquakes are also shown in the also shown in the same figure.same figure.

The adjacent figure The adjacent figure presents a Logic Tree presents a Logic Tree for the New Madrid for the New Madrid Seismic Zone. Seismic Zone.

Using a logic tree to incorporate model Using a logic tree to incorporate model alternatives into a seismic hazard analysis alternatives into a seismic hazard analysis leads to a distribution of possible seismic leads to a distribution of possible seismic hazard results. This distribution can be hazard results. This distribution can be represented by a mean seismic hazard map represented by a mean seismic hazard map and a coefficient of variation (COV) map as and a coefficient of variation (COV) map as shown in the figures below. shown in the figures below.

Other issues related to Logic TreesOther issues related to Logic Trees

Selection of specific ground motion prediction Selection of specific ground motion prediction relations. relations.

Multiple opinions are not uniform data sets and Multiple opinions are not uniform data sets and cannot be averaged.cannot be averaged.

Logic trees make sense when used in Logic trees make sense when used in earthquake risk analysis. earthquake risk analysis.

Problems with Logic Tree approachProblems with Logic Tree approachProblems with Logic Tree approach as listed by E. Problems with Logic Tree approach as listed by E. L. Krinitzsky (1995):L. Krinitzsky (1995):

Other attenuations could have been used in Other attenuations could have been used in logic tree.logic tree.

The weightings are arbitrary and are no more The weightings are arbitrary and are no more than guesses. than guesses.

Maximum magnitudes with the percentage Maximum magnitudes with the percentage weightings could have been made into an almost weightings could have been made into an almost infinite series of weighted values.infinite series of weighted values.

Recurrence rate and b-values are totally Recurrence rate and b-values are totally unsuitable for generating design values.unsuitable for generating design values.

ConclusionConclusion

Best way to address procedure related, or Best way to address procedure related, or epistemic uncertainties, is using Logic Trees.epistemic uncertainties, is using Logic Trees.

Ground motion models used should very closely Ground motion models used should very closely represent the future ground motion.represent the future ground motion.

Epistemic uncertainty should be addressed fully. Epistemic uncertainty should be addressed fully.

Importance of the weights decreases as the Importance of the weights decreases as the number of branches used in Logic Tree number of branches used in Logic Tree increases. increases.

Issues rose by different researchers in their Issues rose by different researchers in their papers should also be kept in mind.papers should also be kept in mind.