Mastella, L.S.; Abel, M.; Ros, L.F.D.; Perrin, M. e Rainaud, J.-F. Event
Ordering Reasoning Ontology applied to Petrology and Geological Modelling. In:
Castillo, O.et al. Theoretical /Advances and Applications of Fuzzy Logic and Soft
Computing.: Springer-Verlag, 2007. p.465-475
Event Ordering Reasoning Ontology applied to
Petrology and Geological Modelling
Laura S. Mastella1, 3, Mara Abel1, Luiz F. De Ros2, Michel Perrin3, Jean-François5 Rainaud
Universidade Federal do Rio
Grande do Sul
1
Instituto de Informática and
2
Instituto de Geociências
Porto Alegre, Brazil
3
École des
Mines de Paris
Paris,
France
4
Institut Français
du Pétrole
Rueil-Malmaison,
France
{mastella, marabel, lfderos}@inf.ufrgs.br
[email protected]
[email protected]
Abstract. The inference of temporal information from past event occurrences is
relevant in several applications for geological domains. In such applications, the
order in which events have happened is imprinted in the domain as visualspatial relations among its elements. The interpretation of the relative ordering
in which events have occurred is essential for understanding the geological
evolution in different scales of observation and for various kinds of objects, as
in Petrology and Geological Modelling. From the analysis of the cognitive
abilities of experts in these domains we propose an ontology for event ordering
reasoning within domains whose elements have been modified by past events.
We show that the Event Ontology can work as a pattern for domain
conceptualization to be applied in distinct domains. It can be used to specify the
sequence order of diagenetic paragenesis. It can also be operative for automatic
reconstruction of geological surface assemblages.
Keywords. Knowledge Engineering, Ontology, Sedimentary Petrology,
Geological Modelling.
1. Introduction
The inference of temporal information from past event occurrences [1] is particularly
relevant in domains such as law, medicine, archaeology, geology and many others. A
geologist, for instance, identifies visual-spatial relations among objects (rock
constituents, geological surfaces) as does a physician when analyzing medical images
to identify pathologies. In both cases, the visual-spatial relationships that are observed
are the result of a sequence of past events. Late minerals grow over pre-existing ones
like tumours grow over healthy tissues.
L. S. Mastella, M. Abel, L. F. De Ros, M. Perrin, J.-F. Rainaud
In this work, we deal with two kinds of geological interpretations that are both
involved in reasoning on temporal events. First, we examine how one can reconstruct
the succession of diagenetic events, which affected siliciclastic rocks and
consequently modified their porosities and permeabilities. Secondly, we identify the
events related to the deposition and to the further evolution of sedimentary formations
in order to identify the position of the geological surfaces (horizons, faults), which
limit hydrocarbon reservoirs. We are concerned by representing relative time, i.e. by
the mere order in which the events happened. In addition, we aim at deriving relative
temporal information from another dimension (the visual-spatial relations between the
elements of the domain). In both cases, images are the starting point of the analysis.
Petrologists observe thin section under an optical microscope while geophysicists and
petroleum geologists identify geological surfaces on seismic images.
In order to propose representation primitives and an inference mechanism, a long
process of knowledge acquisition techniques in the petrology domain was carried out.
The analysis of the cognitive abilities of the experts led to the development of a
cognitive model picturing the geologist’s reasoning concerning an imagistic domain
(rock thin sections) [2]. The Event Ontology, which is part of this cognitive model,
was shown to be capable of modelling the expert's reasoning when deriving the
sequence of events which led to the visual-spatial organisation of the domain under
analysis. Here we additionally present an application of Event Ontology for
Geological Modelling. Moreover, we compare the petrology and geological modelling
domains and map the ontology already proposed to both domains, in order to
demonstrate that this model can be considered as a template of domain
conceptualization to be applied in evolving domains.
Section 2 presents some Knowledge Engineering (KE) approaches for modelling
temporal and spatial information and the basics of ontologies. Section 3 describes the
geological domains on which this work is applied. Section 4 presents the cognitive
model for event reasoning. Section 5 describes the application of the developed model
to the domains in study, and finally Section 7 presents some preliminary conclusions.
2. KE Theoretical Foundations
In this section we introduce the main approaches of Knowledge Engineering for
temporal and spatial representation and the basics of ontologies.
Relative and absolute notions of time. In the absolute notion, time consists of a
sequence of discrete points (dates, hours, etc.). In the relativistic view of time, on the
contrary, events and temporal relationships between them precede the notion of time.
When is possible to define absolute time stamps associated to events, developing
inference about ordering becomes a relatively simple task. However, according to [3],
in most real domains, timing information is also conveyed by time relationships, such
as "before" and "after" (referred to above as relative time).
Ontologies. According to most definitions, an ontology is a formal, explicit
specification of a shared conceptualization [4]. Using ontological constructs, it is
possible to describe static knowledge, specifying which are the objects that compose
the domain and according to which structure they are organized. Ontologies are also
used as means of semantic integration. According to [5] very general ontology
Event Ordering Reasoning Ontology applied to Petrology and Geological Modelling
3
formalizing notions such as processes and events, time and space, physical objects,
and so on, can be developed with the explicit goal of providing a ground vocabulary
to domain-specific ontologies. Recently, some authors have aimed at augmenting the
expressive power of ontologies by including temporal information [6]. Most proposals
considers absolute time stamp associated with objects of the ontology. However, in
several application domains, events are not to be interpreted by putting time stamps
over them.
3. The Domains of Study in Geology
Let us describe the geological domains concerned by this work.
Sedimentary Petrology: in the case of hydrocarbon exploration, this science aims
at evaluating the economic prospects of oil fields and reservoirs by interpreting
observations related to rock thin sections.
Several kinds of visual-spatial relations between rock constituents can be observed
such as "A covering B", "A engulfing B". They are called paragenetic relations. These
relations reflect the changes undergone by the rock in the course of the geological
history, which are a result of a sequence of diagenetic events. Diagenetic events are
physical-chemical processes, which acted over the sediments transforming them into
solid rocks and, consequently, modifying the porosities and permeabilities of potential
oil-reservoirs. Using his extensive previous knowledge, a qualified petrologist is able
to point out the ordering of events by observing how the constituents are spatially and
visually related to each other. Using a simple example: If one mineral appears to be
on top of other mineral, it means that the former was generated in the rock later than
the latter. The sequence of events is an important criterion to determine the quality of
a reservoir. In Fig. 1, we show an example of rock sample and the visual-spatial
relations between the minerals that were identified.
2
1
Qz
3
Qz
1
2
Qz
3
3
2
1
Qz
Qz
Fig. 1. Vision of a rock sample: (1) Hematite is covering grains of Quartz (Qz);
(2) Quartz growings are covering hematite; (3) Quartz is being covered by Illite.
Some interpretations techniques used for the evaluation of oil reservoirs were
already modelled in the PetroGrapher system, an intelligent database application to
support the description and interpretation of sedimentary rock samples [7]. The
vocabulary of Petrology was elicited as a result of previous works on the domain [8]
and modelled as a domain ontology.
L. S. Mastella, M. Abel, L. F. De Ros, M. Perrin, J.-F. Rainaud
Geological Modelling: 3D geological models are conventional representations of a
definite portion of underground corresponding to hydrocarbon reservoirs or to
sedimentary basin models. The blocks of geological matter are limited by surfaces
such as sedimentary interfaces or faults, and geological modelling aims at
reconstructing geological surface assemblages in order to obtain models that can
further be populated by petrophysical properties.
Each defined surface of the model is the record of one defined geological event,
which can be considered as having been instantaneous with respect to the geological
time scale. Geological interpretation then consists in giving a geological qualification
(stratigraphic surface, fault) to the surfaces entering into the model, and in implicitly
or explicitly establishing a total or partial chronological order between the geological
events to which they correspond. Since an older geological event cannot modify a
younger one, the chronological order defined by the geological interpretation has
consequences on the geometry and on the topology of the model to be built.
Considering this, a geological syntax was defined as a result of previous work on the
domain [9] and modelled as a geo-ontology [10]. The process of geological
interpretation can be understood considering Fig. 2.
Fig. 2 is a synthetic example of most of the features currently present in geological
assemblages. Several surfaces interrupting each others can be observed: Surface T is
an example of an erosional surface interrupting surfaces E and X. Thus, T is younger
than E and X. Surface a is an example of an on-lap surface, which interrupts surfaces
b and c. Thus, a is older than b and x. Full spatial and temporal relations are thus
established between surfaces a, b and c as a consequence of geological interpretation.
T
E*
T
T*
T
E
X
T*
d*
E*
d
m
F2
F1 Dm2
E
c*
G
m*
E*
b*
b
a*
X
c
E
a
E*
a*
E
G*
a
Dm1
G
a*
Dm1
Fig. 2. Example of a geological scene.
Petrography and geological modelling both consider processes and events that
change spatial configurations. However, theses two domains contrast according to the
scale of observation. While a petrologist observes thin sections of rocks at the
microscope, structural geologists study geological assemblages whose horizontal
dimensions may reach tens or even hundreds of kilometres. Even so, at both scales,
the work of a geologist is comparable to that of a detective: it consists in observing
spatial signatures and in trying to deduce from them the full chain of geological
Event Ordering Reasoning Ontology applied to Petrology and Geological Modelling
5
events that successively affected the domain. In section 5, we will make a closer
comparison between the two domains, in order to identify the elements that play
similar roles in petrology and in geological modelling.
4. A General Ontology of Events
The cognitive model presented here intends to model the evolution of a domain,
which was submitted to various modifications resulting from events successively
occurring in a non-planned order. Each of these events acted in the past as an operator
transforming the domain. Their succession has induced several spatial relations
among the domain elements. Considering the visual-spatial relationships that finally
resulted from the full sequence of events and that can presently be observed, one can
try to guess what were the events that have affected the domain and in which order
they happened. This is the goal of the ontology-supported knowledge engineering
approach that we propose.
4.1. The Event Ontology
We propose an extension to the classic constructs of ontological representation for
evolving domains in order to capture the meaning of events and temporal relations
between them. Such proposed constructs should be applied for modelling domains
whose current state can be fully understood by considering the sequences of events to
which they were submitted. We define the new constructs as follows (Fig. 3):
Fig. 3. The constructs of the Event Ontology.
Event is a construct that acts as domain-transforming operator. It represents the
phenomena that generate or modify the elements of the domain. Events are
characterized by specific domain-dependent attributes, but not necessarily by a time
stamp. They are also described by rules that associate them to their products. Events
are, by their way, associated to each other by temporal relations.
Temporal relation is a construct proposed to represent the ordering relation
between events. In order to reflect such ordering, we have defined the binary relations
before, after and during.
Furthermore, we defined inference rules in order to represent the rules that the
expert uses to produce the interpretation. We have two types of inference rules: event
indication rules and temporal implication rules. In the event indication rules, the
characteristics of the elements (expressed by class attributes in the ontology) are used
to indicate which event originated or modified the element, as in:
if classA.attribute1 = value-x
L. S. Mastella, M. Abel, L. F. De Ros, M. Perrin, J.-F. Rainaud
then classB.attribute2 = value-y
The temporal implication rules are defined in order to allow the inference of binary
temporal relations between events from the visual-spatial relations between the
elements, as in:
if visual_relation(A,B)
then temporal_relation(A,B)
The main concepts that should be represented in the model are the domain
elements, which are the items of the domain that have possibly been generated or
modified by the events. The relationships represented in the model are the visual
relations between the domain elements (for instance, one element is on top of the
other). Representing the visual relations is essential for the inference, because they
show strong evidences of the order in which the events have occurred.
In the following section we explain how the Event Ontology was used as a base
ground in order to map each of the two geological domains considered.
5. Mapping of the Cognitive Model to Geological Domains
We intend to show in this section how we identified the elements that have similar
roles in the domains of Petrography and Geological Modelling and how those
elements were mapped to the Event Ontology.
Sedimentary Petrology:
• Rock Constituents correspond to the minerals and pores that build a rock.
Constituents can be minerals such as quartz or illite, and their more important
properties are habit, location and modifiers. They are Domain Elements.
• Paragenetic Relations describe the visual-spatial arrangements among constituents.
Common paragenetic relations specify that a given mineral covers another mineral
or engulfs another mineral, etc. They are Spatial Relations.
• Diagenetic Events. These events correspond to physical-chemical processes, which
induced changes in rock mineralogy. The experts do not take into account the
absolute period of time during which the various diagenetic events happened, but
only the order in which they happened. Diagenetic events can be dissolution,
replacement, compaction, fracturing, deformation, etc. They are Events.
• Ordering Relation. Diagenetic events can have happened in a simultaneous or in a
sequential way. In order to simplify the computational treatment of the sequence,
we treat the ordering of events in pairs, as an expert does. The relations between
pairs of events are after, before, and during. They are the Temporal Relations.
The ontology of Petrology resulted is as shown in Fig. 4.
• Inference rules. The expert is able to indicate the generating events by analyzing
the characteristics of the rock constituents. For instance, when the attribute
modifier of a constituent holds the value deformed, supposing that no small scale
tectonic deformation occurred, it is possible to conclude that the event that
transformed the constituent is compaction. Hence, it was necessary to represent
this knowledge as event indication rules. These inference rules define an
association between constituents and diagenetic events, e.g. rule below:
Event Ordering Reasoning Ontology applied to Petrology and Geological Modelling
7
if constituent.modifier = deformed
then event.event_name = compaction
Fig. 4. A partial Petrology Ontology
After having identified the events, the expert is able to infer the order in which they
occurred considering the visual-spatial (paragenetic) relations that he observes
between the constituents. For instance, when a mineral appears to be covering (to be
lying on the top of) another mineral, the expert says that the event that formed the first
mineral occurred later than the event that formed the latter. The first part of this
particular expert's rule is assuming a paragenetic relation between constituents.
The second part is defining an ordering relation between events. Thus, we need to
represent this knowledge as temporal implication rules. An example of this type of
rule is the following:
if covering(constituent1, constituent2)
and produced_by(constituent1, event1)
and produced_by(constituent2, event2)
then after(event1, event2)
Geological Modelling. The Geo-Ontology proposed by [10] deals with the broad
arrangements of geological objects that are considered when building models.
• Geo_Objects correspond to actual physical geological objects, which are
Geological surfaces and Geological formations. Geological surfaces correspond
to limits of sedimentary formations (ex: horizons) or to tectonic discontinuities (ex:
faults). A geological formation is a volume made of contiguous material points; it
is fully limited by a set of geological surfaces. They are the Domain Elements.
• Topo_Assertions are spatial relationships between intersecting surfaces, which can
be: interrupts and stops on. They are the Spatial Relations.
• Geo_Event, refers to a geological process occurring during a definite span of time
or to a combination of such processes which correspond to matter creation
(sediment deposition, magma intrusion), matter destruction (erosion), matter
transformation (diagenesis, metamorphism), matter deformation (folds, faults,
thrusts). They are the Events.
• Chrono_Assertions represent the chronological relations that can occur between
Geo_Events. They can be younger than, older than, or contemporary to. They are
the Temporal Relations.
Current geological modelling rest on two main hypotheses [9]:
L. S. Mastella, M. Abel, L. F. De Ros, M. Perrin, J.-F. Rainaud
1. The age hypothesis: Since the events are responsible for creating or
transforming surfaces, each geological surface corresponds to one defined event
and has one defined age. Thus, there is a direct association between
Geo_Objects and Geo_Events.
2. The intersection topology hypothesis: When two surfaces meet, one
necessarily interrupts the other (no X-crossings).
Chrono-topological relationships between horizons can be described by providing
them with attributes such as erosional meaning that they interrupt all older surfaces or
on-lap meaning that younger horizons may stop on them.
The above rules are the main elements of the geological syntax that any geologist
implicitly uses when interpreting crude geological data. This same syntax should also
be used when building 3D models. Previous work operated in École des Mines de
Paris has shown also that, in order to be geologically consistent, underground models
should be built in accordance with a few chrono-spatial rules. Those rules can be
expressed as, for example:
if stopsOn(surfaceA,surfaceB)
and (Erosional(surfaceB) or Fault(surfaceB))
then youngerThan(surfaceB,surfaceA)
if stopsOn(surfaceA,surfaceB)
and (OnLap(surfaceB))
then olderThan(surfaceB,surfaceA)
It means that when a geologist interprets the topological relation between the
objects we can infer the temporal relations. The ontology of Geological Modelling
resulted is as follows (Fig. 5):
Fig. 5. Ontology for Geological Modelling.
So, from the GeoOntology and from the Petrology Ontology we could identify the
following equivalences, using the Event ontology as a base for the mapping (Fig. 6):
Event Ordering Reasoning Ontology applied to Petrology and Geological Modelling
9
Fig. 6. Mapping of the Petrology and GeoModelling Ontologies to the Event
ontology.
It thus appears that the two domains have a similar event based organization in the
knowledge level. Similar reasoning methods can be applied in the two domains to
interpret the succession of events to which geological assemblages were submitted
both at the petrology and at the geological modelling scales.
6. Validation of the Event Ontology
The proposed Event Ontology has been applied to the petrography domain, being
implemented as an inference module within the PetroGrapher system [7]: the
diagenetic sequence interpretation module. Real rock samples were described by the
geologist in the PetroGrapher system and he also provided a previous interpretation
of the sequence of diagenetic events, which was compared to the interpretation
produced by the algorithm. The detailed experiment is described in [2]. The resulting
event sequence is the same as the one inferred by an expert in most cases. For some
rock samples the algorithm produces sequences of events that are not totally
connected. However, in some cases, not even the expert is able to produce a complete
sequence of events, because some paragenetic relations may be visible (and then
described) in one sample and not in another one. Although the resulting sequence may
sometimes be incomplete, it is certainly relevant to the domain, because, any
sequence of events that can be inferred from a rock description is essential in
understanding how the porosity and the permeability of the rock were affected, and
how this influences the quality of the oil reservoir. This module is incorporated in the
industrial version of PetroGrapher system1.
7. Conclusion
We presented an Event Ontology, which allows correlating spatial and temporal
relations and shows that it can work as a pattern of domain conceptualization to be
applied in different geological disciplines. The models presented are able to describe
1
®
The commercial name of the PetroGrapher system is PETROLEDGE , which is being
distributed by Endeeper (http://www.endeeper.com/).
L. S. Mastella, M. Abel, L. F. De Ros, M. Perrin, J.-F. Rainaud
the reasoning of an expert who observes and interprets visual-spatial relations in
search for the best explanation about the sequence of events that caused them.
From the representation of the topological-temporal relation between two
geological objects (Geological Evolution Schema – GES, [9]) it is possible to
automatically rebuild from unsegmented geological surfaces a 3D geological model
fully consistent both topologically and geologically.
Present day rocks and present day rock assemblages are the result of a complex
history consisting in a succession of events related to various physical, chemical or
mechanical processes. The art of the geologist consists in inferring from geological
observation at different scales a geological interpretation which is nothing else that a
possible or probable reconstruction of the geological history.
Considering two different scales and different types of geological objects, we have
tried to show by using knowledge engineering techniques, that geological
interpretation obeys to definite reasoning rules, which are similar from one geological
domain to another, at least in some aspects. Although it is preliminary, this result
appears to us as important since it may contribute to making fully explicit the
geological interpretation procedures used during oil & gas exploration and to thus
facilitating the collaboration between the various experts involved.
Acknowledgments. L. Mastella acknowledges the CAPES Foundation for
financial support on her Doctoral work. M. Abel and L.F. De Ros are supported by
the Brazilian Research Council - CNPq. We thank P. Verney, Doctoral student at
ENSMP and IFP for discussions about the formalization of Structural Geology.
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