Nonrenewable Resources

, Volume 6, Issue 3, pp 157–236 | Cite as

Quantitative estimates of the geology of large regions and their application to mineral-resource assessment

  • John C. Griffiths
  • A. D. Pilant
  • Chester M. Smith


The unit regional value of the mineral resources of a large region may be estimated by accumulating past production records and prorating them over the area of the region. The geological characteristics of a large region is a prime conditioning variable for this purpose. To be useful, however, the geology of a large region must be represented in a standardized form. The “geology,” as here measured, refers to a standardized set of rock types common to the legends in geological maps. By using standardized procedures, the legends of 413 geologic maps at 292 different scales that cover the Earth’s land surface were transformed into a set of 65 three-digit numbers. The set of numbers called the time-petrographic index is associated with the contemporaneous tectonic environments that led to the formation of the rocks and their associated mineral deposits. Application of the time-petrographic index to geologic maps leads to more precise estimates of the mineral-resource values of a large region.

Key Words

Unit regional value time-petrographic index point-counting mineral resource values petrographie classifications 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Addad, M. K., 1972, A contemplation and assessment of the 1960-1961 classification of the rocks of the central eastern desert,in The basement complex of Egypt: Annals of the Geological Survey of Egypt, Egyptian Geological Survey and Mining Authority, Cairo, p. 19–45.Google Scholar
  2. Aitken, B. G., and Echeverria, L. M., 1984, Petrology and geochemistry of komatiites and tholeiites from Gorgona Island, Colombia: Contributions to Mineralogy and Petrology, v. 86, p. 94–105.CrossRefGoogle Scholar
  3. Arndt, N. T., and Nisbet, E. G., eds., 1982, Komatiites: London, George Allen and Unwin, 526 p.Google Scholar
  4. Atkin, R. H., 1974, Mathematical structure in human affairs: London, Heinemann Educational Books, 212 p.Google Scholar
  5. Bear, L. M., 1963, Geological map of Cyprus: Nicosia, Geological Survey Department, Nicosia, scale 1 :250,000, 1 sheet.Google Scholar
  6. Berendson, P., Boreherding, R. M., Doveton, J., Gerhard, L., Newell, K. D., Steeple, D., and Watney, W. L., 1988, Texaco Poersel #1, Washington County, Kansas-Preliminary geologic report of the pre-Phanerozoic rocks : Kansas Geological Survey, Open File Report 88-22, 116 p.Google Scholar
  7. Berkey, C. P., and Morris, F. K., 1927, Geology of Mongolia,in Reeds, C. A., ed., Natural history of Central Asia: New York, The American Museum of Natural History, 475 p. Biederman, E. W., Jr., 1986, Atlas of selected oil and gas reservoir rocks from North America: New York, John Wiley and Sons, 399 p.Google Scholar
  8. Bisschops, J. H., 1969, The Roraima Formation in Surinam,in Proceedings of the 7th Guiana Geological Conference, Paramaribo, 1966 : Konninklijke Nederlandse Geologisch Mijnbouwkundige, Genootschap Verhandelingen, Geologische Serie, v. 27, p. 109–118.Google Scholar
  9. Boswell, P. G. H., 1927, The geology of the country around Ipswich: London, H. M. Stationery Office, 115 p.Google Scholar
  10. Bowen, C. H., 1953, Petrology and economic geology of the Sharon conglomerate in Geuga and Potter Counties, Ohio : Engineering Experimental Station Bulletin 153, 58 p.Google Scholar
  11. Buchbinder, B., and Gill, D., 1976, Numerical classification of multivariate petrographie presence-absence data by association analysis in the study of the Miocene Ziqlaq reef complex of Israel,in Merriam, D. F., ed., Quantitative techniques for the analysis of sediments: New York, Pergamon Press, p. 23–31.Google Scholar
  12. Bucher, W. H., 1950, Megatectonics and geophysics: Transactions of the American Geophysical Union, v. 31, p. 495–507.Google Scholar
  13. Bureau de Recherches Géologiques et Miniéres, 1980, Geology of France and Notice Explicative, 102 p.Google Scholar
  14. Cayeux, L., 1929, Les roches sedimentaries de France: Paris, Imprimerie Nationale, 774 p.Google Scholar
  15. Charter, C. F., 1937, Soil survey (reconnaissance) of Antigua and Barbuda, Leeward Islands: Antigua, B. W. I, Secretariat.Google Scholar
  16. Chayes, F., 1956, Petrographie modal analysis: New York, John Wiley & Sons, 113 p.Google Scholar
  17. Dewey, H., 1948, British regional geology-South-west England, 2d Ed.: London, H. M. Stationery Office, 136 p.Google Scholar
  18. Dewey, H., and Flett, J. S., 1911, British pillow-lavas and the rocks associated with them : Geological Magazine, p. 202–209, 241–248.Google Scholar
  19. Dickinson, W. R., 1970, Interpreting detrital modes of graywacke and arkose: Journal of Sedimentary Petrology, v. 40, p. 695–707.Google Scholar
  20. Dickinson, W. R., 1982, Compositions of sandstones in circum-Pacific subduction complexes and fore-arc basins: American Association of Petroleum Geologists Bulletin, v. 66, p. 121–137.Google Scholar
  21. Dickinson, W. R., 1984, Interpreting provenance relations from detrital modes of sandstones,in Zuffa, G. G., ed., Provenance of arenites: Boston, Reidel Publishing Company, p. 333–361.Google Scholar
  22. Dickinson, W. R., Beard, L., Brakenridge, G. R., Erjavec, J. L., Ferguson, R. C, Inman, K. F., Knepp, R. A., Lindberg, F. A., and Ryberg, P. T., 1983, Provenance of North American Phanerozoic sandstones in relation to tectonic setting: Geological Society of America Bulletin, v. 94, p. 222–235.Google Scholar
  23. Diehl, P. E., 1979, The stratigraphy, depositional environments, and quantitative petrography of the PreCambrian-Cambrian Wood Canyon Formation, Death Valley: PhD dissertation, The Pennsylvania State University, University Park, 365 p.Google Scholar
  24. Edmunds, F. R., 1977, Multivariate analysis of petrographie and chemical data from the Aldridge Formation, Southern Purcell mountain range, British Columbia, Canada: PhD dissertation, The Pennsylvania State University, University Park, 366 p.Google Scholar
  25. Emerson, B. K., 1917, Geology of Massachusetts and Rhode Island : U.S. Geological Survey Bulletin 597, 289 p.Google Scholar
  26. Engelder, R. P., 1979, Application of the unit regional value concept to a study of the mineral resources of Australia: PhD dissertation, The Pennsylvania State University, University Park, 256 p.Google Scholar
  27. Erez, J., and Gill, D., 1977, Multivariate analysis of biogenic constituents in recent sediments off Ras Burka, Gulf of Elat, Red Sea: Mathematical Geology, v. 9, p. 77–98.CrossRefGoogle Scholar
  28. Everitt, B., 1974, Cluster analysis: London, Heineman Educational Books, Ltd., 122 p.Google Scholar
  29. Fairbridge, R. W., and Bourgeois, J. eds., 1978, The encyclopedia of sedimentology: Stroudsburg, Dowden, Hutchinson and Ross, 901 p.Google Scholar
  30. Folk, R. L., 1968, Petrology of sedimentary rocks-course syllabus: Austin, Hemphill’s, University of Texas, 170 p.Google Scholar
  31. Fuller, J. O., 1955, Source of the Sharon conglomerate of northeastern Ohio: Geological Society of America Bulletin, v. 66, p. 159–176.CrossRefGoogle Scholar
  32. Glagolev, A. A., 1933, On the geometrical methods of quantitative mineralogical analysis of rocks: Transactions of the Institute Economic Mineralogy, U.S.S.R., v. 59, p. 1–47 (English summary, p. 47).Google Scholar
  33. Gould, P., 1981, A structural language of relations,in Craig, R. G., and Labovitz, M. L., eds., Future trends in geomathematics: London, Pion, Ltd., p. 281–312.Google Scholar
  34. Grabau, A. W., 1931, The Permian of Mongolia,in Reeds, C. A., ed., Natural history of Central Asia: New York, The American Museum of Natural History, 665 p.Google Scholar
  35. Greenly, E., and Williams, H., 1930, Methods in geological surveying: London, Thomas Murbey & Company, 420 p.Google Scholar
  36. Grey, C, and Shepps, V. C, I960, Geologic map of Pennsylvania : Pennsylvania Topographic and Geological Survey Map 41, 4th series.Google Scholar
  37. Griffiths, J. C, 1939, The mineralogy of the glacial deposits between the rivers Neath and Towy, south Wales: Proceedings of the Geological Association, v. 50, p. 433.Google Scholar
  38. Griffiths, J. C, 1942, Report on petrology and petrography of the deposits,in Kugler, H. G., MacKenzie, S. C., Stainforth, R. M., and Griffiths, J. C., eds., Report on exploration for oil in British Guiana : Geological Survey of British Guiana Bulletin 10, p. 60–73.Google Scholar
  39. Griffiths, J. C., 1952, Reaction relation in the finer-grained rocks: Clay Minerals Bulletin, v. 1, p. 251–257.CrossRefGoogle Scholar
  40. Griffiths, J. C., 1956, Petrographical investigations of the Salt Wash sediments : U.S. Atomic Energy Commission, Technical Report RME 3112, pt. 1 and 2, 84 p.Google Scholar
  41. Griffiths, J. C., 1958, Porosity and petrography of the Cow Run Sand: Journal of Sedimentary Petrology, v. 25, p. 15–30.Google Scholar
  42. Griffiths, J. C., 1959, Size and shape of rock fragments in Tuscarora scree, Lamar, central Pennsylvania: Journal of Sedimentary Petrology, v. 29, p. 391–401.Google Scholar
  43. Griffiths, J. C., 1966, A genetic model for the interpretive petrology of detrital sediments: Journal of Geology, v. 74, p. 655–672.Google Scholar
  44. Griffiths, J. C., 1967, Scientific method in the analysis of sediments: New York, McGraw-Hill Book Co., 508 p.Google Scholar
  45. Griffiths, J. C., 1968, Geological data for classification,in Proceedings of a symposium on decision-making in mineral exploration: British Columbia Research Council, v. 41, p. 37–42.Google Scholar
  46. Griffiths, J. C., 1969, Modelling the petrology of detrital sediments,in Merriam, D. F., ed., Computer applications in the earth sciences: New York, Plenum Publishing Corporation, p. 73–97.Google Scholar
  47. Griffiths, J. C., 1972, Some aspects of classification,in Protz, R., and Martini, I. P., eds., Classification of soils and sedimentary rocks-Proceedings of a Symposium on classification of soils and sedimentary rocks, University of Guelph, Guelph, Ontario, Center for Resources Development, p. 123–146.Google Scholar
  48. Griffiths, J. C., 1978a, Sediment parameters,in Fairbridge, R. W., and Bourgeois, J., eds., Encyclopedia of earth sciences, ser. 4 of Encyclopedia of sedimentology: Stroudsburg, PA, Dowden, Hutchinson and Ross, p. 724–731.Google Scholar
  49. Griffiths, J. C., 1978b, Mineral resource assessment using the unit regional value concept: Mathematical Geology, v. 10, p. 441–472.CrossRefGoogle Scholar
  50. Griffiths, J. C., 1981, Systems behavior and geoscience problemsolving,in Merriam, D. F., ed., Computer applications in the earth sciences-an update of the 70’s: New York, Plenum Publishing Corporation, p. 1–21.Google Scholar
  51. Griffiths, J. C., 1983, Geological similarity by Q-analysis: Mathematical Geology, v. 15, p. 85–108.CrossRefGoogle Scholar
  52. Griffiths, J. C., 1988, Measurement, sampling and interpretation,in Chung, C. F., Fabbri, A. G., and Sinding-Larsen, R., eds., Quantitative analysis of mineral and energy resources: Boston, Reidel Publishing Company, p. 37–56.Google Scholar
  53. Griffiths, J. C., Bates, T. F., and Shadle, H. W., 1956, Guide to field trip of fourth National Clay Conference,in Clay minerals in sedimentary rocks-Proceedings of the fourth National Conference on Clays and Clay Minerals : National Academy of Sciences Publication 456, p. 1–20.Google Scholar
  54. Griffiths, J. C., and Ondrick, C. W, 1968, Sampling a geological population : Kansas State Geological Survey Computer Contributions, v. 30, 53 p.Google Scholar
  55. Griffiths, J. C., and Singer, D. A., 1971, Unit regional value of nonrenewable natural resources as a measure of potential for development of large regions: Sydney, Geological Society of Australia Special Publication, p. 227–238.Google Scholar
  56. Griffiths, J. C., Watson, A. T., and Menzie, W. D., 1980, Relationship between mineral resource and geological diversity,in Miall, A. D. ed., Facts and principles of world petroleum occurrence : Canadian Society of Petroleum Geology Memoir 5, p. 329–341.Google Scholar
  57. Hadding, A., 1927, A survey of the pre-Quaternary sedimentary rocks of Sweden-3The Paleozoic and Mesozoic conglomerates of Sweden : Meddelanden, Lunds Geologisk Mineralogiska Institution, pt. 2, v. 23, no. 5, 171 p.Google Scholar
  58. Hadding, A., 1929, A survey of the pre-Quaternary sedimentary rocks of Sweden-3The Palaeozoic and Mesozoic sandstones of Sweden : Meddelanden, Lunds Geologisk-Mineralogiska Institution, pt. 2, v. 25, no. 3, 287 p.Google Scholar
  59. Haq, B. U., and van Eysinga, W. B., 1987, Geological time table, 4th Ed.: Amsterdam, Elsevier Scientific Publishers, 1 sheet.Google Scholar
  60. Houlik, C. W., Jr., 1973, Interpretation of carbonate-detrital silicate transitions in the Carboniferous of western Wyoming: American Association of Petroleum Geologists, v. 57, p. 498–509.Google Scholar
  61. Hubert, J. F., 1960, Petrology of the Fountain and Lyons Formations, Front Range, Colorado : Colorado School of Mines Quarterly, v. 55, no. 1, 142 p.Google Scholar
  62. Hume, W. F., 1934, Geology of Egypt: Government Press, Cairo, 300 p.Google Scholar
  63. Hurlbut, C. S., 1971, Dana’s manual of mineralogy, 18th Ed.: New York, John Wiley & Sons, 579 p.Google Scholar
  64. Jacobsen, L., 1959, Petrology of Pennsylvanian sandstones and conglomerates of the Ardmore Basin : Oklahoma Geological Survey Bulletin 79, 144 p.Google Scholar
  65. Khvorova, I. V., 1987, Deposits of island-arc systems: Moscow Institute Geology Academy Science, p. 3–18 (translated from Litolozyia i Poleznye Ikopaemye, New York, Plenum Publishing Corporation).Google Scholar
  66. Krishnan, M. S., 1960, Geology of India and Burma, 4th ed.: Madras, Higginbothams, 536 p.Google Scholar
  67. Krynine, P. D., 1948, The megascopic study and field classification of sedimentary rocks: Journal of Geology, v. 56, p. 130–165.Google Scholar
  68. Krynine P. D., 1950a, Petrology, stratigraphy, and origin of the Triassic sedimentary rocks of Connecticut : Conneticut Geology & Natual History Survey Bulletin 73, 247 p.Google Scholar
  69. Krynine, P. D., 1950b, Petrology and genesis of the Third Bradford Sand : The Pennsylvania State College Mineral Industry Experimental Station Bulletin, v. 29, 134 p.Google Scholar
  70. Krynine, P. D., 1951, A critique of geotectonic elements: Transactions of the American Geophysical Union, v. 32, p. 743–748.Google Scholar
  71. Krynine, P. D., 1956, Alice in graywackeland: Journal of Paleontology, v. 30, p. 1007–1008.Google Scholar
  72. Labovitz, M. L., 1978, Unit regional value of the dominion of Canada: PhD dissertation, The Pennsylvania State University, University Park, 366 p.Google Scholar
  73. Labovitz, M. L., and Griffiths, J. C., 1982, An inventory of undiscovered Canadian mineral resources: Economic Geology, v. 77, p. 1642–1654.CrossRefGoogle Scholar
  74. Labovitz, M. L., Menzie, W. D., and Griffiths, J. C., 1977, COMOD-A program for standardizing mineral resource commodity data: Computers & Geosciences, v. 3, p. 497–537.CrossRefGoogle Scholar
  75. Loveless, A. R., 1960, The vegetation of Antigua, West Indies: Journal of Ecology, v. 48, p. 495–527.CrossRefGoogle Scholar
  76. McBride, E. F., 1962, Flysch and associated beds of the Martinsburg Formation (Ordovician), central Appalachians: Journal of Sedimentary Petrology, v. 32, p. 39–91.Google Scholar
  77. Mellon, G. B., 1958, The Petrology of the Blairmore Group, Alberta, Canada: PhD dissertation, The Pennsylvania State University, University Park, 172 p.Google Scholar
  78. Menzie, W. D., 1977, The unit regional value of the Republic of South Africa: PhD dissertation, The Pennsylvania State University, University Park, 235 p.Google Scholar
  79. Menzie, W. D., Labovitz, M. L., and Griffiths, J. C., 1977, Evaluation of mineral resources and the unit regional value concept,in Ramani, R. V., ed., Application of computer methods in the mineral industry; Society of Mining Engineers, Institute of Mining, Metallurgy and Petroleum Engineering, p. 322–339.Google Scholar
  80. Meyer, H. J., 1964, Petrography of the Catskill sandstone facies in central Pennsylvania: PhD dissertation, The Pennsylvania State University, University Park, 136 p.Google Scholar
  81. Missan, H., Cooper, B. R., el Raba’a, S. M., Griffiths, J. C., and Sweetwood, C., 1978, Workshop on areal value estimation: Mathematical Geology, v. 10, p. 433–439.CrossRefGoogle Scholar
  82. Morton, A. C., 1984, Heavy minerals in provenance studies,in Zurfa, G. G., ed., Provenance of Arenites: Bosten, Reidel Publishing Company, p. 249–277.Google Scholar
  83. Mounsey, H., ed., 1988, Building databases for global science: London, International Geographical Union Global Database Planning Project, 1st, 419 p.Google Scholar
  84. Oetking, P. F., 1963, Geological highway map of Texas : Dallas Geological Society, 1 map.Google Scholar
  85. Ondrick, C. W., 1968, Petrography and geochemistry of the Rensselaer Graywacke, Troy, New York: PhD dissertation, The Pennsylvania State University, University Park, 218 p.Google Scholar
  86. Otto, G. H., 1938, The sedimentation unit and its use in field sampling: Journal of Geology, v. 46, p. 569–582.Google Scholar
  87. Patil, G. P., and Taille, C, 1977, Diversity as a concept and its measurement,in Patil, G. P., coord., Ecological diversity in theory and practice : Proceedings of the second International Ecological Congress Satellite Program in Statistical Ecology, North Atlantic Treaty Organization, 239 p.Google Scholar
  88. Pettijohn, F. J., Potter, P. E., and Siever, R., 1973, Sand and sandstone: New York, Springer-Verlag, 618 p.Google Scholar
  89. Pielou, E. C., 1975, Ecological diversity: New York, John Wiley & Sons, 165 p.Google Scholar
  90. Powell, J. W., 1890, Tenth annual report of the director of the United States Geological Survey, 1888-1889 : 774 p.Google Scholar
  91. Priem, H. N. A., Boelrijk, N. A. I. M., Hebeda, E. H., Verdunnen, E. A. Th, and Verschure, R. H., 1973, Age of the Precambrian Roraima Formation in northeastern South America-Evidence from isotopic dating of Roraima pyroclastic volcanic rocks in Suriname: Geological Society of America Bulletin, v. 84, p. 1677–1684.CrossRefGoogle Scholar
  92. Quinn, A. W., 1971, Bedrock geology of Rhode island : U.S. Geological Survey Bulletin 1295, 68 p.Google Scholar
  93. Renfro, H. B., Feray, D. E., and King, P. B., 1973, Geological highway map of Texas : U.S. Geological Survey Highway Map Series, Map 7.Google Scholar
  94. Rodgers, J., Cameron, E. N., Gates, R. M., and Ross, R. J., 1956, Preliminary geological map of Connecticut : Connecticut Geology & Natural History Survey.Google Scholar
  95. Rosenfeld, M. A., 1953, Petrographie variation in the Oriskany Sandstone complex: PhD dissertation, The Pennsylvania State College, University Park, 220 p.Google Scholar
  96. Said, R., 1962, The geology of Egypt: Amsterdam, Elsevier Publishing Company, 377 p.Google Scholar
  97. Shadie, H. W., and Griffiths, J. C., 1955, An attempt to establish oil-reservoir favorability criteria based on quantitative petrographie analysis: The Pennsylvania State University, Mineral Industry Experimental Station Bulletin, v. 68, p. 61–66.Google Scholar
  98. Siever, R., 1949, Trivoli sandstone of Williamson County, Illinois: Journal of Geology, v. 57, p. 614–818.Google Scholar
  99. Siever, R., 1953, Petrology and sedimentation of Upper Chester sandstones, Illinois: Journal of Sedimentary Petrology, v. 23, p. 207–219.Google Scholar
  100. Singer, D. A., 1971, Multivariate statistical analysis of the unit regional value of mineral resources: PhD dissertation, The Pennsylvania State University, University Park, 210 p.Google Scholar
  101. Singer, D. A., 1972, Ellipgrid a FORTRAN IV program for calculating the probability of success in locating elliptical targets with square, rectangular, and hexagonal grids : Geocom Programs, no. 4, 16 p.Google Scholar
  102. Singer, D. A., and Wickman, F. E., 1969, Probability tables for locating elliptical targets with square, rectangular and hexagonal point-nets : The Pennsylvania State University Mineral Sciences Experimental Station Special Publication Number 1–69,100 p.Google Scholar
  103. Snelling, N. J., ed., 1985, The geological record : Geological Society of London Memoir 10,265 p.Google Scholar
  104. Sokal, R. R., and Sneath, P. H. A., 1963, Principles of numerical taxonomy: San Francisco, W. H. Freeman & Company, 359 p.Google Scholar
  105. Suter, H. H., 1951, The general and economic geology of Trinidad, B. W. I., pt. 2 of Petrology, mineralogy, tectonics and geological history,in Beard, E. H., ed., 1951, Colonial geology and mineral resources: London, H. M. Stationery Office, p. 271–307.Google Scholar
  106. Taliaferro, N. L., 1943, Franciscan-Knoxville problem: American Association of Petroleum Geologists Bulletin, v. 17, p. 109–219.Google Scholar
  107. Thiel, G. A., 1935, Sedimentary and petrographie analysis of the St. Peter Sandstone: Geological Society of America Bulletin, v. 46, p. 559–614.Google Scholar
  108. Tukey, J. W., 1977, Exploratory data analysis: Reading, Massachusetts, Addison-Wesley Publishing Company, 688 p.Google Scholar
  109. van Andel, T. H., 1958, Origin and classification of Cretaceous, Paleocene, and Eocene sandstones of western Venezuela: American Association of Petroleum Geologists Bulletin, v. 42, p. 734–763.Google Scholar
  110. Velleman, P. F., and Hoaglin, D. C., 1981, Applications, basics, and computing of exploratory data analysis: Boston, Duxbury Press, 420 p.Google Scholar
  111. Viljoen, R. P., and Viljoen, M. J., 1969, Evidence for the composition of the primitive mantle and its products of partial melting from a study of the mafic and ultramafic rocks of the Barberton Mountain Land :in Upper Mantle Project Special Publication, Geological Society of South Africa 2, p. 275–295.Google Scholar
  112. Vistelius, A. B., 1964, Informational characteristics of frequency distributions in geochemistry: Nature, v. 202, p. 1206.CrossRefGoogle Scholar
  113. von Bertalanffy, L., 1948, General system theory: New York, G. Braziller, 289 p.Google Scholar
  114. Wilkinson, T., 1986, WATFILE/Plus data manipulation system: Waterloo, Ontario, WATCOM Publications Ltd., 353 p.Google Scholar
  115. Willis, B., 1901, Individuals of stratigraphie classification: Journal of Geology, v. 9, p. 557–569.CrossRefGoogle Scholar
  116. Wishart, D., 1987, Clustan user manual: Fife, Scotland, Computations Laboratory of St. Andrews, 250 p.Google Scholar
  117. Wood, G. V., 1960, A comparison of three quartzites: Ph.D. dissertation, The Pennsylvania State University, University Park, 159 p.Google Scholar
  118. Zuffa, G. G., 1984, Provenance of arenites: Boston, Reidel Publishing Company, 408 p.Google Scholar

Copyright information

© International Association for Mathematical Geology 1997

Authors and Affiliations

  • John C. Griffiths
  • A. D. Pilant
    • 1
  • Chester M. Smith
    • 2
  1. 1.Physics DepartmentMichigan Tech UniversityHoughton
  2. 2.Pennsylvania State UniversityUniversity Park, Pennsylvania

Personalised recommendations