Abstract
There has been rather little attention given to sampling, although Rao and Sengupta (1970) reviewed at length the early work of Olson and Potter* (1954), using, however, the vector rather than the arithmetic mean. Rao and Sengupta also discuss sample size and costs. In practice, most field geologists have not given much attention to the details of sampling and probably considerably oversample most formations. Although not intended for the student of paleocurrents, Whitten’s (1966) discussion of sampling mechanically deformed sediments is useful, comparative reading. His Chapter 3, Sampling and Size in Data Collection, gives comparative insight into sampling of directional structures, and his Chapter 13, Sedimentary Characteristics Preserved in Folded and Metamorphosed Rocks, is especially relevant for the sedimentologist working in metamorphic terrains — an area of study that will probably expand in years to come and bring sedimentologists profitably into closer contact with metamorphic petrologists.
Computers and pocket calculators now remove most of the drudgery from the analysis of paleocurrent data, and now, and additionly, sedimentologists are much more familiar with a wide range of statistical techniques. The consequence? Easy, quick, and sophisticated data analysis
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Annotated References
Background
Elliot, I. L., and W. K. Fletcher, eds., 1975: Geochemical exploration 1974 (Developments in economic geology, 1). Amsterdam: Elsevier Publ. Co., 720 p. Seven statistical papers; considerable mathematical and statistical skill required.
Harbaugh, J. W., and D. F. Merriam, 1968: Computer applications in stratigraphic analysis. New York, J. Wiley and Sons, Inc., 282 p. Clear exposition of statistical methods used.
King, L. J., 1969: Statistical analysis in geography. Englewood Cliffs, N. J., Prentice-Hall, Inc., 288 p. Generally covers the subject, including factor and principal component analysis. Analysis of location patterns may be useful in some dispersion studies.
Krumbein, W. C., and F. A. Graybill, 1965: An introduction to statistical models in geology. New York, McGraw-Hill Book Co., 475 p. One of the first books on this su bj ect and a classic.
Marsal, D., 1967: Statistische Methoden für Erdwissenschaftler. Stuttgart, E. Schweizerbart’sche Verlagsbuchhandlung, 152 p. Elementary, but with many good examples from geology. Easy German, too.
Hay, A. M., and M. A. A. Rahman, 1974: Use of chi-square for the identification of peaks in orientation data. Comment: Bull. Geol. Soc. Am. 85, 1963–1966. The latest of several recent papers on this subject; contains all the previous references.
Jones, T. A., 1968: Statistical analysis of orientation data. J. Sediment. Petrol. 38, 61–67. Discussion of circular normal distribution with all the relevant references up to 1967. Paper discusses full circle (0-360°) as well as semi-circle (0-180°) data.
Kelling, G., 1969: The environmental significance of cross-stratification parameters in an Upper Carboniferous fluvial basin. J. Sediment. Petrol. 39, 857–875. One of the few uses of hierarchical sampling and analysis of variance to decipher a paleocurrent system based on cross-bedding.
Mardia, K. V., 1972: Statistics of directional data. London: Academic Press, 357 p. The only book that we know of on this subject.
Reyment, R. A., 1971: Introduction to quantitative paleoecology. Amsterdam: Elsevier Publ. Co., 226 p. Chapter 3, “Orientation Analysis” is clear, complete, and comprehensive as well as having many worked, well-discussed examples. Primary discussion centers about orientation in the plane of the bedding, using the vector mean and its dispersion, but there are also a few examples involving the binomial distribution, and chi-square, i.e., orientation without circles. Very strongly recommended.
Sanderson, D. J., 1973: Some inference problems in paleocurrent studies. J. Sediment. Petrol. 43, 1096–1100. Principally a review of the literature on this subject, most of the references being included.
Saunderson, Houston C., 1975: A comparison of empirical and theoretical frequency distributions for two dimensional palaeocurrent data from the Brampton esker and associated sediments. Geografiska Annaler 57, 189–200. A large number of climbing ripple 0 bservations are needed to estimate paleocurrents in eskers, if the one studied is at all representative
Scheidegger, A. E., 1965: On the statistics of the orientation of bedding planes, grain axes, and similar sedimentological data. U. S. Geol. Surv. Prof. Paper 525-C, 164–167. Computation of mean direction and inclination for three dimensional orientation data using tensors. This is an extension to sedimentology from an earlier use of the same method for finding fault plane solutions for earthquakes.
Watson, G. S., 1966: The statistics of orientation data. J. Geol. 74, 785–797. Basic paper, widely cited.
Sources for Computer Programs
Carlile, R. E., and B. E. Geillett, 1974: Fortran and computer mathematics. Tulsa, Petroleum Pub. Co., 400 p. Programming plus matrices, linear equations and least squares
Harbaugh, J. W., G. Bonham-Carter and W. M. Merrill, 1971: Programs for computer simulation in geology. Stanford Univ., Dept. Geol., Office Naval Res., Geog. Branch, Contract N 0014-57-A 0112-004, Task 389-154, various paging. Twenty programs and three appendices, mostly about things sedimentary; sums up about five years work. Of interest, if you are considering simulating paleocurrent patterns.
Laboratory for Computer Graphics and Spatial Analysis, 1971: Symap manual. Cambridge, Harvard Univ., 157 p. Some selected Fortran programs, nine so far. Each has a brief expository account of the technique and its application.
References
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Potter, P.E., Pettijohn, F.J. (1977). Methods of Study (1963–1976). In: Paleocurrents and Basin Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61887-1_19
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