Quantitative Stratigraphy poster

Quantitative Stratigraphy


Frederik P. Agterberg, Geological Survey of Canada, Ottawa K1A 0E8, Canada

[Email: agterberg@gsc.emr.ca]

Felix M. Gradstein, Saga Petroleum a.s., N-1301 Sandvika, Norway

[Email: felix.gradstein@saga.telemax.no]


Geological correlation of strata plays an important role in basin analysis. It requires the determination of a sequence of unique points for non-recurrent events common to the sedimentary record as observed at different sites. The first and last occurrences of fossils are examples of unique events that can be used for correlation between stratigraphic sections; other examples include marker horizons (e.g., bentonites; gamma spikes), seismic events, and sequence boundaries. In general, it is possible to scale these stratigraphic events along a relative time scale which may be transformed into linear time (in millions of years). The ultimate objective of stratigraphic correlation is to estimate the age for any point in a section with its error bar thus permitting isochron contouring.


An important contention of biostratigraphic correlation is that the events, probably grouped in biozones, have been properly determined and defined, and can indeed be used for correlation. This is not a trivial matter: existing stratigraphic codes show how to construct stratigraphic units but they do not define how to correlate them. Traditionally, the actual correlation of strata takes place in the subjective domain of regional experts on a particular basin or time period. Procedures for correlation or stratigraphic equivalence depend on subjective evaluation of the unique relation of each separate site record to the derived and accepted standard. It follows that correlation as commonly practised in geology cannot be readily verified without a detailed, and probably exhaustive review of all the underlying facts. Traditionally there is no method of formulating the uncertainty in fixation of individual records to the regional or global standard. Hence biostratigraphy often is more considered an art rather than a science. The basic problem of using subjective judgement only is not so much that it produces right or wrong stratigraphy, but that a single solution is proposed. Instead of this it should be attempted to establish reasonable criteria for successful correlation, either in millions of years or in depth in meters.


Methods of quantitative stratigraphy combine mathematical logic with stratigraphic principles (e.g., law of superposition of strata; speciation, possible acme, and extinction of taxa) allowing the user to retain full control over input and results. Although there are many early examples of mathematical reasoning in stratigraphy (e.g., Lyell's subdivision of the Tertiary; Oppel zones; Brinkmann's statistical biostratigraphy), systematic approaches commenced only about 30 years ago. Part of this work was performed under the auspices of the International Geological Correlation Program (IGCP Project 148: Evaluation and Development of Quantitative Stratigraphic Correlation Techniques, 1976-1985) and the International Commission on Stratigraphy (Committee for Quantitative Stratigraphy, from 1985 onward). The purpose of this WWW poster is to introduce basic concepts of quantitative stratigraphy, particularly as applied to fossil distributions frequently found in exploration wells in frontier basins. Fundamental concepts will be briefly explored and examples of objective application provided.


1. If a taxon is relatively abundant in a stratigraphic section (e.g., Heterosphaeridium difficile in Display 1, diagram 1a), it may be possible to define different types of biostratigraphic events for it. Normally a taxon occurs in relatively few samples from along an exploratory well. Events distributions are illustrated in Display 1, (diagram 1B). It illustrates that microfossils and nannofossils observed in exploratory wells (and the stratigraphic events derived from them: mainly last occurrences in these applications) have exceedingly skew frequency distributions. In general, the great majority of taxa are observed in one or a few wells only. Very few taxa if any occur in all or nearly all stratigraphic sections studied for a basin. One explanation of the positive skewness of these types of frequency distributions is that the rock volumes sampled in exploration drilling are relatively small.


2. Space-time relations are illustrated in Display 2. This hypothetical example provides one possible explanation for differences in the local ranges of existence of fossils between sections. However, in exploratory drilling most inconsistencies in successions of first and last occurrences of taxa can be attributed to incomplete sampling as shown in Display 1.


3. Zonations are essential tools for biostratigraphic correlation. diagram 3A shows types of zones commonly used by stratigraphers; diagram 3B shows an average interval zone. Conceptually, the average interval zone is similar to the Oppel zone of diagram 3A except that the deviations from the average for the observed first or last occurrences of the taxa (if these occur in a well) are much greater. By means of averaging techniques (see later displays) it may be possible to estimate the intervals between stratigraphic events along a relative time scale. Then the stratigraphically average highest and lowest occurrences of the taxa considered are assigned positions along a distance scale (diagram 3C, left side). Both the origin and the unit of distance on this scale are arbitrary. The same type of information can be represented as a dendrogram (diagram 3C, right side). Clusters in the dendrogram can be regarded as biozones and are often very useful for regional (basin-wide) correlations.


4. The RASC method for ranking and scaling of stratigraphic events results in average positions of stratigraphic events along a relative time scale (Display 3). Most events in Display 4 (Albian-Turonian scaled optimum sequence, offshore mid-Norway) are average last occurrences of Foraminifera, but there are also other types of biostratigraphic events (LCO = Last Common Occurrence; FCO = First Common Occurrence) and a lithostratigraphic event (Cenomanian/Turonian boundary gamma spike). The numbers printed between the fossil names and plotted along the scale to the left are intervals estimated from cross-over frequencies arising when the order (or superpositional relationship) of two events in a section differs from that in one or more other sections. Intervals between successive events along the RASC scaled optimum sequence are averages computed from events that are relatively abundant. Events marked by stars are "unique" events occurring in one or a few wells only. The unique event option of RASC allows insertion of these rare events. In general, significant breaks (e.g., between the Hedbergella difficile LCO and Dicarinella imbricata/Dorocysta litotes zones) coincide with unconformities accompanied by stratigraphic hiatuses.


5. The average observed last occurrence occurs below the true last occurrence of a taxon which may be more difficult to estimate than the average because of local reworking and other factors. When taxa from many wells were averaged, the well with the largest stratigraphically upward deviation may provide the best approximation of the true last occurrence. These largest deviations are shown in diagram 5A of Display 5 for Cenozoic Foraminifera from the Labrador Shelf and Grand Banks (24 wells). Along the RASC scale, many highest occurrences of taxa are about 1.16 units less than their average positions. It can be shown that this systematic difference in RASC distance is equivalent to approximately 10 m.y. Generalizing it can be said that methods to estimate the locations of biostratigraphic events along a scale are of two types: "conservative" or "average". In conservative methods it is attempted to find the true first and last occurrences; this tends to give longer range zones than those resulting from averaging (diagram 5B).


6. Conservative and average methods can both be used for stratigraphic correlation. As early as 1964 Shaw published a comprehensive method of graphic correlation illustrated by means of first and last occurrences of Cambrian trilobites in the Riley Formation of central Texas (original data from Palmer, 1955). As already pointed out in Display 5, Shaw's method is conservative whereas RASC is an average method. Trilobite events observed in Palmer's Morgan Creek section, are plotted in Display 6 (diagram 6A). The vertical scale shows relative order of all events in this section. In general, two or more events can be observed to be coeval in a section or well For example, a single trilobite of a specific taxon results in coinciding first and last occurrence in Display 6. The curve fitted to all data is called "line of correlation". The relative event level scale can be changed into a true distance scale by using the "line of correlation" which is a curve fitted to the observed events plotted against distance (measured in ft from the base of the section in this example). Deviations from the line of correlation in a section can be used to construct an error bar (1) for events shown for selected RASC distances in three sections (diagram 6B). The RASC lines of correlation are similar to lines obtained by Shaw and those based on Palmer's original subjective zonation.


REFERENCES

Agterberg, F.P., 1990, Automated Stratigraphic Correlation, Developments in Palaeontology and Stratigraphy, v. 13: Elsevier, Amsterdam, 424 p.

Davaud, E., 1982, The automation of biochronological correlation, in J.M. Cubitt and R.A. Reyment, eds., Quantitative Stratigraphic Correlation: Wiley, Chichester, pp. 85-99.

Edwards, L.E., 1978, Range charts and no-space graphs: Computers & Geosciences, v. 4., pp. 247-258.

Gradstein, F.M., 1985, Ranking and scaling in exploration micropaleontology, in F.M. Gradstein, F.P. Agterberg, J.C.

Brower and W. Schwarzacher, Quantitative Stratigraphy, Unesco, Paris, and Reidel, Dordrecht, pp. 109-160.

Gradstein, F.M., and Agterberg, F.P., in press, Uncertainty in stratigraphic correlation, in Proceedings, 'High

Resolution Sequence Stratigraphy', Norwegian Petroleum Society Conference, Stavanger, 6-8 November, 1995: Elsevier, Amsterdam.

Hay, W.W., 1972, Probabilistic stratigraphy: Eclogae Geol. Helv., v. 65, pp. 255-266.

Hedberg, H.D., ed., 1976, International Stratigraphic Guide: Wiley, New York, N.Y., 200 pp.

Palmer, A.R., 1954, The faunas of the Riley formation in central Texas: Jour. Paleont., v. 28, pp. 709-786.

Shaw, A.B., 1964, Time in Stratigraphy: McGraw-Hill, New York, N.Y., 365 p.

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