Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 05 Nov 2007

Pioneers in Mathematical Geology

and
Page Range: 314 – 324
DOI: 10.17704/eshi.23.2.j422754m21177430
Save
Download PDF

Statistical and mathematical techniques have been used in the earth sciences for about one-hundred years, but only after the introduction of the electronic computer in the mid-Twentieth Century did a revolution in the science take place. The story of the quantification of geology is best told through the works of those who fostered the dramatic change. Here is chronicled the contributions of six pioneers in numerical geology in short exposés by authors close to, and knowledgeable of, the people and their work. The pioneers include F. Chayes (American), J. C. Griffiths (American/Welsh), W. C. Krumbein (American/German), G. Matheron (French), R. A. Reyment (Australian/Swede), and A. B. Vistelius (Russian). These magnificent six also played a major role in forming the International Association for Mathematical Geology in 1968 at the International Geological Congress in Prague, Czechoslovakia.

Brinkmann, Roland, Statistisch-biostratigraphische Untersuchungen an mitteljurassischen Ammoniten über Artbegriff und Stammesentwicklung, Abhandlungen der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse, n.f., 1929, 13:1-249.

Chayes, Felix, Ratio correlation: A manual for students of petrology and geochemistry (Chicago: University of Chicago Press, 1971).

De Wijs, Henri S., Statistics of ore distribution. I. Frequency distribution of assay values, Geologie en Mijnbouw, 1951, 30:365-375.

De Wijs, Henri S., Statistics of ore distribution. II. Theory of binomial distribution applied to sampling and engineering problems, Geologie en Mijnbouw, n.s., 1953, 15:12-24.

Eisenhart, Churchill, A test for significance of lithological variation, Journal of Sedimentary Petrology, 1935, 5:137-145.

Ewing, C. J. C., A comparison of the methods of heavy mineral separation, Geological Magazine, 1931, 68:136-140.

Griffiths, John C., Scientific method in analysis of sediments (New York: McGraw-Hill Book Co., 1967).

Guarascio, Massimo, Michel David, and Charles J. Huijbregts, Advanced Geostatistics in the Mining Industry. Proceedings of the NATO Advanced Study Institute held at the Istituto di Geologia Applicata of the University of Rome, Italy, 13-25 October 1975 (Dordrecht: D. Reidel Publishing Company, 1976).

Howarth, Richard J., A history of regression and related model-fitting in the earth sciences (?1636-2000), Natural Resources Research, 2001, 10:241-286.

Howarth, Richard J., From graphical display to dynamic model: Mathematical geology in the earth sciences in the Nineteenth and Twentieth Centuries, in The Earth Inside and Out: Some Major Contributions to Geology in the Twentieth Century, ed. David R. Oldroyd (London: Geological Society of London, Special Publication 192, 2002), 59-97.

Kapteyn, Jacobus C., Skew frequency curves in biology and statistics (Groningen: Noordhoff, 1903).

Kolmogorov, Andrey N., Über das logarithmisch normale Verteilungsgesetz der Dimensionen der Teilchen bei Zersückelung, Doklady Akademiya Nauk SSSR, 1941, 31:99-101.

Krige, Daniel G., A statistical approach to some basic mine valuation problems on the Witwatersrand, Journal of the Chemical Metallurgical and Mining Society of South Africa, 1951, 52:119-139.

Krumbein, William C., Some problems in applying statistics to geology, Applied Statistics, 1960, 9: 82-91.

Krumbein, William C., and Franklin A. Graybill, An introduction to statistical models in geology (New York: McGraw-Hill Book Co., 1965).

Krumbein, William C., and Francis J. Pettijohn, Manual of sedimentary petrography (New York: Appleton-Century-Crofts, Inc., 1938).

Krumbein, William C., and Laurence L. Sloss, High-speed digital computers in stratigraphic and facies analysis, American Association of Petroleum Geologists Bulletin, 1958, 42:2650-2669.

Liu Chengzuo, and Li Yuwei, Development of mathematical geology in China, Mathematical Geology, 1983, 15:483-492.

Loewinson-Lessing, Franz Y, On the delimitation of the families of basalts and andesites by means of statistical methods [Russian with English summary], Izvestiya Geologicheskago Komiteta, Petrograd, 1926 [for 1925], 44:411-422.

Matheron, Georges, Traité de Géostatistique Appliquée, Mémoires du Bureau de Rechercheres Géologiques et Minières, 1962, 14:1-333.

Matheron, Georges, Traité de Géostatistique Appliquée, Tome II, Le krigéage: Mémoires du Bureau de Rechercheres Géologiques et Minières, 1963, 24:1-333.

Merriam, Daniel F., The International Association for Mathematical Geology—a brief history and record of accomplishments, Syracuse University Geological Contribution, 1978, 5:1-6.

Merriam, Daniel F., Roots of quantitative geology, in Down-to-Earth Statistics: Solutions looking for geological problems, ed. D. F. Merriam, Syracuse University Geology Contribution, 1981, 8:1-15.

Merriam, Daniel F., The quantification of geology: from abacus to pentium, a chronicle of people, places, and milestones, Earth-Science Reviews, 2004, 67:55-89.

Miller, Robert L., and James L. Kahn, Statistical Analysis in the Geological Sciences (New York: John Wiley and Sons, 1962).

Otto, George H., Comparative tests of several methods of sampling heavy mineral concentrates, Journal of Sedimentary Petrology, 1933, 3:30-39.

Otto, George H., The use of statistical methods in effecting improvements in a Jones sample splitter, Journal of Sedimentary Petrology, 1937, 7:110-132.

Pearson, Karl, Contributions to the mathematical theory of evolution. 1. On the dissection of asymmetrical frequency curves, Philosophical Transactions of the Royal Society, London, 1894, A185: 71-110.

Pearson, Karl, Contributions to the mathematical theory of evolution. 2. Skew variation in homogeneous material, Philosophical Transactions of the Royal Society, London, 1895, A186:343-414.

Pearson, Karl, Contributions to the mathematical theory of evolution. 3. Regression, heridity and panmixia, Philosophical Transactions of the Royal Society, London, 1896, A187:253-318.

Pearson, Karl, Mathematical contributions to the theory of evolution. 5. On the reconstruction of the stature of prehistoric races, Philosophical Transactions of the Royal Society, London, 1898, A192:169-244.

Razumovsky, Nikolai K., Nature of the distribution of the metal contents in ore deposits, Doklady Akademiya Nauk SSSR, 1940, 28:815-817.

Razumovsky, Nikolai K., On the role of the logarithmically normal law of frequency distribution in petrology and geochemistry, Doklady Akademiya Nauk SSSR, 1941, 33:48-49.

Reyment, Richard A., History of the birth of the IAMG, IAMG Program and Abstracts, Silver Anniversary Meeting (Prague, Czech Republic) (Prague: International Association for Mathematical Geology, 1993), vii-ix.

Reyment, Richard A., and Enrico Savazzi, Aspects of multivariate statistical analysis in geology (Amsterdam: Elsevier, 1999).

Richardson, Wilfred A., The frequency-distribution of igneous rocks. Part II. The laws of distribution in relation to petrogenetic theories, Mineralogical Magazine, 1923, 20:1-19.

Rowe, Arthur W., An analysis of the genus Micraster, as determined by rigid zonal collecting from the Zone of Rhynchonella Cuvieri to that of Micraster cor-angirinum, Quarterly Journal of the Geological Society, London, 1899, 44:171-233.

Schmid, Kurt, Biometrische Untersuchungen aus Foraminiferen aus d. Phacen von Ceram, Eclogae Geologicae Helvetiae, 1934, 27:46-128.

Shewhart, Walter A., Economic control of quality of manufactured product (New York: Van Nostrand, 1931).

Sichel, Herbert S., An experimental and theoretical investigation of bias error in mine sampling, with special reference to narrow gold reefs, Transactions of the Institution of Mining and Metallurgy, London, 1947, 56:403-474.

Sichel, Herbert S., New methods in the statistical evaluation of mine sampling data. Transactions of the Institution of Mining and Metallurgy, London, 1952, 61:261-288.

Simpson, Steven M., Jr., Least squares polynomial fitted to gravitational data and density plotting by digital computers, Geophysics, 1954, 19:255-269, 644.

Trueman, Arthur E., The use of Gryphea in the correlation of the Lower Lias, Geological Magazine, 1922, 59:256-268.

Trueman, Arthur E., Results of some recent statistical investigations of invertebrate fossils, Biological Review of the Cambridge Philosophical Society, 1930, 5:296-308.

Vistelius, Andrei B., Studies in Mathematical Geology (New York: Consultants Bureau, 1967).

Vistelius, Andrei B., Principles of Mathematical Geology (Dordrecht: Kluwer Academic Publishers, 1992; updated English translation of Russian edition, Leningrad: Nauka, 1980).

Wentworth, Chester K., A scale of grade and class terms for clastic sediments, Journal of Geology, 1922a, 30:377-292.

Wentworth, Chester K., The shapes of pebbles, United States Geological Survey Bulletin, 1922b, 730-c:91-114.

Wentworth, Chester K., Method of computing mechanical composition types in sediments Geological Society of America Bulletin, 1929, 40:771-790.

  • Download PDF