A Framework and Methods for Characterizing Uncertainty in Geologic Maps

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A Framework and Methods for Characterizing
Uncertainty in Geologic Maps

• Donald A. Keefer
• Illinois State Geological Survey

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Uncertainty. Why do we need to worry about it?

• Computerization of geologic data and maps has
  made it easier to use these maps and data in
  solving different problems
• Sophisticated users are calling for information
  on the accuracy and uncertainty of geologic maps
• Uncertainty assessments can provide information
  that can
• be of use during a mapping project by informing
  the geologist about possible errors in the
  interpretation of one or more units
• guide wise use of the maps for decision support
  in different disciplines

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Why are uncertainty assessments so uncommon?

• Lack of clarity on what uncertainty means
• The absence of a widely used framework for
  defining and understanding uncertainty in
  geologic maps
• The absence of a suite of methods that can be
  readily used by most geologists and that is
  correlated to the various sources of uncertainty
  that are defined within this framework
• Most geologists dont see them as useful

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Uncertainty in Geologic Maps

• Uncertainty can be defined as
• the expected distribution of possible values for
  a property, or
• the error potential in the reported value of a
  property
• Geologic maps are the results of complex
  interpretations based on many different data
  values and usually multiple types of different
  data
• The uncertainty of a geologic map is a
  combination of several different sources of
  uncertainty
• Accurate quantitative calculation of uncertainty
  is probably impossible for maps, particularly
  without a systematic framework for understanding
  the components of uncertainty
• Map uncertainty calculations need to be seen as
  estimates, even if the measurements are
  quantitative

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Four major sources of uncertainty in geologic
maps

• Data accuracy and precision
• The amount and spatial distribution of data
• The complexity of the geologic system being
  mapped
• Geologic interpretations

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• Estimating the uncertainty of a geologic map
  based on these 4 major sources will provide
  insight on
• how the accuracy of the map varies
• the relevance of specific uncertainties to
  different applications
• where different interpretations are based more on
  data or on conceptual models

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Uncertainty Source 1Data Accuracy and Precision

• Lack of accuracy or precision of observations,
  measurements or calculations
• Data uncertainties affect the information and the
  interpretations that can be reliably identified
  from the data
• Bardossy and Fodor (2001) identify several
  methods for estimating uncertainty. Of these,
  probabilistic, possibilistic and hybrid methods
  are most promising for quantitatively estimating
  uncertainty in geologic data

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Uncertainty Source 2Amount and Spatial
Distribution of Data

• Uncertainties in final map due to non-uniform and
  sparse distributions of data
• Creates uncertainties in both the size of map
  features that can be reliably identified within a
  map and the accuracy of the edges of individual
  mapped units
• Data distribution uncertainties are affected by
  data accuracy and precision

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Methods for estimating 2 uncertainty

• Area of Influence (Singer and Drew, 1976)
• Non-traditional application of cross validation
• Semivariogram analysis with conditional simulation

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An example of the Area of Influence method being
applied to a data set. Data points are shown as
black dots.
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The method can accommodate uncertainty
in correctly identifying targets when they are
sampled. Here is another example where there is
a 30 chance that the target will not be
correctly identified, even when it is
encountered.
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Cross Validation Analysis identifying
anomalous values and their potential impact on a
map
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Uncertainty Source 3Complexity of Geology

• Inherent complexity of deposit geometry and
  properties within the mapping area
• Complexity affects both the resolvable detail
  from each data type and the scale and fraction of
  geologic features that are identifiable within
  the maps
• These uncertainties are unaffected by data
  accuracy and precision, spatial distribution of
  data and our ability to understand and describe
  the actual distributions and properties of the
  units within the mapping area

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How do we describe geologic complexity?

• Bardossy and Fodor (2001) suggest variability is
  the property that should be used to estimate this
  source of uncertainty
• Many measures of variability are available
• Complexity changes vertically and horizontally
  within any map area. This means that methods are
  needed which can observe and accommodate these
  kinds of changes
• Application needs can be used to guide selection
  of complexity measures

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Methods for estimating 3 uncertainty

• Exploratory Spatial Data Analysis (ESDA)
• Many useful methods available
• Atypical methods can be useful, particularly
  analysis of proportions for rock types,
  estimation of transition probabilities for rock
  types
• Use of various-sized 2-D and 3-D moving windows
  for calculation of localized statistics
• Semivariogram analysis with exploration of
  consequences of data errors
• Cross validation

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Semivariogram Analysis for Estimating Uncertainty
due to Geologic Complexity
Can also use methods which allow exploration of
consequences of data errors.
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Uncertainty Source 4Errors in Interpretations

• Interpretation errors affect the reliability of
  the map units and properties that are described
  on the map
• Interpretation errors are affected by all three
  of the other sources of uncertainty
• Reliable estimation of interpretation errors
  requires consideration of
• Types of interpretations made
• How other errors propagate in later
  interpretations

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Common Types of Interpretations in Geologic Maps

• Defining geological framework of the mapping
  units
• Correlating observations to map units for each
  data point
• Correlating and interpolating between data
  locations
• Finalizing interpolation for the end products

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Methods for estimating 4 uncertainty

• Calculation and evaluation of residuals between
  data and maps
• Comparison of properties between interpreted
  data, map distributions, conceptual models and
  outcrop/modern analogues
• Detailed and explicit description of conceptual
  model with recognition given to observed vs
  expected anisotropy, length scales and rock type
  proportions and transition probabilities
• Semivariogram analysis and comparisons between
  data, map conceptual models outcrop/modern
  analogues
• Analysis of conditional simulation results
• Evaluation of other three sources of uncertainty
  and possible consequences to interpretations made

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Explicitly Describing Conceptual Models Via
Assessment of Regional Characteristics

• Delineation of zones with distinctive variations
  in mapped properties
• These zones can be based on depositional
  properties inherent to possible conceptual
  models
• ice movement
• location and nature of ice boundaries
• general depositional framework
• type and thickness of sediment distributions,
• expected variabilities (a.k.a., heterogeneities,
  anisotropies) in facies, porosity, permeability,
  etc.

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Semivariogram Analysis for Estimating Uncertainty
due to Errors in Interpretation
Distinct anisotropy
Conceptual Model
Larger total variance
Small variability at short distances
Subtle anisotropy
Well Data
Smaller total variance
Large variability at short distances
Sometimes a conceptual model is informed by more
than just well data
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Semivariogram Analysis for Estimating Uncertainty
due to Errors in Interpretation
Distinct anisotropy
Conceptual Model
Well Data
Small variability at short distances
Sometimes the well data are consistent with the
conceptual model properties.
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Exploring the Map Uncertainty due to Errors in
Interpretation using Conditional Simulation
Tiskilwa Formation Average Thickness Standard
Deviation in Thickness Values
Sand below the Batestown Member Average
Thickness Standard Deviation in Thickness Values
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What does this framework do for us?

• Helps ensure
• All components of uncertainty are considered
• Possible interdependencies between sources of
  uncertainty are identified and estimated
• Appropriate estimation methods are used
• Provides geologists with flexibility and
  opportunity for consistent and accurate
  assessments
• The use of several different estimation methods
  when evaluating each sources of uncertainty can
  provide additional insight and can increase the
  relevance of the assessment for map users and
  decision makers

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Considerations for selection of appropriate
uncertainty estimation methods

• Mapping objectives
• Size of map area
• Nature of uncertainty within the maps
• Intended map products
• Application needs which will utilize uncertainty
  estimations
• Geologic expertise of expected users of
  uncertainty estimations
• Other possible uses of the maps