Geological perspective correlation is a theory in geology describing geometrical regularities in the layering of sediments. Seventy percent of the Earth's surface are occupied by sedimentary basinsWatts, A.B., The Formation of Sedimentary Basins. In "Understanding the Earth", Chapter 15, Cambridge University Press., 1992 – volumes consisted of sediments accumulated during million years, and alternated by long interruptions in sedimentation (hiatuses). The most noticeable feature of the rocks, which filled the basins, is layering (stratification)."stratification | geology". Encyclopædia Britannica. Stratigraphy is a part of Geology that investigates the phenomenon of layering. It describes the sequence of layers in the basin as consisted of stratigraphic units. Units are defined on the basis of their lithology and have no clear definition.Chapter 5. Lithostratigraphic Units". International Commission on Stratigraphy. 2013–2014. Geological Perspective Correlation (GPC) is a theory that divided the geological cross-section in units according strong mathematical rule: all borders of layers in this unit obey the law of perspective geometry.Young, John Wesley (1930), Projective Geometry, The Carus Mathematical Monographs (#4), Mathematical Association of America
Sedimentation layers are mainly created in shallow waters of oceans, seas, and lakes. As new layers are deposited the old ones are sinking deeper due to the weight of accumulating sediments.Allen, Philip A.; John R. Allen (2008). Basin analysis : principles and applications (2. ed., [Nachdr.] ed.). Malden, MA [u.a.]: Blackwell. The content of sedimentary layers (lithological and biological), their order in the sequence, and geometrical characteristics keep records of the history of the Earth, of past climate, sea-level and environment. Most knowledge about the sedimentary basins came from exploration drilling when searching for oil and gas. The essential feature of this information is that each layer is penetrated by the wells in a number of scattered locations. This raises the problem of identifying each layer in all wells – the geological correlation problemVan Wagoner J., Mitchum R., Campion, K. and Rahmanian V. Siliciclastic Sequence Stratigraphy in Well Logs, Cores, and Outcrops: Concepts for High-Resolution Correlation of Time and Facies AAPG Methods in Exploration Series, No. 7, 1990. The identification is based on comparison of 1) physical and mineralogical characteristics of the particular layer (lithostratigraphy), or 2) petrified remnants in this layer (biostratigraphy).Kearey, Philip (2001). Dictionary of Geology (2nd ed.) London, New York, etc.: Penguin Reference, London, p. 123 The similarity of layers is decreasing as the distance between the cross-sections increases that leads to ambiguity of the correlation scheme that indicates which layers penetrated at different locations belong to the same body (see A). To improve the results geologists take in consideration the spatial relations between layers, which restricted the number of acceptable correlations. The first restriction was formulated in XVII century: the sequence of layers is the same in any cross-section. The second one was discovered by Haites in 1963:T. Binnert Heites. (1963). Perspective correlation. APG Bulletin vol. 47, N 4. In an undisturbed sequence of layers (strata) the thicknesses (H1 and H2) of any layer observed in two different locations obey the law of perspective geometry, i.e. the perspective ratio K = H1/H2 is the same for all layers in this succession. This theory attracted attention around the world., and particularly in Russia The theory is also a basis of the method of graphical correlation in biostratigraphy widely used in oil and coal industries.Nemec W. (1988). Coal Correlations and Intrabasinal Subsidence. In: K. L. Kleinspehn et al. (eds.), New Perspectives in Basin Analysis © Springer-Verlag New York Inc.
Overview
The geometry is the main lead to natural resources exploration.
For example, the oil geologists are looking for permeable layers of particular geometry, which allows keeping the oil in placeLevorsen, A.I. (1967), Geology of Petroleum, W.H.Freeman and Company, San Francisco, 724 p. (for instance, the domed shape anticlinal trap). The ore geologists are looking for faults in the sediments – the ways, which deliver the melted mantle materials to the upper crust.Evans A. Ore Geology and Industrial Minerals. 2005 Knowledge about underground geometry of the sedimentary basins comes from geological observations, geophysical measurements and from drilling.Freudenrich C., Strickland J. How Oil Drilling Works. https://science.howstuffworks.com/environmental/energy/oil-drilling.htm Drilling gives the most detailed information about the position, thickness, physical, chemical and biological characteristics of each layer, but the point is that each well presents all this information in one location on the layer. Because the geometry of a layer can be very complicated it becomes a difficult problem and requires a significant number of drilled wells. The challenge is identifying in each well the interval that belongs to the same layer now or in the pastVoronin, Y.A., Methodological issues of application of mathematical methods and computers in geology. Published by the Computer Center, Siberian Division of the USSR Academy of Sciences. Novosibirsk, Yakutsk: 1973. (see A). To do this geologists use all available characteristics of the layer. Only after this it is possible to begin the recovery of the geometry of the layer (to be more precise – the geometry of the top and bottom surfaces of the layer). This procedure is called geological correlation, and the results are presented as acorrelation scheme (A). It is natural that at the beginning of the exploration, when the number of wells is small, the correlation scheme contains expensive mistakes.Randle C., Bond C., Lark M., Monaghan A. Can uncertainty in geological cross-section interpretations be quantified and predicted? Geosphere (2018) 14 (3): 1087–1100. https://doi.org/10.1130/GES01510.1
Basics of geological correlation The Danish scientist Nicolas Steno (1638–1686) is credited with three principles of sedimentationSteno, Nicolas (1916). Nicolas Steno's Dissertation Concerning a Solid Body Enclosed by Process of Nature within a Solid: An English Version with an Introduction and Explanatory Notes. Translated by Winter, John. New York, The Macmillan company; London, Macmillan and company, limited.|pages=229–230 superposition: in undeformed stratigraphic sequences the oldest strata will be at the bottom of the succession, original horizontality: layers of sediment are originally deposited horizontally, lateral continuity: layers of sediments initially extend laterally in all directions. The principles 1 allows defining the temporary relations between neighboring geological bodies, the principle 2 organizes the geometrical pattern of the succession of layers, the principle 3 helps uniting the parts of the layer found in separated geological cross-sections. Practical correlation has a lot of difficulties: fuzzy borders of the layers, variations in composition and structure of the rocks in the layer, unconformities in the sequence of layers, etc. This is why errors in correlation schemes are not seldom. When the distances between available cross-sections are decreasing (for example, by drilling new wells) the quality of correlation is improving, but meanwhile the wrong geological decisions could be made that increases the expenses of geological projects. From Steno's principle of initial horizontality follows that the top borders of the layers (tops) were initially flat, and remained flat until the complete succession stays undisturbed by subsequent tectonic movements, but no regularities about the geometric relations between these flat surfaces in the succession were known. The first to shed light on the problem was Canadian geologist Binner Heites: in 1963 he published the Geological Perspective Correlation hypothesis. Perspective geological correlation is a theory that establishes strong geometrical restrictions on the geometry of the layers in sedimentary deposits.
Perspective geometry in undisturbed succession of layers
In 1963 the Canadian geologist Binner Heites discovered a strong regularity of the layering in sedimentary basins: the thicknesses of layers within each stratigraphic unit are governed by the law of perspective correspondence. It means that in undisturbed succession on the correlation scheme the straight lines drawn through the border points of the same layer in two cross-sections intersect in one point – center of perspectivity (see B). For geological purposes more convenient geometrical presentation of perspective relations is the correlation plot proposed by JekhowskyJekhowsky, B. de, La methode des distances minimales, nouveau procede quantitative de correlation stratigraphique, exemple d'application on paleontologie. Rev. Inst. Franç. Du Petrole, Paris, 1963, vol. XVIII, No. 5, 629–653. (see C): the depths of the layer's borders in one geologic cross-section are plotted along axis h′ (h1′, h2′, h3′,...), and the position of the same layers in another cross-section are plotted along axis h′′ (h1′′, h2′′, h3′′, ...). Points 1, 2, 3 ... with coordinates (h1′, h1′′), (h2′, h2′′), and (h3′, h3′′), accordingly, are called correlation points, and a curve drawn through these points, a correlation line. Black dots (connectors) represent the relative position of correlated borders on the plot. When the layers geometry satisfies the conditions of perspective correspondence the correlation line is a straight line. In the particular case of parallel layers the inclination of the correlation line is 450. The Perspective Geological Correlation also states that each sedimentary basin consists of a number of stratigraphic units (sequence of layers without unconformities), and in each unit the relations between the thicknesses of the layers in two cross-sections satisfy the perspective geometry conditions with individual ratios K.
Heites also concludes that all strata in each unit were governed by the same rate of deposition, and their borders are synchronous time-planes. Each layer has different thicknesses in different locations, but they lasted equally long. It was a significant input in chronostratigraphy.
The following are consequences of the basic statements: In different stratigraphic horizons the slopes of the correlation lines are different. If two adjacent sections have the same slope then both sections belong to the same stratigraphic horizon. The gap between the lines indicates a fault. If on the correlation line that presents the undisturbed stratigraphic succession one correlation point doesn't fit the line it means that: the correlation of the tops of the corresponding layer is wrong, or lithologic replacement.
Connections to traditional lithostratigraphy