Sampling the Subsurface in Final Status Decommissioning Surveys

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Sampling the Subsurface in Final Status
Decommissioning Surveys

• Carl V. Gogolak
• U.S. DHS Environmental Measurements Laboratory

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Sampling the Subsurface

• How is designing a sampling survey for subsurface
  materials different from designing a sampling
  survey for surface materials within the first 15
  cm of soil?
• At issue is how to design the survey more
  efficiently, because the sampling effort is
  considerably higher for subsurface sampling than
  it is for surface soil sampling.
• It doesnt have to be perfect, it only has to be
  better than what we are doing now, will a
  justifiable technical basis and no hidden
  assumptions

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Designing more efficient surveys

• The number of samples required in a survey can
  be reduced by increasing the information
  available by other means than simply taking more
  direct measurements. This can be done in two
  ways
• 1) increase the information available from
  professional knowledge of site processes,
  historical data, pollutant transport etc.
• 2) make more efficient use of the hard data that
  is already available by the use of more advanced
  statistical methods.

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Improved Survey Efficiency in MARSSIM

• Incorporates prior information qualitatively in
  Survey Unit Classification
• Sampling Design based on anticipated data
  variability of independent samples simple random
  sampling on systematic grid
• Data analysis based on nonparametric tests for
  independent identically distributed data
• Elevated areas found by scanning ELIPGRID can
  be used for the risk of missing an area

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Possibilities for further design efficiency

• Incorporate prior information quantitatively as
  soft data that can be combined with hard
  concentration data from samples- Bayesian
  Statistics
• Sampling Design based on maximizing the
  information that will be added (not all locations
  are equally informative)
• Geostatistical Data analysis that incorporates
  known spatial relationships among data locations
• Geophysical data may be used for scanning -
  Bayesian extensions to ELIPGRID

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Incorporating soft information

• Data other than the results of specific
  measurements at a location within the survey
  unit, soft information, can be incorporated
  into the process so that fewer hard data points
  will be required.
• Bayesian methods are used in statistics to make
  use of information available from prior
  knowledge.
• Geostatistical methods are used to make more
  efficient use of spatial data.

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Designing more efficient surveys

• The information added in this way can only aid
  the decision-making process if
• 1) the assumptions are reasonable (i.e. really
  add more of what we actually know about the
  physical processes underlying the data rather
  than just multiplying assumptions)
• 2) the methodology is implementable, i.e., can be
  made simple enough to be used in practice.

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TOOLS

• ASAP Adaptive Sampling and Analysis
• Developed at ANL
• Simple implementation of Bayesian Analysis
• Binomial distribution for number of samples
  exceeding DCGL
• Conjugate beta distribution for prior probability
  of exceeding the DCGL based on professional
  judgment (same as Sign p in MARSSIM)
• Indicator kriging of hard sample data updates
  prior probabilities
• Update based on number of pseudo-samples
  related to inverse of kriging variance

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TOOLS

• SADA Spatial Analysis for Decision Assistance
• Developed at UT
• Graphical User Interface for data display
• 2D and 3D capability
• Incorporates GSLIB geostatistical methods
• Freeware
• No third party software needed
• Flexible and customizable platform for
  development of ASAP and extensions to MARSSIM
  data design and analysis

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Summary of the Procedure

• (1) Roughly estimate, using whatever information
  is at hand, the probability that a sample taken
  at any given location, z, in the survey unit
  would result in a measurement exceeding the
  release criterion.
• (2) Roughly estimate the uncertainty of the
  estimate made in step 1.

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Prior Probability of Exceeding 3.0
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Uncertainty in the Prior Probability of Exceeding
3.0
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Summary of the Procedure

• (3) Convert (in software) these estimates of
  and F for the prior distribution of into the
  parameters " and of a Beta distribution.
• The information value of the prior knowledge
  implied by the specification of a particular Beta
  distribution with parameters a and ß is the same
  as that which would be obtained from a series of
  results (Bernoulli trials) with a -1 samples
  above the release criterion and ß-1 samples below
  the release criterion.

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Prior Probabilities

• One is estimating
• and where agt0 and ßgt0 are the parameters of a
  Beta distribution.

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Some combinations of a and b with the
corresponding values of m and s.
a b m s 1 1 0.500 0.289 1 2 0.333 0.236 1 3 0.
250 0.194 1 4 0.200 0.163 1 5 0.167 0.141 1 6 0
.143 0.124 1 7 0.125 0.110 1 8 0.111 0.099 1 9
0.100 0.090
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Some Beta Distributions
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Summary of the Procedure

• (4) Take data at n sample locations, and convert
  the results to an indicator variable which is
  equal to 1 if the measurement exceeds the release
  criterion, and 0 otherwise.
• SADA can be used to optimize the locations.

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Hard Data
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Summary of the Procedure

• (5) Perform indicator kriging using an
  exponential variogram model with appropriately
  estimated values of the parameters c0, c, and a.

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Exponential Variogram
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Summary of the Procedure

• (6) Update the parameters " and of the Beta
  distribution to obtain the posterior distribution
  of the probability of exceedence.

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Data above 3.0 are indicator transformed to 1,
below 3.0 to 0.
Indicator kriging interpolates those
probabilities between sample locations to a
value p(z) at each location z
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Updating Prior Probabilities

• Following the suggestion of Johnson (1996) the
  parameters of the beta distribution are updated
  using to x n p(z) with
• where c0 is the nugget, and c is the sill, of
  the assumed exponential semivariogram . The
  posterior update of a is a x. The posterior
  update of b is b n - x.

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Summary of the Procedure

• (7) Calculate updated estimates of the expected
  value, , and standard deviation, F, of the
  probability that a sample taken at the location
  z in the survey unit would result in a
  measurement exceeding the release criterion.

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Update of Prior Probabilities
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Update of Uncertainties
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Future development of SADA

• 1. Survey Sampling Design Optimizing the Number
  of Samples
• 2. Starting with (combined) professional judgment
  () obtain
• a secondary sampling design
• Develop a metric for optimizing the sample size
• 3. Variography and Variogram Specification
• using a Markov-Bayes type assumption on the soft
  data
• Exponential with no nugget global variance sill
  range guess
• 3rd dimension still tough
• 3. Elevated areas Bayesian Elipgrid
• 4. Develop Criteria for Determining Compliance