A formal model for the geologic time scale and global stratotype
section and point, compatible with geospatial
information transfer standards
Simon J.D. Cox*
CSIRO Exploration and Mining, P.O. Box 1130, Bentley, 6102 WA, Australia
Stephen M. Richard*
Arizona Geological Survey, 416 W. Congress St., #100, Tucson, Arizona 85701, USA
ABSTRACT
The geologic time scale is a complex data
structure composed of abstract elements
that represent time intervals and instants
and their relationships with specific concrete representations in the geologic record
as well as the observations made of those
concrete representations. The International
Union of Geological Sciences’ International
Commission on Stratigraphy guidelines
recommends a very precise usage of the relationships between these components in
order to establish a standard time scale for
use in global correlations. However, this
has been primarily described in text. Here,
we present a formal representation of the
model using the Unified Modeling Language (UML). The model builds on existing
components from standardization of geospatial information systems. The use of a
formal notation enforces precise definition
of the relationships between the components. The UML platform also supports a
direct mapping to an eXtensible Markup
Language (XML)–based file format, which
may be used for the exchange of stratigraphic information using Web-service
interfaces.
Keywords: time scale, stratigraphy, information model, XML, UML.
INTRODUCTION
Goals
The goal of this paper is to provide an information model for the geologic time scale.
*E-mails: [email protected]; steve.richard@
azgs.az.gov.
A formal notation is used so as to provide a
rigorous description of the various elements
required to describe the structure and calibration of the time scale in a manner that
allows the logical consistency of the model
to be evaluated. This is important, since although stratigraphic methodology is one of
the most rigorously studied aspects of geological practice, it has evolved throughout
the era of historical geology. There have been
significant changes in best practice, in particular in the shift from characterizing units to
defining the boundaries between them. Nevertheless, the time scale itself remains based
on named units and eras. Other residues of
earlier practice remain visible in the description of the time scale, particularly where
agreement on the application of current practices is incomplete. In this context, a rigorous
characterization of the relationships between
the elements of the time scale, the evidence
in the geologic record, and the application of
specific procedures to effect numeric calibration of the scale is essential.
A secondary goal is to develop a machineprocessable format for the exchange of information related to the time scale. The modeling notation selected (Unified Modeling
Language [UML]) is a commonly used software engineering standard, so the model can
be implemented easily on various standard
platforms. In particular, an eXtensible Markup Language (XML) document schema can
be derived directly from the model. The
XML implementation supports lossless data
transfer using standard Web protocols, and it
provides a basis for formal encoding and
computer processing of information that is
the basis for defining geologic time scales.
Structure of the Paper
This paper is structured as follows. An introduction and summary of key aspects of
stratigraphic methodology is provided in the
first section. Next, we briefly introduce information standardization activities that provide
the modeling framework and notation used in
this study. We then describe a general framework for temporal reference systems and develop a formal model for the geologic time
scale and its calibration within that framework. This conceptual model is used as the
basis for an XML implementation of the model, presented using example documents describing the International Union of Geological
Sciences (IUGS)’s International Commission
on Stratigraphy (ICS) time scale with global
stratotype section and point (GSSP) references. Some theoretical issues arising from the
models are discussed. A summary of UML
notation is given in Appendix 1.
THE GEOLOGIC TIME SCALE
Units, Boundaries, and Stratotypes
The conventional geologic time scale is a
reference system defined by a contiguous sequence of time intervals, each identified with
a name. These are recursively subdivided, resulting in a hierarchy composed of intervals
of various ranks. The units in the scale are
ordered, so the relative temporal positions of
geologic objects and events may be recorded
or asserted, denoted by the names of units
from the scale.
As originally conceived, units of the geologic time scale identify intervals, each corresponding to the time during which a partic-
Geosphere; December 2005; v. 1; no. 3; p. 119–137; doi: 10.1130/GES00022.1; 6 figures; 1 table.
For permission to copy, contact [email protected]
q 2005 Geological Society of America
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S.J.D. COX and S.M. RICHARD
ular sequence of rocks (stratigraphic unit) was
deposited. Historically, the units were chosen
because, within the region where they were
defined, they could be recognized through uniform lithological and biostratigraphic characteristics, which correlated with a relatively
consistent geological environment in a single
period. The representative object or prototype
in a stratigraphy defined in this way is a type
section for the geologic unit of interest, formally called a unit stratotype. This approach
supports stratigraphic practice in which assignment of strata to a unit is based on the
presence of characteristics that match the strata to the type section for the unit. The basis
for the matching, or correlation, may be lithologic, paleontologic, or geochronologic, defining lithostratigraphic, biostratigraphic, and
chronostratigraphic units.
Construction of a consistent time scale using the unit stratotype approach depends critically on stratigraphic completeness and the
ability to geochronologically correlate bodies
of rock globally. However, the corollary of a
model based on continuity within units is that
the boundaries between units correspond with
changes in the geological environment and
discontinuities in the stratigraphic record.
Such discontinuities, and the incongruity of
lithostratigraphic and biostratigraphic units
with chronostratigraphic units, result in inconsistent and ambiguous correlation in the vicinity of chronostratigraphic unit boundaries.
For these reasons, the complementary approach to specification of the time scale is
now preferred, focusing on the boundaries
rather than the intervals. Within this model,
the focus is on a representative point within
the geologic horizon corresponding to the
boundary of interest, formally called a boundary stratotype and often known as the ‘‘golden
spike.’’ Observations made at the point provide a basis for characterizing the boundary.
For example, estimates of the precise age of
the boundary may be made using geochronologic techniques on specimens sampled from
the stratotype point. These observations support progressive chronometric calibration of
the time scale one boundary at a time.
Boundary stratotypes are defined, wherever
possible, within sections where the geologic
record is continuous across the boundary. The
material above and below the point provide
context for the boundary, showing evidence
relating to the geological history adjacent to
the boundary. With enough stratotype points,
each representing boundaries of units of sufficiently fine rank, the partial units represented
in the sections containing the points overlap
to provide a basis for characterizing the com-
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plete time scale. However, a complete compilation is possible only based on sections that
explicitly include boundaries. Implicitly, the
shift from unit stratotypes to boundary stratotypes recognizes that, although the time
scale is based on time intervals covering the
domain, its logical consistency is contingent
on a globally recognizable, unambiguously ordered sequence of events.
Governance and Calibration
The guidelines of the ICS formalize this
practice (Remane et al., 1996). These are used
by the GSSP project. The GSSP provides a
forum for the specification of boundary stratotypes used for correlation on a global scale.
Local stratigraphic definitions will still be
used for local stratigraphic correlations, but
global stratotypes provide the ultimate reference for inter-regional correlation. Local
stratigraphic schemes must be related to the
GSSP stratotypes through a coherent chain of
correlations in order to be connected to the
global time scale. Alternatively, geochronometric methods may be used for objects within those parts of the time scale where chronometric values for the boundaries have been
accepted.
Physical changes in the rock record observed at the boundary horizon are inferred to
result from a geologic event or events. Ideally,
these are manifested globally by similar or related physical changes in sediment deposited
at the same time. Correlation of the boundary
horizons by correlation of physical changes in
other stratigraphic sections is the basis for establishing the relative age of strata throughout
Earth.
A GSSP is a particular sequence of stratified rocks defined to contain a particular,
physically located stratigraphic point that
serves as the reference object to define the
boundary between units in the time scale. In
chronologic terms, each point corresponds to
a time instant at the boundary between time
intervals that compose the time scale, while in
stratigraphic terms, the stratigraphic point defines the lower boundary of rocks formed during a named interval.
In the context of the GSSP project, boundary stratotypes provide the ultimate definition
of elements of the time scale from the beginning of the Ediacaran up to but (probably) not
including the beginning of the Holocene. For
the earlier parts of the time scale, boundaries
between intervals are defined chronometrically by assigning a numerical age to the boundary. These numerically defined boundaries are
Geosphere, December 2005
called global standard stratigraphic ages
(GSSA).
Ages recorded using named units from the
geologic time scale allow ordering without requiring numeric values. However, while the
assignment of numeric values is not necessary
for use of the time scale, it is convenient to
calibrate the time scale against a time line. For
those boundaries defined by a stratotype, it
provides a locality from which specimens may
be collected, the age of which may then be
measured using quantitative techniques. When
the material in the stratotype is unsuitable or
insufficient for estimating the numerical age,
then specimens from locations that can be correlated with the stratotype may be used instead. The experimentally determined dates
from such specimens provide an estimate of
the chronologic position (numeric coordinate
on a time line) of the boundary.
Formalization
This overview of the construction and calibration of the geologic time scale refers to a
variety of concepts, instances of which are related to each other in various ways. Effective
use of the time scale for stratigraphic correlation requires that these concepts and their
interrelationships be precisely understood.
There is a significant body of literature that
describes the system, an introduction to which
is provided by Walsh et al. (2004) and references therein, in the ICS guidelines (Remane
et al., 1996), and in the overview to the International Stratigraphic Chart (International
Commission on Stratigraphy, 2004).
However, the model for the construction
and calibration of the geologic time scale has
been described primarily in prose. This leaves
open the possibility of ambiguity and omission. The most formal representation of the
conceptual model is provided by the schemata
(column headings) of various tabulations of
the time scale and associated components. In
this paper, we attempt to improve on this by
providing a description of the system in a
standard framework used for modeling technical information, using a standard symbolic
notation. The framework is object-oriented
(OO) modeling and analysis, and the notation
that we use is the class diagram from the UML
(Object Management Group, 2004).
We use the UML notation for three reasons:
(1) it provides a rich description of concepts
and their interrelationships that allows us to
capture most of the nuances required, while
its graphical nature allows these to be communicated to readers of various levels of expertise; (2) it is commonly used in software
FORMAL MODEL FOR GEOLOGIC TIME SCALE
engineering, so models defined in UML can
be easily converted into software representations, including XML (Yergeau et al., 2004),
Java, C11, C#, etc.; and (3) it is the notation
used by the leading organizations involved in
standardization of geospatial information systems. This allows us to construct specialized
software components for the geosciences that
leverage existing technology.
A particular advantage of the OO approach
is that the key information can be partitioned
into different objects, and relationships between objects can be described independent of
the level of detail known about each of the
objects. While it is out of scope in this paper
to provide an introduction to OO modeling
and analysis (there are many introductory
books), a brief summary of UML as used in
this report is provided in Appendix 1.
STANDARDS CONTEXT
General Geospatial Information
Most investigations in geology have a
strong geospatial flavor, and database and geographic information system (GIS) technology
are commonly used for the management and
display of geologic data. It is therefore both
convenient and efficient to develop models
and encodings for geologic information that
leverage developments in geospatial standards. The standardization framework that we
use also addresses temporal issues in a manner
that allows us to combine the concerns in a
single model and encoding.
The methodology used in this report follows procedures and notation used in specifications issued by the International Organization for Standardization Technical Committee
211 (ISO/TC 211) and by the Open Geospatial
Consortium (OGC). These organizations have
been active since the mid-1990s, working to
standardize models, representations, and processing services for geographic information.
ISO/TC 211 is responsible for around 40
international standards and reports in the ISO
19100 series. These specifications primarily
describe conceptual or abstract models and approaches. OGC plays a complementary role in
developing and testing specifications for geospatial data access and processing services,
and implementation encodings for some of the
information models developed through ISO.
Of interest to us in the context of this report
are the following:
ISO 19109, Rules for Application Schema,
formally recognizes the existence of communities with needs for thematically specific information models and provides a
‘‘feature model’’ that serves as the basic
framework for classifying the items of interest in the application domain;
ISO TS 19103, Conceptual Schema Language,
lays out the UML profile used as the notation across the ISO 19100 series;
ISO 19108, Temporal Schema, describes a
consistent model for temporal objects and
reference systems; and
ISO DIS 19136, Geography Markup Language (GML), is an XML schema for components for geographic information.
GML (Cox et al., 2004) was developed by
OGC, and includes an implementation of the
temporal schema from ISO 19108. In this report, we lean heavily on the theoretical framework provided by ISO 19108 and its XML
implementation in GML. The models shown
in this report utilize the UML notation defined
in ISO 19103.
A model and encoding for observations and
measurements (O&M) has also been published through OGC (Cox, 2003). This provides a basis for describing specialized date
measurements used for calibration of the time
scale.
Geoscience Information
In addition to these activities that standardize generic geospatial information, there are
several related projects directly addressing the
geosciences. These include:
eXploration and Mining Markup Language
(XMML) (http://xmml.arrc.csiro.au)—GMLbased XML encoding for mineral exploration
data. This includes components related to observations and measurements that are used in
this report.
The North American Data Model (NADM)
(http://nadm-geo.org)—conceptual models for
information associated with geologic maps,
presented using UML. This includes models
for earth materials, geologic units, genesis,
geologic structure, etc., which define a basic
framework for representing geoscience information in computer information systems.
NADM was developed by a group of geologists and information specialists from state
and federal geological surveys in Canada and
the United States.
GeoSciML—a project under the auspices of
the IUGS Commission for Geoscience Information, to develop a GML-based XML encoding for geosciences. The principal stakeholders are statutory data custodians, and the
focus is on the information required to support
the maintenance of geologic maps. However,
this is being done through a high-level conceptual model that has many components that
Geosphere, December 2005
will be of interest to the broader geoscience
community.
GeoSciML is building on earlier work, in
particular, that of the XMML and NADM
projects. The geologic time scale encoding described in this report is likely to be incorporated in GeoSciML.
STANDARDS COMPONENTS USED IN
THE TIME SCALE MODEL
Base Classes
Most of the classes shown in the following
sections and diagrams inherit some standard
properties from common base classes. The
base classes are taken from ISO 19108 and
from the UML representation of GML 3,
GeoSciML, and O&M. Important base classes
referred to in this report include:
Definition carries a mandatory ‘‘name’’ property, plus an unlimited set of aliases, and
has an optional ‘‘description,’’ which carries the text of the definition or a link to a
source.
Observation is an event, producing a ‘‘result’’
describing the value of some property of its
target (e.g., a specimen). The result may
take many forms: a Measurement is a special case that results in a numeric value with
unit-of-measure. Every Observation has a
featureOfInterest and uses a Procedure.
Procedure is a description of a process, such
as an instrument, sensor, sample preparation, calculation, simulation, etc.
Section, Station are identifiable locations with
a shape corresponding to a curve and point,
respectively, usually associated with making observations and retrieving specimens.
Specimen is material retrieved by sampling at
a location or on another feature, typically
used as the subject of an observation or
measurement.
Temporal Reference Systems
Figure 1 shows components concerning generic temporal objects and reference systems.
The classes prefixed ‘‘TMp’’ are taken directly
from ISO 19108, while the other classes represent the extensions required for the model
in this paper.
All temporal reference systems derive from
a common TMpReferenceSystem. This has a
mandatory property, domainOfValidity, which
describes the spatiotemporal scope of the reference system (e.g., common era, global or
Cambrian, Australia). Four concrete specializations are defined as follows:
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S.J.D. COX and S.M. RICHARD
Figure 1. Model for temporal reference systems, adapted from ISO 19108:2003. TimeOrdinalEraBoundary class is a modification required for stratigraphy and archaeology. Note: a parent class not shown in the diagram is indicated by its name in italics above the
name of the derived class.
TMpCalendar is a reference system based on
years, months, and days.
TMpClock is based on hours, minutes, and
seconds in a particular day.
TMpCoordinateSystem provides the basis for
numerically describing temporal position.
This uses two properties to define a time
line: an origin, which ties the scale to an
external temporal reference position, and
interval, which provides the basic unit or
precision, such as seconds or millions of
years.
TimeOrdinalReferenceSystem (TORS) provides the system required for a time scale
based on named intervals. A TORS is composed of an ordered sequence of one or
more component TimeOrdinalEra (TOE) elements. A TOE may be recursively decomposed into ordered member TOE elements,
thus allowing a hierarchical system to be
constructed. Each era is characterized by its
name (inherited from Definition). Note that
122
the term ‘‘era’’ is used generically, and is
used for component intervals of all ranks.
In the definition of TOE, we have found it
necessary to introduce a variation to the ISO
definition. In the standard model (ISO 19108:
2003), the limits of TMpOrdinalEra are defined precisely by attributes of type DateTime.
However, in historic, archaeological contexts,
and certainly in the geologic time scale, while
the order of eras within a TORS is known, the
positions of the boundaries are often not precisely known and can only be estimated. We
suggest that standard practice is better represented by a model using an explicit TimeOrdinalEraBoundary (TOEB) element to carry
information concerning the transition between
two TOEs. The temporal position of the era
boundary is given by an associated TimeInstant, but the TOEB exists in its own right
even if its position is not known. In the context of the geological time scale, the TOEB is
Geosphere, December 2005
central since it is the temporal concept that is
associated with the boundary stratotype.
Finally, the TMpPosition data type carries a
‘‘frame’’ property, which indicates which reference frame is used, usually an instance of
one of the temporal reference systems.
MODEL FOR GEOLOGIC TIME
SCALE
In the portrayal of the model in this report,
the information is partitioned between several
diagrams for convenience (Figs. 2–5). The
union of these describes a general model for
time scales and the relationships with evidence in the geologic record. It is intended to
include all components necessary to describe
the practice specified in the ICS guidelines
(Remane et al., 1996), but it also includes elements and relationships that relate it to other
methodologies, in particular, for defining local
or regional time scales. In order to illustrate
FORMAL MODEL FOR GEOLOGIC TIME SCALE
Figure 2. Basic geologic time scale (many attributes suppressed for clarity).
the application of the model to the GSSP, a
summary diagram is provided in which relationships that are not required by the ICS
guidelines are omitted (Fig. 5).
The Geologic Time Scale
Figure 2 shows the way the generic components are extended for geochronologic
purposes.
GeologicTimescale is a kind of TORS that
is composed of one or more ordered TOEs
together with two or more TOEBs.
GeologicTimescale is, thus, a temporal complex that includes both the eras and the bound-
aries composing the reference system as firstorder
elements.
Geochronologic
specializations of each are provided.
GeochronologicEra is a kind of TimeOrdinalEra with boundaries defined by geologic evidence. It specializes TimeOrdinalEra
by adding a ‘‘rank’’ attribute, whose value is
one of the standard terms, such as eon, era,
period, etc. Some additional properties are discussed in a following section.
Two specializations of TOEB are introduced. GeochronologicBoundary represents
an era boundary defined with reference to
some geologic evidence. Its properties are discussed in detail in the following section.
Geosphere, December 2005
NumericEraBoundary is provided for those
boundaries defined chronometrically. It has no
additional associations, but a ‘‘status’’ attribute is provided.
Geologic Evidence and the Time Scale
Figure 3 shows relationships of the conceptual objects with certain physically realizable
geologic feature types, including units and
sections, samples of which may play roles as
stratotypes. Both eras and boundaries are represented in the geologic record.
A ChronostratigraphicUnit is the (notional)
feature composed of all the rocks formed dur-
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S.J.D. COX and S.M. RICHARD
Figure 3. Relationship of geological features to elements of the time scale (many attributes suppressed for clarity).
ing the associated GeochronologicEra. Both
ChronostratigraphicUnit and the commonly
used LithostratigraphicUnit are kinds of
GeologicUnit. Similarly, a ChronostratigraphicBoundary is the (notional) compound
surface marking the upper or lower bound of
a unit. Both ChronostratigraphicBoundary and
LithostratigraphicBoundary are kinds of
StratigraphicBoundary. In practice, the complete shape of any ChronostratigraphicUnit
and ChronostratigraphicBoundary instance
will not be precisely known, so while the existence of a unit and its boundaries is a fact,
they will never be fully described. The
ChronostratigraphicUnit is the complete body
of rock formed during (formedDuring) a
GeochronologicEra, and the ChronostratigraphicBoundary correlates with (correlatesWith) a GeochronologicBoundary. A ChronostratigraphicUnit carries a ‘‘rank’’ attribute,
whose value is one of the standard terms such
as system, stage, zone, etc.
Conventional samples of both units and
boundaries may be defined, with a spatial dimensionality two orders less than the parent.
For a solid unit, this sample is a section
(whose shape is a curve), while for a surface
the sample is a point. These are shown in the
model as StratigraphicSection and StratigraphicPoint, respectively. A StratigraphicPoint is always contained within a
StratigraphicSection, which is its hostSection.
In principle, a StratigraphicSection may host
any number of StratigraphicPoints. While an
unlimited number of samples of the concrete
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geological unit or boundary may be made, a
single instance must provide the reference locality or stratotype for the associated era or
era-boundary, respectively.
A further important concept is the
StratigraphicEvent. In general, events are associated with time primitives of either zero or
a finite extent (i.e., time instants or time periods). However, in the context of the geological time scale, a useful event has negligible
duration, and is associated with a boundary
and characterized by a StratigraphicPoint.
Calibration of the Time Scale
The time scale is calibrated by estimating
the position or time-coordinate of boundaries
within it (Gradstein and Ogg, 2004). Determination of geologic age fundamentally relies
on isotopic dating of mineral phases that can
be related to the age of the enclosing rock (see
Faure, 1977), or to the correlation of calculated changes in Earth’s orbital parameters as a
function of time to patterns of physical property variations related to those parameters in
stratigraphic sequences (Laskar, 1999; Shackleton et al., 1999). Thus, estimation of the position of a boundary is based on observations
made on specimens collected from stratigraphic sections that contain, or may be correlated
with, a boundary stratotype, or observations
made concerning the position of a boundary
stratotype within patterns displayed in its host
section. Figure 4 introduces classes supporting
Geosphere, December 2005
the process of estimating the numeric position
of a boundary.
DateMeasurement is a kind of measurement
whose result is a (numeric) value with reference to a TimeCoordinateSystem (Fig. 1). In
common with all observations, it relates to a
physical target or featureOfInterest, usually either (1) a specimen, or (2) a sampling site
such as a StratigraphicPoint in its context
within its host StratigraphicSection. The measurement uses a DatingProcedure, preferably
a precise numeric method such as one of the
radiometric methods or based on astronomical
cycles. If these are not suitable for the physical evidence, then less precise methods are
used.
The GeochronSpecimen is some material
that samples a site. The site will strictly be a
small interval bracketing a point of interest
(i.e., a short section), but may often be treated
as a point at the scale of interest. If the material at the stratotype itself is unsuitable for
date determination, then the featureOfInterest
related to the actual measurement may sample
a different locality that is correlated with the
stratotype, or with another known relationship
with the stratotype.
Finally, StratigraphicDateEstimate represents an identified interpretation of temporal
position and is substitutable for TimeInstant.
The observationalBasis of the StratigraphicDateEstimate may be one or more observations (e.g., DateMeasurements). Thus, the association labeled ‘‘Geometry’’ between
TimeInstant and TimeOrdinalEraBoundary
FORMAL MODEL FOR GEOLOGIC TIME SCALE
Figure 4. Calibration of the time scale through date determinations on specimens or points.
usually refers to a StratigraphicDateEstimate
when the GeochronologicBoundary descendent is involved
Note the various cardinalities on the associations. A measurement is associated with a single
procedure and a single target object. Specimens
may be associated with a point or interval. Measurements may be made on a target. Some of
the associations are only traversable in one direction: a procedure does not know about all the
measurements made using it; a DateMeasurement does not know if it is used as the
basis for a StratigraphicDateEstimate.
Representation of the ICS Model
The model shown in Figures 1–4 provides
a description of a relatively comprehensive set
of relationships between objects involved in
the definition and calibration of the geologic
time scale. This includes a number of associations that reflect relationships between ob-
jects in the system, but which are not required
or are deprecated in modern stratigraphic
practice, as defined in the guidelines of the
ICS (Remane et al., 1996).
The diagram in Figure 5 shows a complete
model, constructed by combining elements introduced in Figures 1–4, but suppressing classes and associations that either conflict with
or are not used by the practice described in
the guidelines (Remane et al., 1996). Furthermore, in this diagram most of the required
class attributes are shown. For example, a
number of attributes describe details of points
and sections, some of which are inherited
from parent classes as indicated by the
annotation.
We may summarize the story told in this
model as follows.
GeologicTimescale is a specialized TORS
and is composed of an ordered sequence of
TOE elements, along with the TOEB elements
that act as reference points. TOE elements are
Geosphere, December 2005
recursively nested and assigned a rank within
a standard hierarchy. GeochronologicEra and
GeochronologicBoundary are specializations
of the standard eras and boundaries.
One StratigraphicPoint plays the role of
stratotype for a GeochronologicBoundary,
which records a GeochronologicEvent. The
GeochronologicBoundary corresponds with
the initiation of rock formation during the
GeochronologicEra for which the StratigraphicPoint is the lower boundary-stratotype.
Under ICS guidelines there is no corresponding association of a unique stratigraphic section with a GeochronologicEra. Unit stratotypes may be used for regional and local
purposes, but their use is deprecated for specification of the global time scale.
DateMeasurements are made on either (1) a
StratigraphicPoint in its context (e.g., for determinations based on astronomical cycles), or
(2) on a GeochronSpecimen (e.g., for radiometric date determinations). Specimens may
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S.J.D. COX and S.M. RICHARD
126
Geosphere, December 2005
FORMAL MODEL FOR GEOLOGIC TIME SCALE
TABLE 1. MAPPING BETWEEN REQUIREMENTS OF ICS GUIDELINES AND ELEMENTS IN THE MODEL PRESENTED IN THIS PAPER
ICS requirement
Name of the boundary
GSSP definition
Stratigraphic rank and status of the boundary
Stratigraphic position of the defined unit
Type locality of the GSSP
Corresponding model element
GeochronologicBoundary::name
StratigraphicSection::description
StratigraphicPoint::boundary:GeochronologicBoundary::nextEra
:GeochronologicEra::rank
StratigraphicPoint::status
StratigraphicPoint::boundary:GeochronologicBoundary::nextEra
:GeochronologicEra::name
Or
StratigraphicSection::era:GeochronologicEra::name
StratigraphicSection::begin
Geologic setting and geographic location
StratigraphicSection::geologicSetting
StratigraphicSection::boundedBy
Lithology/sedimentology/paleobathymetry
StratigraphicSection::geologicDescription
Map
Accessibility, both logistically and politically
StratigraphicSection::accessibility
Conservation
StratigraphiSection::conservation
Identification in the field
Stratigraphic completeness of the section
Global correlation using, where applicable,
biostratigraphy, magnetostratigraphy, stable
isotope stratigraph, and other stratigraphic
tools and methods
Best estimate of age in millions of years
References to background studies
be sampled in the stratotype section, or another StratigraphicSection that is correlated with
the stratotype. A StratigraphicDateEstimate
provides the preferred value of the position of
the GeochronologicBoundary. The estimate is
usually based on one or more DateMeasurements, but may be derived from some
other basis.
A StratigraphicDateEstimate has a quality
associated with it, which allows the estimated
error to be recorded. StratigraphicDateEstimate along with both StratigraphicPoint
and StratigraphicSection have status attributes
that can be used to record whether these are
ratified through GSSP.
A suitable StratigraphicPoint has an association with one or more StratigraphicEvents,
which are associated with observable evidence
in the section that defines the point, such as
the appearance or disappearance of particular
fossil taxa, or the beginning or end of some
climatic phenomenon. Note, however, that in
the ICS approach, it is the StratigraphicPoint
StratigraphicPoint::description
StratigraphicSection::completeness
StratigraphicPoint::primaryGuidingCriterion
StratigraphicPoint::additionalCorrelationProperty[0..*]
StratigraphicPoint::boundary:GeochronologicBoundary::position
:StratigraphicDateEstimate::timePosition
StratigraphicPoint::reference
StratigraphicPoint::boundary:GeochronologicBoundary::position
:StratigraphicDateEstimate::reference
StratigraphicSection::reference
itself (the golden spike) that provides the ultimate reference for the boundary, so its position will remain unchanged even if new evidence modifies the interpretation of the
stratigraphic event (Walsh et al., 2004).
StratigraphicEvent inherits from the event
class (not shown) an eventTime association
with a notional time object. However, as used
here, it is assumed that the position of a
StratigraphicEvent is not available directly,
but may be recovered by tracing the association with a boundary or prototype point, for
which estimates of the position are available.
The ICS guidelines (Remane et al., 1996)
provide a set of information that must be supplied for a proposed GSSP. Table 1 shows how
these are implemented in the UML model presented here. All the required information has
suitable slots in the model, so this means that
the record of a submission to ICS could take
the form of a document structured according
to this model.
IMPLEMENTATION
XML Document Format
UML is a convenient means to represent an
information model. To make use of the model,
we require an implementation that allows instances that conform to the model to be expressed. Some software development environments support automatic configuration and
code generation of data structures and representations based on a UML model. The instances may take various forms, including tables and messages.
In this work we focus on a message format
using XML (Yergeau et al., 2004). XML is a
text-based method for serialization of structured
and semi-structured data primarily developed
for transfer using Web protocols, but may also
be used to define file-formats for persistent
storage. A particular advantage of the plain-text
encoding is that it allows inspection and modification using basic text-processing tools to
Figure 5. The elements of the time scale model used by the Global Stratotype Section and Point (GSSP) project. This is based on the
model shown in Figures 1–4, but only the relationships that are formally used in the GSSP project are shown. The colors provide an
informal high-level classification: those in yellow are generic time scale components, green are generic sampling and observation elements,
light brown are related to concrete objects in the field, and blue are abstract components associated with the geologic time scale.
N
Geosphere, December 2005
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S.J.D. COX and S.M. RICHARD
supplement processing using specialized software. However, it is important to note that
XML is not a presentation format, and the information in an XML document should be
transformed and formatted for human consumption. This might include transformations
of values from mathematical formats into conventional presentation forms. For example, latitude and longitude appear as signed decimal
degrees in a GML document, but cartographic
practice prefers a sexadecimal (degrees-minutesseconds-hemisphere) representation; geological dates are negative numbers relative to the
standard origin, but are usually viewed as positive numbers corresponding to age (see further discussion below).
As discussed above, XML representation of
data using GML is at the core of various Webservice interfaces defined for access to geospatial data by the Open Geospatial Consortium, such as Web Feature Service (Vretanos,
2005). GML is being ratified through ISO/TC
211 and currently has the status of Draft International Standard 19136.
Serialization Rules
A pattern for XML serialization is provided
by ISO 19118 and GML 3 (Cox et al., 2004).
This depends on the model using the UML
profile defined in ISO 19103 and GML 3,
mentioned above. In summary, the serialization method implements the metamodel in the
following ways:
1. The structure of the XML document corresponds to a view of the UML model as a
tree rooted at the class of interest;
2. Both classes and properties (UML attributes and associations) appear as XML elements in the XML instance document;
3. The XML element name matches the
class or property name (i.e., UML attribute
names, or in the case of associations, the rolename at the target class);
4. Where the value of a property has a
complex structure (i.e., shown as a class rather
than a data type in the UML model) it may
be given either as a structure of sub-elements
nested within the property element (‘‘inline’’),
or via a reference to a value elsewhere using
an ‘‘xlink:href’’ attribute on the property element; and
5. Generalization is implemented as substitution group affiliation in the XML schema.
Rule 1 is concerned with accommodating
the fact that, in general, a UML model is a
graph of links between classes, while XML’s
nested element pattern embodies a set of relationships that have a tree form.
Rules 2 and 3 mean that the resulting instance document is ‘‘striped,’’ with nested elements alternating between class and property
names, and where the appearance of a class as
a descendent of another class is always mediated by a container element corresponding
to a property.
The method uses an intermediate World
Wide Web Consortium (W3C) XML Schema
(Fallside et al., 2004) that implements the
model and supports schema-validation of instance documents.
Examples
Following the model and encoding rules described above, a representation of (parts of)
the geologic time scale and its calibration following the ICS guidelines is shown in Listings
1–5.
Listing 1 represents the complete geologic
time scale, though only the three eras of rank
Eon are shown, along with descriptions of the
two intermediate boundaries. An illustration
of the finer decomposition of parts of the
Phanerozoic and Late Permian is shown in
Listing 2.
Listing 1. The geologic time scale decomposed to eon level.
,?xml version5‘‘1.0’’ encoding5‘‘UTF-8’’?.
,gt:GeologicTimeScale gml:id5‘‘ICSTimeScalepEonsOnly’’.
,gml:description.The geologic timescale, as defined by ICS—decomposed to eons only,/gml:description.
,gml:name.ICS Geologic Timescale—eons only,/gml:name.
,gml:domainOfValidity.Earth,/gml:domainOfValidity.
,!– 55555555555555—.
,gt:component.
,gt:GeochronologicEra gml:id5‘‘AR’’.
,gml:name.Archean,/gml:name.
,gt:start xlink:href5‘‘urn:x-seegrid:items:exceptions:undefined’’/.
,gt:end xlink:href5‘‘#ARpPR’’/.
,gt:rank.Eon,/gt:rank.
,/gt:GeochronologicEra.
,/gt:component.
,gt:component.
,gt:GeochronologicEra gml:id5‘‘PR’’.
,gml:name.Proterozoic,/gml:name.
,gt:start xlink:href5‘‘#ARpPR’’/.
,gt:end xlink:href5‘‘#PRpPH’’/.
,gt:rank.Eon,/gt:rank.
,/gt:GeochronologicEra.
,/gt:component.
,gt:component.
,gt:GeochronologicEra gml:id5‘‘PH’’.
,gml:name.Phanerozoic,/gml:name.
,gt:start xlink:href5‘‘#PRpPH’’/.
,gt:end xlink:href5‘‘#present’’/.
,gt:rank.Eon,/gt:rank.
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FORMAL MODEL FOR GEOLOGIC TIME SCALE
,/gt:GeochronologicEra.
,/gt:component.
,!– 555555555555555555555555—.
,!—Reference times—.
,!—Positions of Global Stratotype Points as given in http://www.stratigraphy.org/gssp.htm 2004–04–25—.
,!– 555555555555555555555555—.
,gt:referencePoint.
,gt:NumericEraBoundary gml:id5‘‘ARpPR’’.
,gml:description xlink:href5‘‘citations.xml#Ev14p139p1991’’/.
,gml:name.Base Proterozoic,/gml:name.
,gml:name.Base Paleoproterozoic,/gml:name.
,gml:name.Base Siderian,/gml:name.
,gt:previousEra xlink:href5‘‘#AR’’/.
,gt:nextEra xlink:href5‘‘#PR’’/.
,gt:position.
,gml:TimeInstant gml:id5‘‘PRpOrigin’’.
,gml:timePosition frame5‘‘tcs.xml#geologyMA’’.22500.,/gml:timePosition.
,/gml:TimeInstant.
,/gt:position.
,gt:status.GSSA,/gt:status.
,/gt:NumericEraBoundary.
,/gt:referencePoint.
,gt:referencePoint.
,gt:GeochronologicBoundary gml:id5‘‘PRpPH’’.
,gml:description.Three different estimates of the position of this boundary are included.,/gml:description.
,gml:name.Base Phanerozoic,/gml:name.
,gml:name.Base Paleozoic,/gml:name.
,gml:name.Base Cambrian,/gml:name.
,gml:name.Base Lower Cambrian,/gml:name.
,gt:previousEra xlink:href5‘‘#PR’’/.
,gt:nextEra xlink:href5‘‘#PH’’/.
,gt:position.
,gt:StratigraphicDateEstimate gml:id5‘‘PHpOrigin’’.
,gml:timePosition frame5‘‘tcs.xml#geologyMa’’.-540.0,/gml:timePosition.
,gt:quality.
,meta:QuantitativeAssessment.
,meta:explanation.Error,/meta:explanation.
,meta:values uom5‘‘Ma’’.5,/meta:values.
,/meta:QuantitativeAssessment.
,/gt:quality.
,gt:status.Informal,/gt:status.
,gt:observationalBasis xlink:href5‘‘dates.xml#PHpOrigin1’’/.
,gt:observationalBasis xlink:href5‘‘dates.xml#PHpOrigin2’’/.
,gt:observationalBasis xlink:href5‘‘dates.xml#PHpOrigin3’’/.
,gt:metadata.,gsml:ObjectMetadata.,gsml:sourceReference xlink:href5‘‘citations.xml#chronos’’/.,/gsml:ObjectMetadata.
,/gt:metadata.
,/gt:StratigraphicDateEstimate.
,/gt:position.
,gt:event xlink:href5‘‘urn:x-seegrid:items:exceptions:unknown’’/.
,gt:stratotype xlink:href5‘‘gssp.xml#PHpOriginPoint1’’/.
,/gt:GeochronologicBoundary.
,/gt:referencePoint.
,/gt:GeologicTimeScale.
Note that in this and the subsequent examples, the XML document is composed of
elements from several different namespaces
(Bray et al., 1999). The components that are
specific to the geologic time scale are in a
namespace for which the ‘‘gt’’ prefix is used.
Components from other parts of GeoSciML
use the prefix ‘‘gsml.’’ General components
inherited from GML are indicated by the
‘‘gml’’ namespace prefix, some supporting el-
Geosphere, December 2005
ements from the ‘‘meta’’ namespace, and
components relating to observations and measurements and sampling, are from the ‘‘om’’
and ‘‘sa’’ namespaces.
The time scale is contained within a
129
S.J.D. COX and S.M. RICHARD
GeologicTimeScale element, and is composed
of a set of GeochronologicEra, NumericBoundary, and GeochronologicBoundary
elements.
The role of each GeochronologicEra in the
GeologicTimeScale is indicated by its container component element. GeochronologicEra
carries a name, start, end, and rank properties.
Ordering of the GeochronologicEras is encoded in the sequence of elements in the XML
document. Following a standard GML pattern
(Cox et al., 2004), the values of the start and
end properties are given via references that
link to definitions of boundaries available
elsewhere. The value of each link is a URIReference (Berners-Lee et al., 1998), pointing
to a fragment in a document identified by a
URI. In the examples shown here, many of the
references are internal to the same document,
so the short-form of pointer is used, comprising a pound symbol followed by the handle of
the target element.
Both the NumericBoundary and GeochronologicBoundary play the same role, as
referencePoints in the GeologicTimeScale,
and as the values of start or end properties of
the relevant eras. Note that these have multiple
names, which are equivalent. The ArcheanProterozoic boundary is a NumericBoundary
whose position is given as a TimeInstant. On
the other hand, the Proterozoic-Phanerozoic
boundary is a GeochronologicBoundary, for
which the position is a StratigraphicDateEstimate, based on several (links to) DateMeasurements. For a more complete illustration of StratigraphicDateEstimate and DateMeasurement, see Listing 3 below. The
boundary is associated with an event, and has
a stratotype, whose value is a link to a description of a StratigraphicPoint. For a more
complete illustration of StratigraphicEvent,
and StratigraphicPoint, see the discussion of
Listing 4 below.
Note that each of the elements representing
distinct identifiable objects (i.e., those that instantiate classes shown in Fig. 5) carries
‘‘gml:id’’ attribute. The value of this is unique
within the document, and provides a handle
for the document element and its contents,
which supports cross-references to this com-
ponent. Although it is not necessary for the
handle to have any semantic significance, here
we use the standard symbols for the handle
for eras as a mnemonic device (except that G
instead of « is used for the Cambrian Period.
This allows encoding using the reduced character set available on most standard keyboards), and for boundaries we concatenate
the symbols for the two adjoining eras with
an underscore.
Listing 2 shows an expansion of the Phanerozoic eon. This has three member
GeochronologicEra elements, describing the
Paleozoic, Mesozoic, and Cenozoic eras. The
conventional decomposition of the Paleozoic
is shown by five member elements carrying
links (to descriptions of eras not shown here)
and a final member element which contains a
GeochronologicEra element describing the
Permian period. The latter is decomposed further into GeochronologicEra elements representing (a subset of) the relevant epochs and
ages. Elements describing subage and chron
ranks are not shown.
Listing 2. The Phanerozoic era, decomposed to age level (Late Permian only).
,gt:GeochronologicEra gml:id5‘‘PH’’.
,gml:name.Phanerozoic,/gml:name.
,gt:start xlink:href5‘‘#PRpPH’’/.
,gt:end xlink:href5‘‘#present’’/.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘PZ’’.
,gml:description. Paleozoic Era.
Note that this era definition contains references to some eras that are not yet described here:
viz. G, O, S, D, C.,/gml:description.
,gml:name.Paleozoic,/gml:name.
,gt:start xlink:href5‘‘#PRpPH’’/.
,gt:end xlink:href5‘‘#PZpMZ’’/.
,gt:member xlink:title5‘‘Cambrian’’ xlink:href5‘‘#G’’/.
,gt:member xlink:title5‘‘Ordovician’’ xlink:href5‘‘#O’’/.
,gt:member xlink:title5‘‘Silurian’’ xlink:href5‘‘#S’’/.
,gt:member xlink:title5‘‘Devonian’’ xlink:href5‘‘#D’’/.
,gt:member xlink:title5‘‘Carboniferous’’ xlink:href5‘‘#C’’/.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘P’’.
,gml:description. Permian-Carboniferous time scale is derived from calibrating a master composite section to selected radiometric ages,/gml:description.
,gml:name.Permian,/gml:name.
,gt:start xlink:href5‘‘#CpP’’/.
,gt:end xlink:href5‘‘#PZpMZ’’/.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘P1’’.
,gml:name.Cisuralian,/gml:name.
,gt:start xlink:href5‘‘#CpP’’/.
,gt:end xlink:href5‘‘#P1pP2’’/.
,gt:group xlink:href5‘‘#P’’/.
,gt:rank.Epoch,/gt:rank.
,/gt:GeochronologicEra.
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,/gt:member.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘P2’’.
,gml:name.Guadalupian,/gml:name.
,gt:start xlink:href5‘‘#P1pP2’’/.
,gt:end xlink:href5‘‘#P2pP3’’/.
,gt:group xlink:href5‘‘#P’’/.
,gt:rank.Epoch,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘P3’’.
,gml:name.Lopingian,/gml:name.
,gt:start xlink:href5‘‘#P2pP3’’/.
,gt:end xlink:href5‘‘#PZpMZ’’/.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘p8’’.
,gml:name.Wuchiapingian,/gml:name.
,gt:start xlink:href5‘‘#P2pP3’’/.
,gt:end xlink:href5‘‘#p8pp9’’/.
,gt:group xlink:href5‘‘#P3’’/.
,gt:rank.Age,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘p9’’.
,gml:name.Changhsingian,/gml:name.
,gt:start xlink:href5‘‘#p8pp9’’/.
,gt:end xlink:href5‘‘#PZpMZ’’/.
,gt:group xlink:href5‘‘#P3’’/.
,gt:rank.Age,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:group xlink:href5‘‘#P’’/.
,gt:rank.Epoch,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:group xlink:href5‘‘#PZ’’/.
,gt:rank.Period,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:group xlink:href5‘‘#PH’’/.
,gt:rank.Era,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:member.
,gt:GeochronologicEra gml:id5‘‘MZ’’.
,gml:description. Mesozoic Era
Note that this era definition contains references to some eras that are not yet described here:
viz. T, J K.,/gml:description.
,gml:name.Mesozoic,/gml:name.
,gt:start xlink:href5‘‘#PZpMZ’’/.
,gt:end xlink:href5‘‘#MZpCZ’’/.
,gt:member xlink:title5‘‘Triassic’’ xlink:href5‘‘#T’’/.
,gt:member xlink:title5‘‘Jurassic’’ xlink:href5‘‘#J’’/.
,gt:member xlink:title5‘‘Cretaceous’’ xlink:href5‘‘#K’’/.
,gt:group xlink:href5‘‘#PH’’/.
,gt:rank.Era,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
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S.J.D. COX and S.M. RICHARD
,gt:member.
,gt:GeochronologicEra gml:id5‘‘CZ’’.
,gml:description. Cenozoic Era
Note that this era definition contains references to some eras that are not yet described here:
viz. Pg, Ng.,/gml:description.
,gml:name.Cenozoic,/gml:name.
,gt:start xlink:href5‘‘#MZpCZ’’/.
,gt:end xlink:href5‘‘#present’’/.
,gt:member xlink:title5‘‘Paleogene’’ xlink:href5‘‘#Pg’’/.
,gt:member xlink:title5‘‘Neogene’’ xlink:href5‘‘#Ng’’/.
,gt:group xlink:href5‘‘#PH’’/.
,gt:rank.Era,/gt:rank.
,/gt:GeochronologicEra.
,/gt:member.
,gt:rank.Eon,/gt:rank.
,/gt:GeochronologicEra.
Listing 2 primarily illustrates how the component GeochronologicEra elements are nested, following the structure of TimeOrdinalReferenceSystem given by ISO 19108.
Listing 3 shows the details of two GeochronologicBoundary elements, which delimit the Changhsingian age shown in Listing 2. The estimate
of the time position of each is carried by a StratigraphicDateEstimate element, each of which in turn points to their observationalBasis in the
form of DateMeasurements shown in Listing 4. The structure of DateMeasurement follows the Observations and Measurements model (Cox,
2003) to capture various metadata about the details of the measurement. In the cases shown here, the target of all DateMeasurements is indicated
simply as the stratotype, but in general a feature such as a GeochronSpecimen may be indicated, supporting a full record of the details of the
experimental process. Each boundary has event and stratotype elements which carry links to a StratigraphicEvent and StratigraphicPoint,
respectively.
Listing 3. Two Geochronologic Boundry descriptions and associated StratigraphicDataEstimate and the DateMeasurement elements
relating to one of the eras shown in Listing 2.
,gt:referencePoint.
,gt:GeochronologicBoundary gml:id5‘‘p8pp9’’.
,gml:name.Base of Changhsingian,/gml:name.
,gt:previousEra xlink:href5‘‘#p8’’/.
,gt:nextEra xlink:href5‘‘#p9’’/.
,gt:position.
,gt:StratigraphicDateEstimate gml:id5‘‘p9pOrigin’’.
,gml:timePosition frame5‘‘tcs.xml#geologyMA’’.-253.8,/gml:timePosition.
,gt:quality.
,meta:QuantitativeAssessment.
,meta:explanation.Error,/meta:explanation.
,meta:values uom5‘‘Ma’’.0.7,/meta:values.
,/meta:QuantitativeAssessment.
,/gt:quality.
,gt:status.Informal,/gt:status.
,gt:observationalBasis xlink:href5‘‘dates.xml#p9pOrigin1’’/.
,gt:metadata.,gsml:ObjectMetadata.,gsml:sourceReference xlink:href5‘‘citations.xml#Ogg1’’/.,/gsml:ObjectMetadata.
,/gt:metadata.
,/gt:StratigraphicDateEstimate.
,/gt:position.
,gt:event xlink:href5‘‘gssp.xml#p8pp9p1’’/.
,gt:stratotype xlink:href5‘‘gssp.xml#gssppbasepchanghsingian’’/.
,/gt:GeochronologicBoundary.
,/gt:referencePoint.
,gt:referencePoint.
,gt:GeochronologicBoundary gml:id5‘‘PZpMZ’’.
,gml:name.Base of Mesozoic,/gml:name.
,gml:name.Base of Triassic,/gml:name.
,gml:name.Base of Lower Triassic,/gml:name.
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FORMAL MODEL FOR GEOLOGIC TIME SCALE
,gml:name.Base of Induan,/gml:name.
,gt:previousEra xlink:href5‘‘#p9’’/.
,gt:previousEra xlink:href5‘‘#P’’/.
,gt:previousEra xlink:href5‘‘#PZ’’/.
,gt:nextEra xlink:href5‘‘#MZ’’/.
,gt:nextEra xlink:href5‘‘#T’’/.
,gt:nextEra xlink:href5‘‘#t1’’/.
,gt:position.
,gt:StratigraphicDateEstimate gml:id5‘‘MZpOrigin’’.
,gml:timePosition frame5‘‘tcs.xml#geologyMA’’.-251.0,/gml:timePosition.
,gt:quality.
,meta:QuantitativeAssessment.
,meta:explanation.Error,/meta:explanation.
,meta:values uom5‘‘Ma’’.0.4,/meta:values.
,/meta:QuantitativeAssessment.
,/gt:quality.
,gt:status.GSSP Ratified 2001,/gt:status.
,gt:observationalBasis xlink:href5‘‘dates.xml#MZpOrigin1’’/.
,gt:metadata.,gsml:ObjectMetadata.,gsml:sourceReference xlink:href5‘‘citations.xml#E24p102p2001’’/.,/gsml:ObjectMetadata.,/gt:metadata.
,/gt:StratigraphicDateEstimate.
,/gt:position.
,gt:event xlink:href5‘‘gssp.xml#PZpMZp1’’/.
,gt:stratotype xlink:href5‘‘gssp.xml#gssppbaseptriassic’’/.
,/gt:GeochronologicBoundary.
,/gt:referencePoint.
Listing 4 contains the details of DateMeasurements that are the basis for StratigraphicDateEstimates. This listing is referred to as dates.xml
in Listing 3.
Listing 4. Details of DateMeasurements that are the basis for StratigraphicDataEstimates. This listing is referred to as dates.xml in
Listing 3.
,gml:featureMember.
,gt:DateMeasurement gml:id5‘‘p9pOrigin1’’.
,gml:description.Calibration of a master composite section to selected radiometric ages,/gml:description.
,om:time.
,gml:TimeInstant gml:id5‘‘p9pOriginpMeasured’’.
,gml:timePosition.2001,/gml:timePosition.
,/gml:TimeInstant.
,/om:time.
,om:location xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,om:procedure xlink:href5‘‘http://www.stratigraphy.org/procedures/geochronology/compositeSectionCalibration’’/.
,om:observedProperty xlink:href5‘‘urn:x-ogc:def:phenomenon:OGC:Age’’/.
,om:quality.
,meta:QuantitativeAssessment.
,meta:explanation.Error,/meta:explanation.
,meta:values uom5‘‘Ma’’.0.7,/meta:values.
,/meta:QuantitativeAssessment.
,/om:quality.
,om:featureOfInterest xlink:href5‘‘gssp.xml#gssppbasepchanghsingian’’/.
,om:result uom5‘‘Ma’’.253.8,/om:result.
,/gt:DateMeasurement.
,/gml:featureMember.
,gml:featureMember.
,gt:DateMeasurement gml:id5‘‘MZpOrigin1’’.
,gml:description.U-Pb ages bracket GSSP,/gml:description.
,om:time.
,gml:TimeInstant gml:id5‘‘MZpOriginpMeasured’’.
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,gml:timePosition.1998,/gml:timePosition.
,/gml:TimeInstant.
,/om:time.
,om:location xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,om:procedure xlink:href5‘‘http://www.stratigraphy.org/procedures/geochronology/UpPb’’/.
,om:observedProperty xlink:href5‘‘urn:x-ogc:def:phenomenon:OGC:Age’’/.
,om:quality.
,meta:QuantitativeAssessment.
,meta:explanation.Error,/meta:explanation.
,meta:values uom5‘‘Ma’’.0.4,/meta:values.
,/meta:QuantitativeAssessment.
,/om:quality.
,om:featureOfInterest xlink:href5‘‘gssp.xml#gssppbaseptriassic’’/.
,/om:quality.
,om:featureOfInterest xlink:href5‘‘gssp.xml#gssppbaseptriassic’’/.
,om:result uom5‘‘Ma’’.251.0,/om:result.
,gt:metadata.
,gsml:ObjectMetadata.
,gsml:sourceReference.
,meta:SimpleCitation gml:id5‘‘B1998’’.
,gml:name.Bowring et al., 1998,/gml:name.
,/meta:SimpleCitation.
,/gsml:sourceReference.
,/gsml:ObjectMetadata.
,/gt:metadata.
,/gt:DateMeasurement.
,/gml:featureMember.
Finally, Listing 5 illustrates the structure of the descriptions of StratigraphicEvent and StratigraphicPoint elements referred to by the event
and stratotype properties of the GeochronologicBoundary elements in Listing 3. Note that since a StratigraphicPoint element potentially describes
a golden spike in the calibration of the time scale, this has a status property to indicate if it has been ratified through the GSSP program.
Listing 5. The StratigraphicPoint and StratigraphicEvent elements associated with the boundries shown in Listing 3.
,gml:featureMember.
,gt:StratigraphicPoint gml:id5‘‘gssppbasepchanghsingian’’.
,gml:description.Leading candidates are in China,/gml:description.
,meta:reference xlink:href5‘‘citations.xml#Ogg1’’/.
,sa:surveyDetails xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,sa:relatedObservation xlink:href5‘‘dates.xml#p9pOrigin1’’/.
,sa:position xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,gt:boundary xlink:href5‘‘ICStimescale.xml#p8pp9’’/.
,gt:hostSection xlink:title5‘‘China’’/.
,gt:offset uom5‘‘m’’ xsi:nil5‘‘true’’/.
,gt:primaryGuidingCriterion.Conodont biostratigraphy,/gt:primaryGuidingCriterion.
,gt:event xlink:href5‘‘#p8pp9p1’’/.
,gt:status.Informal,/gt:status.
,/gt:StratigraphicPoint.
,/gml:featureMember.
,gml:featureMember.
,gt:StratigraphicPoint gml:id5‘‘gssppbaseptriassic’’.
,gml:description.Base of Bed 27c, Meishan, Zhejiang, China,/gml:description.
,meta:reference xlink:href5‘‘citations.xml#E24p102p2001’’/.
,sa:surveyDetails xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,sa:relatedObservation xlink:href5‘‘dates.xml#MZpOrigin1’’/.
,sa:position xlink:href5‘‘urn:x-ogc:def:nil:OGC:unknown’’/.
,gt:boundary xlink:href5‘‘ICStimescale.xml#PZpMZ’’/.
,gt:hostSection xlink:title5‘‘Bed 27c, Meishan, Zhejiang, China’’/.
,gt:offset uom5‘‘m’’.0.0,/gt:offset.
134
Geosphere, December 2005
FORMAL MODEL FOR GEOLOGIC TIME SCALE
,gt:primaryGuidingCriterion.Conodont biostratigraphy,/gt:primaryGuidingCriterion.
,gt:event xlink:href5‘‘#PZpMZp1’’/.
,gt:additionalCorrelationProperty.Termination of major negative carbon-isotope excursion,/gt:additionalCorrelationProperty.
,gt:additionalCorrelationProperty.About 1 myr after peak of Late Permian extinctions.,/gt:additionalCorrelationProperty.
,gt:status.GSSP Ratified 2001,/gt:status.
,/gt:StratigraphicPoint.
,/gml:featureMember.
,gml:featureMember.
,gt:StratigraphicEvent gml:id5‘‘p8pp9p1’’.
,gml:description.Near lowest occurrence of conodont Clarkina wangi,/gml:description.
,om:time xlink:href5‘‘ICStimescale.xml#p8pp9/gt:position’’/.
,om:location.
,om:LocationCode.
,om:geographicDescription.Global,/om:geographicDescription.
,/om:LocationCode.
,/om:location.
,/gt:StratigraphicEvent.
,/gml:featureMember.
,gml:featureMember.
,gt:StratigraphicEvent gml:id5‘‘PZpMZp1’’.
,gml:description.Conodont, lowest occurrence of Hindeodus parvus,/gml:description.
,om:time xlink:href5‘‘ICStimescale.xml#P1pP2/gt:position’’/.
,om:location.
,om:LocationCode.
,om:geographicDescription.Global,/om:geographicDescription.
,/om:LocationCode.
,/om:location.
,/gt:StratigraphicEvent.
,/gml:featureMember.
The examples shown in Listings 1–5 show
a representative subset of a time scale. A complete time scale would reuse the patterns
shown here for the full set of eras of all ranks
and their associated boundaries.
SOME THEORETICAL IMPLICATIONS
Reference Systems and Time Scales
There has been some discussion of the relationship between the geologic time scale and
other measurement systems (Walsh et al.,
2004). The model for temporal reference systems summarized above provides a useful
framework for this. Broadly, there are three
kinds of reference system or scales involved
here:
Ratio or absolute scale—a value on a ratio
scale describes the ‘‘amount of’’ something.
The amount, or measure, is given as an unsigned number that is scaled by some unit of
measure. This may be expressed in arbitrary
precision (though not necessarily accurate or
meaningful). Mass, length, and concentration
are measured on ratio scales. In a temporal
context, the length of a time interval or the
age of an object may be given as a number of
seconds, years, etc.
Interval scale or coordinate system—a value on an interval scale describes position relative to a datum or origin. The distance from
the datum is given as an amount scaled by a
unit of measure, in arbitrary precision. The
position of the origin of an interval scale is
arbitrary, so positions on both sides of a datum are possible, hence the value must be
signed. The value of a potential must be expressed using an interval scale. In a temporal
context, a position or date may be expressed
as a numeric value relative to a time coordinate system. In geochronology, the conventional origin for numeric scales is 1950,
though this is only distinguishable from ‘‘the
present’’ for very high precision dating methods dealing with the relatively recent past.
Ordinal reference system or ordinal scale—
values given as an ordinal unit or classifier,
denoted by a symbol such as a word or code.
Relative sizes or positions may be described
using an ordinal reference system, with a fixed
precision determined by the extent of the ordinal unit, which may vary across the scale.
Ordinals may be used for classification of absolute values (e.g., the well-known grain-size
classifications in sedimentology) as well as
position (the geologic time scale), so the ordinal scale may be calibrated against either a
Geosphere, December 2005
coordinate system or ratio scale. It is important to note that while an ordinal system depends on the ordering of the events that define
the boundaries between units in the system;
the positions of these boundary events is not
necessarily known. Walsh et al. (2004) refer
to ordinal units as classificatory pigeonholes.
The differences between the types of scale
are also shown by the operations that are valid
on values using them and their results. The
relative quantities of two measures may be determined by subtraction or division, with the
result being a measure or a ratio, respectively.
The relative separation of two positions on an
interval scale may only be determined by subtraction, with the result being an amount on a
ratio scale.
The common practice of giving geologic
age as an unsigned number is consistent with
considering age to describe the ‘‘amount of
years’’ in an object. Age and temporal
position are often used interchangeably in
geochronology, with little confusion, because
of the practice of setting the datum as the present. In the context of the encoding shown
here, the position of a boundary is given as a
signed number on an interval scale, while the
result of an age determination should be a
measure on a ratio scale. However, in order to
135
S.J.D. COX and S.M. RICHARD
utilize the standard structures provided by ISO
19108:2003 and GML, the StratigraphicDateEstimate inherits the position property
from TMpInstant, and thus gives the value as
a (signed) position on an interval scale.
Ordinal Reference System versus
Constrained Topology
The GeologicalTimeScale described here is
structured as a TimeComplex, composed of
eras and boundaries corresponding to the time
edges and time nodes of a temporal topology
complex (ISO 19108:2003). There are two issues with expressing the time scale as a topology complex, however.
The first is that this would require multipleinheritance, with the TORS class deriving
from both TMpReferenceSystem and
TMpTopologyComplex. While useful in principle, multiple inheritance is notoriously problematic in practice, and alternatives such as
interfaces are commonly used. Thus, in ISO
19108 the concepts of ordinal reference system and topology complex are kept separate.
This reflects a preference for single-inheritance
in the model, with the ordinal reference system grouped with reference systems rather
than topology complexes.
The second issue concerns the constraints
that must be imposed so that the complex can
fulfill the requirements of a reference system.
These are as follows. The ordinal eras and ordinal era boundaries must form a connected,
covering network or complex for the domain
of the reference system. Furthermore, the
complex must be constrained such that each
era may only be subdivided once by a set of
eras of a lower rank. In terms of the topology
complex, the set of edges that either starts or
ends at any node must include exactly one of
each rank between the highest and lowest rank
represented. The single hierarchy that results
ensures there is no ambiguity in the relative
positions of eras. We might term this an
UnambiguousTimeTopologyComplex.
For example, in the temporal topological
complex shown in Figure 6, we show edges
representing eras as arrows, between nodes
representing boundaries shown as filled circles. The eras have various ranks implied by
the thickness of the line, and are labeled B,
C1, etc. Some of the nodes are labeled BpC,
B4pB5, etc.
The parts of the graph colored green represent a valid ordinal reference system. For
example, a feature assigned the age B22 is
unambiguously earlier than a feature of age
B4, and is during the life of a feature of age
B. These relationships are clear even if the
136
Figure 6. Schematic topological complex, illustrating the constraints required for this to
serve as a reference system.
numerical positions of the end points of some
or all of the eras are not known, or not known
precisely.
The parts of the graph colored blue contain
an alternative primary decomposition of era B,
labeled b1, b2, etc, where the elements of the
decomposition have the same rank as the elements in the existing decomposition. Note
that, unless the positions of the nodes are precisely calibrated on a numeric scale, it is not
possible to determine the relative temporal positions of features whose ages are b3 and B24.
The order of components is ambiguous, so the
complex including both does not qualify as a
valid reference system.
The blue subset may, however, comprise a
different reference system for era B, for example, having a different (spatial) domain of
validity. Note that the temporal relationship
between objects characterized using different
reference systems is in general indeterminate.
This describes the common situation in stratigraphy where the relative age of objects from
different regions may not be possible if local
time scales are in use. Correlation projects attempt to resolve this by discovering, or asserting, relationships between elements of
time systems defined originally for different
domains of validity. If successful, this may result in a merging of different systems to form
a single system (hierarchy) with a domain of
validity that is the union of the domains of the
contributing systems.
SUMMARY
We have presented an integrated model for
the geologic time scale, its formal definition
using type localities according to ICS guidelines, and the measurements involved in calibrating it against a numeric scale. The model
is represented using a formal notation, the
UML Class Diagram, which is widely used in
software engineering and business-process
analysis. Furthermore, we have used a profile
Geosphere, December 2005
of UML that allows us to generate an XML
encoding compatible with geospatial standards
from ISO and OGC. The latter means that information related to the time scale may be
transferred using standard Web-service interfaces, such as Web Feature Service.
The UML model and XML schema, and example instances described in this report, are
available online from https://www.seegrid.
csiro.au/subversion/xmml/trunk/GeoSciML/
draft/model/, https://www.seegrid.csiro.au/
subversion/xmml/trunk/GeoSciML/draft/
schema/, and https://www.seegrid.csiro.au/
subversion/xmml/trunk/GeoSciML/draft/
instances/geoTime/.
APPENDIX 1. INTRODUCTION TO UML
CLASS DIAGRAMS
The UML (Object Management Group, 2001) is
a well-known notation, and is described in many
introductory and advanced books (e.g., Fowler and
Scott, 2000). It may be used to model various technical, social, and natural systems, and is commonly
used for analysis of business processes and in software design, particularly of interfaces.
The UML includes several diagram types. In this
report we use only class diagrams (see Figs. 1–5).
These are superficially similar to the entity-relationship (E-R) notation used in data modeling for relational database design. However, the UML includes refinements to support the description of
systems according to object-oriented principles. In
particular, the relationships between concepts are
classified in various ways, indicated on the diagram
by different line and arrow styles with annotations.
In addition to attributes, other kinds of properties
may be specified for each concept.
Furthermore, we use the capabilities of class diagrams in a constrained way, broadly corresponding
to the profile described in ISO 19103 and in Annex
E of the GML specification (Cox et al., 2003). The
key elements used are summarized in the following
paragraphs.
Each concept of interest is represented as a class,
and shown on the class diagram as a multi-compartment box. The top compartment holds the name
of the classifier, optionally preceded by the name of
the package it belongs to. An instance of a class is
called an object, with an ‘‘is a’’ relationship with
the classifier (e.g., Abby is a person). In the case of
FORMAL MODEL FOR GEOLOGIC TIME SCALE
abstract classes, which exist to support a coherent
class hierarchy but will never supply instances, the
name is shown in italics. Attributes of the class are
listed in the second compartment, each by an entry
of the form ‘‘name:Type,’’ with optional cardinality.
Operations, responsibilities, constraints, tags, etc.,
are shown in additional compartments. We are primarily interested in class attributes.
Relationships between classes are indicated in the
diagram by lines of various styles. In this study, we
use two types of relationship: generalization and
association.
Association is denoted by a line that may be ornamented with various arrowheads and labels at either or both ends. These indicate ‘‘has a’’ relationships between instances of the classes (e.g., Abby
(a person) owns Iko (a cat)). Almost all relationships shown on an E-R diagram are comparable to
UML associations. However, in the UML, these relationships may be named, and each end of the association may also carry a rolename. Cardinality
may be expressed as an integer or a range, where,
for example, ‘‘2..*’’ implies that at least two instances of the association are required but an unlimited number may be provided. No cardinality constraint implies exactly one. The association may be
directed, shown by a stick arrowhead (→), such that
an instance of the class at only one end knows about
instances of the class at the other end. Filled and
open diamond-arrowheads may be used to indicate
tight and loose association (known as composition
and aggregation), but are mostly not used here.
Specialization and/or generalization is denoted by
a line with an open arrowhead (,) adjacent to the
generalized class. This indicates a relationship at the
model level, where the child class bears an ‘‘is a
type of’’ relationship to a parent (e.g., a cat is a
type of animal). Specialization usually adds attributes and relationships to those inherited from the
parent class, but may involve other constraints. As
well as inheritance of properties, generalization usually also implies polymorphism, such that instances
of the child class are considered to be instances of
the parent. Thus, an association with a class implies
a potential association with any of its descendents
(e.g., if a person owns an animal, this might be a
dog, cat, fish, or hamster, etc.). This last feature is
particularly important and is used extensively in the
model here.
It is important to understand that the diagram is
merely a representation of an underlying model.
Furthermore, one diagram will usually not show the
entire model, but rather just a view of a selection
of related classes, perhaps with only certain properties displayed. This is convenient, since it means
that unnecessary detail can be suppressed in order
to allow a diagram to illustrate particular points. But
in order to understand the entire model, it is necessary to combine the information from several
diagrams.
Some classes will appear in more than one dia-
gram, describing a different subset of relationships
with other classes in each diagram. These provide
the joining points between the subsets of the model
shown in different diagrams. The complete set of
properties of a particular class is the union of properties shown where it appears in the various diagrams, together with other information that may not
be shown on any diagram.
Thus, while UML diagrams may be constructed
with generic drawing tools (including paper and
pencil), professional UML tools maintain an abstract representation of the model, and use that to
ensure consistency between different views.
Following the usage prescribed by ISO 19109
and used in GML, class attributes and associations
are referred to collectively as properties, with the
attribute name or association rolename providing
the name of the property. Rolenames are required
on the traversable ends of associations. Furthermore, following a lexical rule prescribed in GML
3, classnames are in UpperCamelCase, while attribute and rolenames use lowerCamelCase as far as
possible.
ACKNOWLEDGMENTS
This study was initiated as a contribution to the
Chronos project. The work has been improved as a
result of discussions with Cinzia Cervato, Morishige Ota, Ilene Rex and Charles Roswell, and comments by reviewer Peter Sadler. Cox’s contributions
were supported by the XMML consortium, CSIRO,
and the Predictive Mineral Discovery Cooperative
Research Center.
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