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

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

“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)

• 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

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

B1

B4

B5

B2 B3

B21

B23B22

B24

Ba Bc

Bb

A DCB

Geologic Time Scale

• Era = named edge– Hierarchically ranked

• Boundary = temporal node

• Traditional studies focused on eras– Where the rocks and

fossils are!

EraName=“Permian”Rank=“System”

EraName=“Lopingian”

Rank=“Series”

NodeName=“Base of Artinskian”

NodeName=“Base of Permian”

GSSPGlobal Standard Stratotype Section and Point

EraName=“Permian”Rank=“System”

EraName=“Lopingian”

Rank=“Series”

NodeName=“Base of Artinskian”

NodeName=“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

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

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

Geologic Time System

1 +begin Initiation 1..*+nextStratEra1

+end Termination

1..*

+previousStratEra

TM_Complex

TM_TopologicalComplex

TM_ReferenceSystem

GeologicTimeScale

UnambiguousTemporalTopoComplex

0..*

1+basis

1..*

M_Node

StratNodeTM_OrdinalEra

StratEra

1

0..1

+Name

TM_TopologicalPrimitive

TM_Edge

Name

1+Definition

TM_ prefix indicates parent model element in ISO 19108

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

Stratotype0..1 Containment 1

+contains

TM_Node

GeologicSurface

BoundaryLevel

EventNode

1

1

DefinedNode

TM_TemporalPosition

«Data Type»TM_Coordinate

+ coordinateValue: Number

0..*

1+position

Numerical age interpretation

Specimen

0..*

Sample

10..*

1..*+target

Observation

DateDetermination0..*

Evidence

1..*

Feature

Stratotype

TM_Primitive

TM_GeometricPrimitive

StratAgeInterpretation

GeologicSurface

BoundaryLevel

EventNode

0..1

TimeLocation

1

0..1 Containment 1

+contains

1

1

LithostratigraphicUnitMicrostratigraphicUnit

1..* {ordered}

1

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

Implementation

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

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

These are the GSSP selected

and ratified components for

the given boundary node

EraName=“Permian”Rank=“System”

EraName=“Lopingian”

Rank=“Series”

NodeName=“Base of Artinskian”

NodeName=“Base of Permian”

Eventdescription=“Conodont,

lowest occurrence of Streptognathodus isolatus”

Eventdescription=“Conodont,

disappearance of Foo bar”

Stratotypedescription=“27 m above base of Bed 19,

Aidaralash Creek, Aktöbe, southern Ural Mountains, northern Kazakhstan”

Stratotypedescription=“Some other place”

These are ordinal

timescale components

These are components required

for correlation and timescale calibration

AgeMeasurementresult=“-299 Ma”

AgeMeasurementresult=“-298 Ma”

Preferred age for this node