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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 problemsSophisticated users are calling for information on the accuracy and uncertainty of geologic mapsUncertainty assessments can provide
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1. A Framework and Methods for Characterizing Uncertainty in Geologic Maps Donald A. Keefer
Illinois State Geological Survey
2. 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
3. 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 don’t see them as useful
4. 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
5. 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
6. 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
7. Uncertainty Source #1:Data 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 Most error calculations have errors in themselves, so they are best understood as estimations.Most error calculations have errors in themselves, so they are best understood as estimations.
8. 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
9. Methods for estimating #2 uncertainty Area of Influence (Singer and Drew, 1976)
Non-traditional application of cross validation
Semivariogram analysis with conditional simulation
13. 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
14. 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
15. 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
16. Semivariogram Analysis for Estimating Uncertainty due to Geologic Complexity Conceptual models were smoother than data values predicted – much more so than expected
Data: large variability over small distances, smaller total variance, weak anisotropy
Conceptual models: small variability over small distances, larger total variance, more anisotropy
Conceptual models were smoother than data values predicted – much more so than expected
Data: large variability over small distances, smaller total variance, weak anisotropy
Conceptual models: small variability over small distances, larger total variance, more anisotropy
17. 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
18. 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
19. 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
20. 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.
21. Semivariogram Analysis for Estimating Uncertainty due to Errors in Interpretation Conceptual models were smoother than data values predicted – much more so than expected
Data: large variability over small distances, smaller total variance, weak anisotropy
Conceptual models: small variability over small distances, larger total variance, more anisotropy
Conceptual models were smoother than data values predicted – much more so than expected
Data: large variability over small distances, smaller total variance, weak anisotropy
Conceptual models: small variability over small distances, larger total variance, more anisotropy
22. Semivariogram Analysis for Estimating Uncertainty due to Errors in Interpretation
23. Exploring the Map Uncertainty due to Errors in Interpretation using Conditional Simulation
24. 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
25. 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