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Digital mapping: quantifying uncertainty 1 Jones et al 25.06.03 14:51
Digital field data acquisition: towards increased quantification
of uncertainty during geological mapping
RICHARD R. JONES,
CognIT a.s, Postboks 610, 1754 Halden, Norway
KENNETH J.W. MCCCAFFREY, ROBERT W. WILSON, and ROBERT E. HOLDSWORTH
Department of Geological Sciences, University of Durham, Durham, DH1 3LE, U.K.
Corresponding author: k.j.w.mccaffrey@durham.ac.uk
Number of words: 5977 (including all text, references, captions, tables).
Abbreviated title: "Digital mapping: quantifying uncertainty" (max. 40 chars)
Abstract __ Traditional methods of geological mapping were developed within the inherent
constraints imposed by paper-based publishing. These methods are still dominant in the Earth
Sciences, despite recent advances in digital technology in a range of fields that include
Geographical Positioning Systems, Geographical Information Systems, 3-D computer
visualisation, portable computer devices, knowledge engineering and Artificial Intelligence.
Digital geological mapping has the potential to overcome some serious limitations of paper-based
maps. Geological maps are usually highly interpretive, but traditional maps show little of the raw
field data collected or the reasoning used during interpretation. In geological mapping,
interpretation typically relies on the prior experience and prior knowledge of the mapper, but this
input is rarely shown explicitly with the final map. Digital mapping techniques open up new
possibilities for quantifying many types of uncertainty associated with the mapping process, and
using this uncertainty to evaluate the validity of competing interpretations.
__________________________________
Although the methodology of geological mapping has remained largely unchanged since William
Smith’s pioneering work two hundred years ago (Smith 1801, 1815), recent developments in
digital technology have the potential to revolutionise the way in which geological field data is
gathered, stored, processed, displayed and distributed. The digitalisation of field mapping is set to
occur through advances in GPS (“Geographical Positioning Systems”), GIS (“Geographical
Information Systems”), highly portable hand-held PDA devices (“Personal Digital Assistants”),
high powered 3-D computer graphics, and satellite communication equipment. In this paper we
present a justification of the fundamental importance of how this new technology can help to
improve some of the inherent limitations of traditional methods of geological mapping.
Digital mapping: quantifying uncertainty 2 Jones et al 25.06.03 14:51
Prior Information
In common usage the concept of "Prior Information" conveys a variety of meanings, largely
dependent upon context, ranging from philosophical to mathematical. This paper is not intended
as an exhaustive discussion on the semantics of prior information, but rather to focus
pragmatically on specific issues that have direct relevance to the process of geological mapping.
Relationship between information and knowledge
In relation to geosciences it is convenient for us to consider “prior information” in a broad way
that also encompasses related concepts such as “data” and “knowledge”. During the last decade
many business sectors, including the hydrocarbon and mining industries have focused heavily on
maximising re-use of corporate knowledge and expertise. This highly profit-driven process has
given rise to very pragmatic research in areas of applied knowledge engineering. Workers in these
fields (e.g. van der Spek & Spijkervet 1997; Liebowitz & Beckman 1998) generally view
“information” as just one part of a knowledge hierarchy that ranges from basic data input to
sophisticated interpretation by an expert (Table 1).
Interdependence of data, information and knowledge
In traditional views concerning the way in which scientific progress occurs, heavy emphasis is
placed on the role of induction to derive scientific theories based on observed phenomena (Fig. 1).
Because there was generally little consideration that sensory inputs might be misleading, objective
“scientific” observations could be treated as facts. This view of scientific methodology was
largely dominant until early in the twentieth Century, and still remains influential in much of
Earth Science education today.
The inductivist view of scientific methodology has been refuted in several ways, and individual
scientific theories are now more generally viewed as belonging to larger knowledge structures
(the “paradigm” of Kuhn 1970, or the “research programme” of Lakatos 1974). Of central
importance in the rejection of induction is that observations cannot be made independently of
prevalent theory, and that the formation of individual theories builds upon prior scientific
knowledge. The significance of this is that there is a solid philosophical foundation for stating that
prior information (sensu lato) is always an influential factor during scientific research, including
geological mapping and other disciplines within the Earth Sciences. Put more simply, this
discussion merely emphasises something that most geologists will take for granted: the end
product of a geological mapping process is a non-unique, subjective interpretation that is
markedly influenced by the previous background, prior experience, and expertise of the geologist,
and is an interpretation made within the context of current geological understanding. Although in
Digital mapping: quantifying uncertainty 3 Jones et al 25.06.03 14:51
general this is implicitly understood by field geologists, there is rarely any attempt to state
explicitly the assumptions or inferences made, or to quantify any uncertainty associated with
interpretation.
Accessibility of knowledge
Researchers who have studied the transfer of knowledge between workers in modern industry
have recognised that there is a great variety in the accessibility of an individual’s knowledge and
expertise (Nonaka 1994; Nonaka & Takeuchi 1995). Whilst some knowledge often exists in an
explicit format that is readily available and that can be communicated and understood by other
colleagues, there is usually also a large amount of implicit knowledge that is not (yet) in a format
that is easily accessible to others (Table 2). Implicit knowledge exists within the head of a person,
but can readily be made available to others (i.e. made explicit) through query and discussion, or
through a conscious decision to document what one knows about a subject. In contrast, a large
amount knowledge possessed by humans is usually tacit (Polanyi 1958, 1966). Tacit knowledge
exists within the head of a person, but is generally in a form that is not easily accessible to other
people, either because its owner is not aware that they possess the knowledge, or will not be able
to express it in a useful, understandable format. An example is the knowledge of how to ride a
bicycle: although you may know how to cycle without having to think, it is very difficult to give
an explicit description of how to perform the task to someone who has never tried themselves.
Traditionally the transfer of tacit knowledge of this type is achieved by repeated learning through
“trial and error”, often in a teacher/pupil or master/apprentice situation. More recently, specialised
knowledge elicitation techniques have been devised that extract tacit knowledge and represent it
in more explicit forms (e.g. Boose 1986; Kidd 1987; Ford & Sterman 1998; White &
Sleeman1999).
Workers who are considered to be “experts” within a particular domain typically possess high
levels of tacit knowledge. This is often particularly acute within geological mapping, where the
quality of output will be greatly dependent upon the skill and expertise of the mapper, although
their proficiency is rarely immediately obvious simply by looking at the final result.
Conditional probability
Ideally, when faced with uncertainty associated with interpretation of individual field
observations, the geologist should attempt to make further field observations in order to resolve
any outstanding issues. In practice, this process will almost always be restricted by limitations
imposed through lack of exposure and limited resources (manpower, time, money), and the
geologist is almost always obliged to supplement direct observation with a mixture of insight,
guile, guesswork, and "gut-feeling". These aspects reflect the geologist’s personal bias, and
Digital mapping: quantifying uncertainty 4 Jones et al 25.06.03 14:51
represent a prior belief which if it can be expressed explicitly, can be used to predict the
likelihood that a particular interpretation is true. This forms the basis of Bayesian statistics, in
which the probability that hypothesis H is true given the occurrence of event E (in context I) is
given by:
p(H | EI) = ( p(H | I) * p(E | HI) ) / p(E | I).
Thus Bayesian probability can provide a mathematical framework for expressing the uncertainty
associated with geological interpretation, and offers a possible way to extend and improve
traditional methods of geological mapping.
Traditional Geological Mapping
The ability to produce accurate field maps and to record associated observational data in a
notebook lies at the core of all Earth Science activities (e.g. Barnes 1981; McClay 1987), and
forms the basis by which geological maps are constructed. Whilst a geological map is a two-
dimensional (2-D) representation of the distribution of rock formations in an area, it also conveys
through symbols and graphics the three-dimensional (3-D) geometry and form of the rocks and
structures in the area. The gathering of field data occurs in a broad range of natural environments
and is typically carried out by individuals or small teams of geoscientists working on foot or using
various forms of transport: this requires that any equipment or techniques used to gather
information are highly mobile and easy to maintain. For these reasons, it perhaps not surprising
that field mapping has since its inception remained as a paper-based activity using maps, field
notebooks and compass-clinometers.
The scientific aims of a study and the time available for fieldwork – which is often dictated by
funding – will determine the type of geological mapping to be carried out. Barnes (1981)
identifies four main types of geological mapping activities:
a) Reconnaissance mapping typically covers a large area and is carried out to find out as much as
possible about a poorly-known region over a short period of field study. Significant amounts of
work may be done using remote sensing techniques or interpretation of aerial photographs.
b) Regional mapping typically results in geological maps at 1:50,000 scale recorded on an
accurate topographic base map. Such mapping is generally the result of systematic programmes
of field-based data gathering, fully supported by photogeological interpretation and integration
of other sub-surface geological or geophysical datasets.
c) Detailed mapping generally refers to maps made at 1:10,000 or larger scales and in many cases
are produced to document key geological relationships in detail. Many require the field
Digital mapping: quantifying uncertainty 5 Jones et al 25.06.03 14:51
geologist to produce their own base map simultaneously using planetable-, chain- or cairn-
mapping techniques (see Barnes 1981 and references therein).
d) Specialized mapping where maps are constructed for specific purposes and do not necessarily
include all aspects of the observed geology. These include mine plans and maps showing
geotechnical, geophysical or geochemical data.
The following information is particularly critical to all field-based data-gathering and
observational activities: accurate location, geological context, and the spatial/temporal
relationship to other data or observations gathered at that or other location(s). In addition, all field
maps and notebooks must be legible, be readable by another geologist and must clearly
distinguish between observed facts and inferences drawn from those facts (Ramsay & Huber
1987). Generally speaking, observations and data are gathered at a series of localities, the
locations of which are marked by hand onto a topographic or aerial photographic base map, with
all data measurements and observations being recorded simultaneously in a field notebook.
Ideally, the extent of visible outcrop (“green-line mapping”) and location of mappable geological
boundaries – including some indication of how well constrained these boundaries are in terms of
the available exposure (using solid, dashed or pecked lines) - will be added to the base map by the
field geologist as they move between localities. Most geologists are encouraged to interpret their
observations and measurements as they map and to modify these interpretation as more
information is acquired. Thus field mapping is a uniquely iterative exercise in which both data-
gathering and interpretation occur simultaneously. This also means, however, that field-based data
gathering presents a number of very significant challenges viewed from a prior information
perspective. In particular, we would highlight four main problems:
• Field mapping involves extensive use of tacit knowledge, in which the a priori assumptions
made both when making interpretations or even when gathering data are either not stated or
may not even be considered – thus ‘facts’ and ‘inferences’ are often not clearly separated in
many, if not all studies.
• The workflow from field-mapping to published map is generally a complex process involving
data collection, interpretation, data reduction and final map drafting. The map is an abstraction
at one specific scale of a large amount of data collected at the outcrop scale. Therefore the vast
majority of ‘inputs’, ‘data’ and ‘information’ are typically excluded from the final result as
they generally cannot all be incorporated into the final paper map. Most maps are therefore
dominated by interpretations (‘knowledge’ + ‘expertise’). In many cases, some of the
interpretation is made in locations far removed from the field either before or after the actual
data-gathering was carried out.
Digital mapping: quantifying uncertainty 6 Jones et al 25.06.03 14:51
• All paper maps are inherently limited in terms of what they show by their scale. In many cases
this means that they lack precise spatial accuracy, meaning that reproducible observations or
measurements are often difficult or impossible.
• The final map generally shows little expression of the uncertainties involved in its production,
and where uncertainty is depicted it is primitive, ad-hoc, and qualitative. A basic representation
of uncertainty is often indicated through the use of different line symbols (e.g. solid lines for
exposed boundaries vs. dashed lines for inferred or conjectural). Thus traditional geological
mapping remains a highly interpretative, subjective art form in which uncertainty is difficult to
quantify in any statistically meaningful way.
Digital Geological Mapping
GIS has evolved from its early use as a computer mapping system and is now defined as ‘an
information management system for organizing, visualizing and analysing spatially-orientated
data’ (Coburn & Yarus 2000 p.1). Since GIS became commercially available in the 1980s, GIS
products are now used in a large number of applications that deal with spatial data, including
social and economic planning, marketing, facilities management, environmental and resource
assessment (Rhind 1992; Longley et al. 2001). In its original guise, GIS largely dealt with 2-D
data that was mapped onto the Earth’s surface (Rhind 1992). It was recognised that in order to
deal with volumetric spatial information or 3-D geometries from sub-surface data, a 3-D GIS or a
GSIS (GeoScientific Information System) was required, and such systems (e.g. GOCAD) have
now been developed for commercial purposes (Turner 1992; Mallet 1992; Turner 2000).
Bonham-Carter (2000) described the core GIS activities in a geoscience project as being:- 1) data
organisation, 2) data visualization, 3) data search, 4) data combination, 5) data analysis and 6)
data prediction and decision support. The combination of these capabilities and the ability to
handle large databases (up to a terabyte) indicate the power of the GIS approach for handling
spatial data and its attraction for geoscience users such as the petroleum and mining industries.
Digital Geological Mapping (DGM) is a methodology by which a geologist collects GPS-located
field data in a digital format. The method has been adapted from digital mapping and surveying
techniques and is becoming widely used in construction, engineering and environmental
industries. In Earth Science fieldwork, apart from a few specific studies, such as determining the
3-D architecture of fault zones and sandstone bodies (Maertens et. al. 2001; Xu et al. 2001), the
methods have yet to be widely adopted. The DGM we describe here is a mapping system that
would be suitable for most geological purposes. The system involves the integration of three key
technological components; 1) a GPS receiver usually capable of obtaining differential correction
data that enable sub-metre positional accuracy; 2) a PDA or other digital data-logger and 3)
mobile GIS software. Mobile GIS is a specialised version of PDA software that can exchange
Digital mapping: quantifying uncertainty 7 Jones et al 25.06.03 14:51
information with more general purpose desktop GIS. When used in 3D mode we suggest that the
DGM provides an onshore equivalent to a wider definition of digital mapping as used by
petroleum industry to make 3D structural interpretations in sub-surface data.
In a GIS, information is usually displayed as a series of layers that can be superimposed with each
comprising a single type of data. Typically this may comprise features or objects that have distinct
shape and size or field data that vary continuously over a surface (Longley et al. 2001), as
summarised in Table 3.
The advantage of a GIS-based mapping system is that any number of different types of data may
be georeferenced and included as a separate layer in the database. These can then be displayed and
analysed in conjunction with newly acquired field data. A generalised work flow for digital
geological mapping, some typical data inputs and an example GIS database are shown in Fig. 2.
Examples of data that may be included are; regional geophysical maps, aerial photography,
satellite imagery, topographic data, previously digitised geological information, sample
catalogues, geochronological data, geochemical data.
2D, 3-D and 2.5D data
In DGM the data are collected in either 2-D or 3-D modes. If the objective is purely to produce a
map of the region then the point data may be stored using an x and y coordinate and lines and
polygons stored as lists of x and y coordinates. Real-time Differential GPS systems regularly give
precision to approximately 1m in the horizontal plane and survey systems that post-process
positional data can attain cm-scale accuracy. The positional precision and accuracy that may be
achieved using GPS is dependant on variations in the input satellite configuration (an error
summarised by the Dilution of Precision statistic calculated continuously by GPS receivers).
Topography or buildings can limit the number of input satellites available to a GPS receiver and
thus accurate positioning near a cliff or a in a deep valley may be difficult to achieve.
Geological information gained from traditional geological mapping has been displayed on 2-D
representations such as geological maps, however this format has disadvantages as described
above. Whilst GIS software products are often used to produce traditional geological maps the
systems also allow more flexible methods of visualisation that can be easily tailored to individual
requirements. For example, on screen data can be viewed at different scales using the zoom and
pan functions with different combinations of data layers visible as required.
GIS data may be overlain or ‘draped’ onto a digital elevation model, in the form of a surface fitted
to a raster map of elevation values, to produce a display that has been referred to as a 2.5D
representation (Longley et al. 2001). These data may then be displayed using a 3-D viewer that
allows rotation to different vantage points as well as zoom and pan. One particularly useful
Digital mapping: quantifying uncertainty 8 Jones et al 25.06.03 14:51
geological application of 2.5D displays is to study how geological formations and structure are
related to topography (Fig. 3).
For accurate 3-D reconstructions of geological architectures, the z-coordinate or elevation for all
positions is essential. Most mobile-GIS applications allow this to be incorporated in the data
table. Despite GPS having poorer resolution in the z direction, in good conditions, a differential
GPS can give a vertical precision of approximately 1m . Alternatively, 2-D data may be converted
to 3-D by locating the positions onto a digital elevation model, however the resolution is limited
by that of the elevation data (typically 50 m).
The advantages of DGM over traditional mapping include improved time efficiency (especially on
data management, analysis and output); with elevation data DGM is inherently 2.5D or more and
the data have high spatial precision and thus a significant reduction in location error and
uncertainty can be achieved.
DGM is capable of incorporating prior information for the following reasons :-
• Scalability in GIS means that an a priori framework, newly collected data, and
interpretation can all be maintained in a single digital model;
• Several types of data can be stored together, all tied to their geospatial position within the
GIS model: attribute data, metadata, photos, sketches, ideas, notes, video, speech etc;
• Having data in digital format is starting point for quantification of uncertainty (see below).
In order to improve the inclusion of prior information in DGM workflows, more work needs to be
done to integrate the various steps involved in the process of data acquisition, interpretation, and
final model. . User-friendly data gathering methods need to be developed to make it possible for
geologists to capture information in ways that are more intuitive, rather than ways dictated by the
non-flexibility of existing hardware and software.
Quantification of Uncertainty in Geological Mapping
Irrespective of whether a mapper uses traditional or digital methods, the acquisition and
interpretation of field data inevitably involves a wide range of different types of uncertainty
(Table 4). Uncertainties accrue from the onset of data acquisition, and accumulate and propagate
throughout the overall interpretation process. Some sources of uncertainty can readily be
expressed in terms of a quantitative assessment of the precision of measurement for a piece of
equipment (e.g. error tolerance of GPS or clinometer measurements). Other uncertainties can be
reduced and quantified by repeating observations so that a measure of variance can be ascertained
(e.g. variation of dip and strike at a single exposure).
Digital mapping: quantifying uncertainty 9 Jones et al 25.06.03 14:51
Interpolation
Geological mapping tends to produce sparse datasets. This is usually because the amount of
exposure is limited, but even when there are high levels of exposure it is generally impractical to
study all exposed rock in detail. Therefore one of the most important aspects of creating a
geological map involves the interpolation of data to fill the areas between intermittent data points
actual measured. Interpolation below (and above) the surface of the earth is of course also central
in producing 2-D cross-sections and 3-D models. Most GIS systems have in-built geostatistical
analysis tools for the interpolation of geospatial point data across a topographical surface (e.g.
“kriging”), and which also provide a statistical measure of uncertainty across the whole surface
(e.g. “variograms”). The most basic approaches to kriging incorporate rather simplistic probability
distributions, and the values of uncertainty derived are simply based on the sparseness of data.
With simple kriging methods there is generally no opportunity for the involvement of prior
information to prime the interpolation, and the kriged surface that is derived might not always be
geologically realistic. In particular, simple kriging will generally attempt to smooth out sharp
variations between adjacent data points, so is not well suited for areas containing discontinuities
such as faults. More sophisticated approaches such as disjunctive kriging are generally more
suitable for most geological interpolations. Future work should concentrate on developing
workflows that makes it easier for the geologist to influence the interpolation process by
specifying prior inputs that will pre-condition the kriging.
Qualitative uncertainties
Many types of uncertainty are difficult to express quantitatively, and are more suited to a
qualitative evaluation by the geologist. Although this may be abhorrent to inductivists that believe
that science consists only of quantitative, objective measurement, a subjective statement such as
“this rock looks sheared and I am reasonably confident that it is a mylonite” is a more useful and
representative observation statement than having to make a binary choice between “this is a
mylonite” and “this is not a mylonite”. An obvious strategy to tackle this situation would be for
field geologists to specifically record an estimate of confidence with every observation, as a
matter of routine. However, most geologists will perceive this data as superfluous, and gathering
it as an additional, unnecessary burden, because there is a general lack of methodology developed
within geological mapping which allows such information to be used in a systematic way.
The potential now exists for this situation to change, following recent advances in mathematics
and computer technology, especially within several branches of artificial intelligence (AI). In
particular, developments in Fuzzy Logic provide a formal framework in which relative terms
(such as “quite sheared”, “very fractured”) can be transformed to discrete numerical values and
represented within binary computer code. Other branches of AI (e.g. Bayesian networks, neural
Digital mapping: quantifying uncertainty 10 Jones et al 25.06.03 14:51
networks, genetic algorithms, constraint satisfaction techniques) have potential for finding
solutions for complicated non-linear models involving very many variables. All these
methodologies have a proven track record of finding good solutions to real problems with a much
shorter amount of computer processing than traditional approaches.
Future Trends in Geological Mapping
For the last two decades the growth in Information Technology (IT) has generally been so great
that geologists have struggled to keep abreast of technological advances. Within geological
mapping earth scientists have been slow to improve workflows and methods of interpretation that
exploit the newly developing technologies. There is no indication that the current rate of growth
within IT is set to diminish, and the following trends are likely to provide improved opportunities
for geoscientists to improve the process of geological mapping:
• portable equipment will continue to become lighter, cheaper, more robust, more powerful,
more intuitive and user-friendly, and more integrated with the user
• an increased number of 2-D and 3-D analytical tools will be incorporated into existing GIS
software to provide an single integrated tool for geological mapping and interpretation.
• interpretation tools will propagate information about uncertainties through the modelling
process so that various interpretations can be tested in parallel and an indication of overall
uncertainty can be given for each interpretation.
• satellite communications technology combined with GRID facilities will bring super-
computing power to field geologists (a “PersonalGRID”). This will increase the possibilities
for ongoing iterative interpretation of field data whilst still in the field.
• speech recognition software combined with semantic based search technology can help to
encourage the geologist to verbalise (= make explicit) more of the decision-making processes
involved in mapping.
Conclusions
Although traditional processes of geological mapping have a proven track record established over
two hundred years, there are nevertheless important methodological shortcomings seen from a
scientific perspective:
• paper-based published maps generally show only a fraction of the field data that have been
collected and used as the basis for the map’s creation. Other data remain hidden in the field
notebook and in the head of the mapper.
Digital mapping: quantifying uncertainty 11 Jones et al 25.06.03 14:51
• published maps rarely make reference to the reasoning used during interpretation of the basic
field data. Reasoning typically relies heavily on prior information and knowledge that
represents the experience of the geologist before the onset of the mapping project.
• paper-based maps are by necessity published at a fixed scale. The skill of the cartographer is to
present as much relevant information as possible whilst maintaining legibility at the chosen
scale, but inevitably there is a loss of precision especially with respect to geospatial
positioning.
• with traditional maps there are generally only very limited possibilities for expressing any
uncertainty concerning the given interpretation, and these are not quantitative.
Whilst the above limitations have always been acceptable as long as there were no viable
alternatives to paper-based publishing, today’s information technology makes it possible to store
the entire life’s work of a geologist on a compact disc that costs less than a pair of boot laces!
Digital mapping has the potential to improve the scientific validity of the mapping process in the
following ways:
• collected field data can be stored together with the interpreted map in a single digital model
within a GIS. In the future it should be possible to capture and store a wider range of
multimedia datatypes (including metadata, photos, sketches, ideas and notes, video, speech
etc.) all tied to the appropriate geospatial position within the GIS model
• prior inputs used as the basis for interpretations can be stated explicitly within the same GIS
model
• the inherent scalability of a GIS model makes it possible to store unlimited data for any
geospatial locality, so that the amount of data is no longer restricted by the scale of the final
published map
• as progressively more analytical tools are incorporated into GIS software, geospatially
referenced data can be analysed and interpreted within a single software environment
• many types of uncertainty that arise during the mapping process can either be quantified or can
be estimated qualitatively in a way that can be represented digitally (using AI techniques).
Digital geological mapping is still in its infancy. Future work should concentrate on the following
challenges:
• the digital workflow should be continuously improved to make it more intuitive and quicker to
capture field data in digital format
• more integration of analysis tools and GIS is needed
Digital mapping: quantifying uncertainty 12 Jones et al 25.06.03 14:51
• methodologies should be further developed that use the uncertainties associated with
individual data or interpretations as the input to produce an overall estimate of uncertainty
associated with a given model. Alternative interpretations can be modelled simultaneously,
with uncertainty calculated for each
• efforts should be made to combine portable GIS with GRID technology.
Acknowledgements __ Thanks to Jonny Imber, Nicola De Paola, Phil Clegg and other members of
RRG and Bernt Bremdal at CognIT for fruitful debate. Steve Freeman and others at RDR made
early progress with DGM. Much of this work was part of the Ocean Margins Link project
(NER/T/S/2000/01018), funded by Statoil UK Ltd, BP and NERC.
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Figure Captions
Fig. 1. Traditional inductivist view of scientific methodology.
Fig. 2. a) Digital Geological Mapping work flow indicating the relationship between different
activities, b) some input data types, c) a display from a GIS database for Achmelvich Bay, NW
Scotland.
Fig. 3. Digital geological mapping of part of the foreland to the Moine Thrust at Loch Assynt, N.
Scotland. a) Map with boundaries displayed on aerial photograph, b) oblique 2.5D view from
south of same data showing that boundary A is sub-horizontal and boundary B dips to the east.
Digital mapping: quantifying uncertainty 14 Jones et al 25.06.03 14:51
Fig. 1.
Fig. 2.
observation = fact scientific theory prediction
induction deduction
Digital mapping: quantifying uncertainty 15 Jones et al 25.06.03 14:51
Fig. 3.
Level Example
5 Expertise (= ability to apply knowledge
effectively to perform tasks accurately and
efficiently within existing constraints)
the finished geological map!
a geological summary of the mapped area
scientific paper describing new fossil found in area
4 Knowledge (= application of information
to be able to make decisions, solve
problems, or perform tasks)
boundary between rock types A and B is in valley
rock A is granite
mineral P is biotite
3 Information (= data in a specified context,
data with meaning) rock A is observed at location GR 234 789
rock A contains minerals P, Q, R
mineral P has colour that is black
2 Data (= inputs that can be represented
explicitly in symbolic form) colour is black
lustre is shiny
GPS location at time T is 123456 from satellite 1
GPS location at time T is 123678 from satellite 2
1 Inputs (= sensory signals, machine
measurements) geologist receives visual sensory signals
GPS unit receives satellite signals
Table 1. The knowledge hierarchy with examples from geological mapping
Knowledge accessibility General examples Examples from mapping
Explicit scientific papers published in journals.
textbooks.
instruction manuals.
detailed outcrop map (“green-line”
mapping).
Implicit unpublished observations.
working hypotheses.
undocumented troubleshooting fixes.
observations not recorded explicitly
on final map.
general geological theory that has
influenced specific interpretation.
Tacit instant recognition of minerals based on “look
and feel” rather than explicit physical tests.
interpretation of seismic sections.
expertise of the mapper.
the mapper’s preconceived bias,
insight, gut-feeling and intuition.
Table 2. Different levels of accessibility of knowledge
Digital mapping: quantifying uncertainty 16 Jones et al 25.06.03 14:51
GIS data Type Geological data Specific example
Point Object Locations of structural stations,
anywhere a measurement is made
or a sample is taken
Bedding strike & dip
Gravity measurement
Geochemical sample
Line Object Boundaries between areas or
linear objects Contact between rock units
Fault trace
Polygon Object Areas of rock units Formation extent
Area of igneous intrusion
Raster Field data sampled on a matrix of
equally sized squares Elevation (Digital Elevation
Model)
LandSat™ image
Table 3. Data types in a typical GIS system
Level Type of uncertainty Examples
Positional “how sure am I of my current location?”
“how reliable is my base map?”
“what is the precision of my GPS measurements?”
“is the borehole straight, or has it deviated without me knowing?”
Measurement “what is the precision of my clinometer?”
“what is the accuracy of my dip/strike readings?”
Scale-dependant variability “how much does the dip and strike vary over the scale of the outcrop?”
“is my reading representative of the surrounding area?”
Observational “is this rock best described as a granite?”
“is this fossil the brachiopod pentamerus?”
“is that a stretching lineation or an intersection lineation?”
Temporal “how reliable is this way-up criteria?”
“is the relative age of these structures identified correctly?”
Data acquisition
Sampling bias “is my data biased by the natural predominance of sub-horizontal exposures?”
“has my sampling been skewed by me focusing only on the zones of high strain?”
Correlation “is this limestone the same unit as the limestone at the last outcrop?”
“is it valid to correlate the S2 fabric here with the S2 fabric observed on the other side
of the area?”
Interpolation “how likely is it that all the ground between these two outcrops of slate also consists
of slate?”
“how much control do I have over the geometry of this fold trace?”
Primary interpretation
Inference from topography “is there really a fault running along the unexposed valley floor?”
“does this sharp change in slope correspond to a lithological boundary?”
Finished 2D map
Geological cross-section
Compound
interpretation
3D structural model
“how can I quantify the uncertainty associated with this sophisticated interpretive
model that I have slowly built up through a long iterative process of data collection
and individual primary interpretations?!”
Table 4. Examples of different types of uncertainty arising during geological mapping.
