The EPRI Bayesian Mmax Approach for Stable Continental Regions SCR Johnston et al' 1994 Robert Young

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The EPRI Bayesian Mmax Approach for Stable
Continental Regions (SCR)(Johnston et al.
1994)Robert YoungsAMEC Geomatrix
Figure A61

• USGS Workshop on Maximum Magnitude Estimation
• September 8, 2008

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Statistical Estimation of mu (Mmax)
Figure A62

• Assumption - earthquake size distribution in a
  source zone conforms to a truncated exponential
  distribution between m0 and mu
• Likelihood of mu given observation of N
  earthquakes between m0 and maximum observed,
  mmax-obs

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Plots of Likelihood Function for mmax-obs 6
Figure A63
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Results of Applying Likelihood Function
Figure A64

• mmax-obs is the most likely value of mu
• Relative likelihood of values larger than
  mmax-obs is a strong function of sample size and
  the difference mmax-obs m0
• Likelihood function integrates to infinity and
  cannot be used to define a distribution for mu
• Hence the need to combine likelihood with a prior
  to produce a posterior distribution

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Approach for EPRI (1994) SCR Priors
Figure A65

• Divided SCR into domains based on
• Crustal type (extended or non-extended)
• Geologic age
• Stress regime
• Stress angle with structure
• Assessed mmax-obs for domains from catalog of SCR
  earthquakes

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Bias Adjustment (1 of 2)
Figure A66

• bias correction from mmax-obs to mu based on
  distribution for mmax-obs given mu
• For a given value of mu and N estimate the median
  value of mmax-obs ,
• Use to adjust from mmax-obs
  to mu

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Bias Adjustment (2 of 2)
Figure A67

• Example
• mmax-obs 5.7
• N(m 4.5) 10
• mu 6.3 produces 5.7

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Domain Pooling
Figure A68

• Obtaining usable estimates of bias adjustment
  necessitated pooling like domains (trading
  space for time)
• Super Domains created by combining domains with
  the same characteristics
• Extended crust - 73 domains become 55 super
  domains, average N 30
• Non-extended crust 89 domains become 15 super
  domains, average N 120

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EPRI (1994) Category Priors
Figure A69

• Compute statistics of mmax-obs for extended and
  non extended crust
• Use average sample size to adjust to mu

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EPRI (1994) Regression Prior
Figure A610

• Regress mmax-obs against domain characterization
  variables
• Default region is non-extended Cenozoic crust
• Dummy variables indicating other crustal types,
  ages, stress conditions, and a continuous
  variable for ln( activity rate ) indicate
  departure from default.
• Model has low r2 of 0.29 not very effective in
  explaining variations

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Example Application Using Category Prior
Figure A611
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Summary
Figure A612

• Bayesian approach provides a means of using
  observed earthquakes to assess distribution for
  mu
• Requires an assessment of a prior distribution
  for mu
• Johnston et al. (1994) developed two types
• crustal type category extended or non-extended
• a regression model (low r2 and high correlation
  between predictor variables)
• Bayesian approach is not limited to the Johnston
  et al. (1994) priors, any other prior may be used