1. A FORMAL MODEL FOR THE GEOLOGICAL TIMESCALE AND GSSP Simon J.D. COX CSIRO Exploration and Mining, ARRC Stephen M. RICHARD, Arizona Geol Survey and U. S. Geological Survey

2. Goal Formal Model for time-scale information Why? ensures accurate communication within sub-discipline harmonization with other info systems, geoscience & other software generation and implementation

3. “ Ordinal Temporal Reference System” - ISO 19108 Temporal position described in terms of an ordered, hierarchical set of named eras –E.g. “Lopingian” Compare with Temporal Coordinate System –number and scale – e.g. “260 Ma” Calendar –day/month/year (western, Hebrew, Japanese, etc)

4. Node – event, point in time, associated with a time instant Theory: Temporal Topological Complex Edges are joined at nodes Edge – directed, has begin & end nodes, realized as a time period Object introduces an identifiable information item

5. Theory: Ordinal Reference System Reference system ⇒ relative positions of any two edges is unique –Before, After, Begins, Ends, During, Equals, Contains, Overlaps, Meets, OverlappedBy, MetBy, BegunBy, EndedBy ≡ Constrained Topologic Complex –Any path between nodes may only be subdivided in one way Different subdivision = different “system” –Each system has a “domain of validity” –multiple systems may exist simultaneously provided their scope does not overlap B1B1 B4B4 B5B5 B2B2 B3B3 B 21 B 23 B 22 B 24 BaBa BcBc BbBb A DCB

6. Geologic Time Scale Era = named edge –Hierarchically ranked Boundary = temporal node Traditional studies focused on eras –Where the rocks and fossils are! Era Name=“Permian” Rank=“System” Era Name=“Lopingian” Rank=“Series” Node Name=“Base of Artinskian” Node Name=“Base of Permian”

7. GSSP Global Standard Stratotype Section and Point Era Name=“Permian” Rank=“System” Era Name=“Lopingian” Rank=“Series” Node Name=“Base of Artinskian” Node Name=“Base of Permian” GSSP focuses on boundaries –the “temporal nodes” –associated with stratigraphic events GSSP boundary stratotype –Stratigraphic section at a specific location –Position in section that shows evidence of the event (‘point’, ‘golden spike’) Calibration is based on age measurements made on specimen(s) collected from the stratotype –Result of Measurement = estimated temporal position of boundary

8. Standard Global Numerical Age* Boundary position is assigned, rather than estimated Used for pre-Ediacaran timescale –preCambrian eras still comprise an Ordinal Temporal Reference System –More common to use chronostratigraphy (= Temporal Coordinate System) * Global Standard Stratigraphic Age (GSSA), nomenclature revision proposed by Walsh et al, 2004

9. Formal model of Geologic Time System and GSSP Hierarchical ordinal system, in which the eras are ranked (e.g. era, period, epoch) Temporal position assigned to interval bounds based on measurements on specimens from GSSP, or from Standard Global Numerical Age

10. Geologic Time System 1 +begin Initiation 1..* +nextStratEra 1 +end Termination 1..* +previousStratEra TM_Complex TM_TopologicalComplex TM_ReferenceSystem GeologicTimeScale UnambiguousTemporalTopoComplex 0..* 1+basis 1..* M_Node StratNode TM_OrdinalEra StratEra 1 0..1 +Name TM_TopologicalPrimitive TM_Edge Name 1 +Definition TM_ prefix indicates parent model element in ISO 19108

11. GSSP-- StratNode TM_ prefix indicates parent model element in ISO 19108 StratNode TM_Primitive TM_GeometricPrimitive StratAgeInterpretation 0..1 TimeLocation 1 GeologicEvent StratigraphicEvent 1..* Manifestation 1..* Feature Stratotype 0..1 Containment 1 +contains TM_Node GeologicSurface BoundaryLevel EventNode 1 1 DefinedNode TM_TemporalPosition «Data Type» TM_Coordinate +coordinateValue: Number 0..* 1+position

12. Numerical age interpretation Specimen 0..* Sample 1 0..* 1..* +target Observation DateDetermination 0..* Evidence 1..* Feature Stratotype TM_Primitive TM_GeometricPrimitive StratAgeInterpretation GeologicSurface BoundaryLevel EventNode 0..1 TimeLocation 1 0..1 Containment 1 +contains 1 1 LithostratigraphicUnit MicrostratigraphicUnit 1..* {ordered} 1

13. Important concepts from outside of stratigraphy position –Geospatial e.g. of stratotype or specimen –Temporal – e.g. of stratigraphic boundary Specimen – object on which observations may be made –e.g. particular piece of rock Observation/Measurement – use of a procedure on a specimen, to estimate the value of a property –e.g. isotopic age, chemical composition –the property value is the result of an observation

14. Implementation Formal model (UML) can “automatically” generate software: –XML transfer format –relational database schema

15. Conclusions ISO 19108 standard provides standard model for temporal reference systems XMML provides a standard model for specimens and measurements Combine these to model important aspects of geologic time systems based on GSSP Some refinement still needed –constrained temporal topological complex –some details of relationships involving stratEvent/stratBoundary/specimen/stratotype etc

16. These are the GSSP selected and ratified components for the given boundary node Era Name=“Permian” Rank=“System” Era Name=“Lopingian” Rank=“Series” Node Name=“Base of Artinskian” Node Name=“Base of Permian” Event description=“Conodont, lowest occurrence of Streptognathodus isolatus” Event description=“Conodont, disappearance of Foo bar” Stratotype description=“27 m above base of Bed 19, Aidaralash Creek, Aktöbe, southern Ural Mountains, northern Kazakhstan” Stratotype description=“Some other place” These are ordinal timescale components These are components required for correlation and timescale calibration AgeMeasurement result=“-299 Ma” AgeMeasurement result=“-298 Ma” Preferre d age for this node