A Framework and Methods for Characterizing Uncertainty in Geologic Maps Donald A. Keefer Illinois State Geological Survey

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

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

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

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

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

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

Uncertainty Source #2 Amount 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

Methods for estimating #2 uncertainty Area of Influence (Singer and Drew, 1976) Non-traditional application of cross validation Semivariogram analysis with conditional simulation

An example of the Area of Influence method being applied to a data set. Data points are shown as black dots.

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.

Cross Validation Analysis identifying anomalous values and their potential impact on a map

Uncertainty Source #3 Complexity 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

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

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

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

Uncertainty Source #4 Errors 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

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

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

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

Semivariogram Analysis for Estimating Uncertainty due to Errors in Interpretation Conceptual Model Well Data Small variability at short distances Distinct anisotropy Subtle anisotropy Large variability at short distances Smaller total variance Larger total variance Sometimes a conceptual model is informed by more than just well data

Semivariogram Analysis for Estimating Uncertainty due to Errors in Interpretation Distinct anisotropy Small variability at short distances Conceptual Model Well Data Sometimes the well data are consistent with the conceptual model properties.

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

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

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