A Framework and Methods for Characterizing Uncertainty in Geologic Maps

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