Event Ordering Reasoning Ontology applied to

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

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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

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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

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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

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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


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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:


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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):


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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

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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.

8. References 1. Thagard, P.S., Cameron P., Abductive reasoning: logic, visual thinking, and coherence, in Logic and scientific methods. 1997, Kluwer. p. 413-427. 2. Mastella, L., et al. Cognitive Modelling of Event Ordering Reasoning in Imagistic Domains. in Proceedings of the 19th International Joint Conference on Artificial Intelligence - IJCAI'05. 2005. Edinburgh, UK. 3. Bolour, A.D., L. J., Abstractions in Temporal Information. Information Systems, 1983. 8(1): p. 41-49. 4. Studer, R.B., V.R. & Fensel, D., Knowledge engineering: principles and methods. Data & Knowledge Engineering, 1998. 25(1/2): p. 161-197. 5. Noy, N.F., Semantic integration: a survey of ontology-based approaches, in ACM SIGMOD Record - COLUMN: Special section on semantic integration. 2004, ACM Press: New York, NY, USA. p. 65 - 70. 6. Bennett, B.G., Antony P., A unifying semantics for time and events. Artificial Intelligence, 2004. 153: p. 13-48. 7. Abel, M.S., Luis Alvaro Lima; Ros, Luiz Fernando de; Mastella, Laura S.; Campbell, John A. & Novello, Taisa, PetroGrapher: managing petrographic data and Knowledge using an intelligent database application. Expert Systems with Applications, 2004. 26(1): p. 9-18. 8. Abel, M.S., Luis Alvaro Lima; Ros, Luiz Fernando De; Campbell, John A. & Mastella, Laura Silveira. PetroGrapher: managing petrographer data and knowledge


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using an intelligent database application. in WORKSHOP ON INTELLIGENT COMPUTING IN PETROLEUM INDUSTRY. 2002. Mexico City, Mexico: [s.n.]. 9. Perrin, M., Geological consistency : an opportunity for safe surface assembly and quick model exploration, in 3D Modeling of Natural Objects, A Challenge for the 2000’s. 1998: Nancy, France. p. 4-5. 10. Perrin, M., et al., Knowledge-driven applications for geological modeling. Journal of petroleum science & engineering, 2005. 47(1-2): p. 89-104.