Skip to main content
SpringerLink
Log in
Book cover

Dictionary of Mathematical Geosciences pp 611–636Cite as

T

  • Chapter
  • First Online:

  • 1071 Accesses

Abstract

A superscript T is often used to denote the operation of matrix transposition. The transpose of a row vector [a 1,…,a n ] is a column vector [a 1,…,a n ] containing the same elements in the same order. For matrices, the transpose of a matrix A, denoted by a superscript T: A T, is obtained by replacing each row of the original matrix by its corresponding column, so if A is an r × c matrix of r rows and c columns, its transpose will be a c × r matrix. Early use of the terms transposition and transposed matrix appear in Caley (1858) and in a geological context in Krumbein and Graybill (1965). See also: Boolean similarity matrix, characteristic analysis, matrix transpose, orthogonal matrix, singular-value decomposition, skew-symmetric matrix, symmetric matrix.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  • ABAN, I.B., MEERSCHAERT, M.M. and PANORSKA, A.K. (2006). Parameter estimation for the truncated Pareto distribution. The American Statistician, 101, 270–277.

    Article  Google Scholar 

  • AGTERBERG, F.P. (1984a). Use of spatial analysis in mineral resource evaluation. Journal of the International Association for Mathematical Geology, 16, 565–589.

    Article  Google Scholar 

  • AGTERBERG, F.P. (1984b). Binomial and trinomial models in quantitative biostratigraphy. Computers & Geosciences, 10, 31–41.

    Article  Google Scholar 

  • AITCHISON, J. (1986). The statistical analysis of compositional data. London, Chapman and Hall.

    Book  Google Scholar 

  • AKI, K. (1977). Three dimensional seismic velocity anomalies in the lithosphere. Zeitschrift für Geophysik, 43, 235–242.

    Google Scholar 

  • AKI, K., CHRISTOFFERSSON, A. and HUSEBY, E.S. (1977). Determination of three-dimensional seismic structure of the lithosphere. Journal of Geophysical Research, 82, 277–296.

    Article  Google Scholar 

  • ALKINS, W.E. (1920). Morphogenesis of brachiopoda. I. Reticularia lineata (Martin), Carboniferous Limestone. Memoirs and Proceedings of the Manchester Literary and Philosophical Society, 64 (2), 1–11.

    Google Scholar 

  • ALLAUD, L.A. and RINGOT, J. (1969). The high resolution dipmeter tool. The Log Analyst, 10 (3), 3–11.

    Google Scholar 

  • ANALYTICAL METHODS COMMITTEE (2003). Terminology – the key to understanding analytical science. Part 1: Accuracy, precision and uncertainty. Royal Society of Chemistry AMC Technical Brief 13, London [online: www.rsc.org/Membership/Networking/InterestGroups/ Analytical/ AMC/TechnicalBriefs.asp].

  • ANELLIS, I. (2004). The genesis of the truth table. Russell, new ser., 24, 55–70.

    Google Scholar 

  • ANELLIS, I.H. (2012). Pierce’s truth functional analysis and the origin of truth tables. History and Philosophy of Logic, 33, 87–97.

    Article  Google Scholar 

  • AURENHAMMER, F. (1991). Voronoï diagrams – A survey of a fundamental geometric data structure. ACM Computing Surveys, 23, 345–405.

    Article  Google Scholar 

  • BACKUS, G.E. and GILBERT, J.F. (1967). Numerical applications of a formalism for geophysical inverse problems. Geophysical Journal of the Royal Astronomical Society, 13, 247–276.

    Article  Google Scholar 

  • BACKUS, G.E. and GILBERT, J.F. (1968). The resolving power of gross earth data. Geophysical Journal of the Royal Astronomical Society, 16, 169–205.

    Article  Google Scholar 

  • BACKUS, G.E. and GILBERT, J.F. (1970). Uniqueness in the inversion of inaccurate gross earth data. Philosophical Transactions of the Royal Society, London, ser. A, 266, 123–192.

    Article  Google Scholar 

  • BAECHER, G.B. (1983). Statistical analysis of rock mass fracturing. Journal of the International Association for Mathematical Geology, 15, 329–348.

    Article  Google Scholar 

  • BAILEY, N. (1731). An universal etymological English dictionary. 5th edn., London, J. and J. Knapton, D. Mindwinter, A. Ward et al.

    Google Scholar 

  • BANCROFT, W.D. (1897). A triangular diagram. Journal of Physical Chemistry, 1, 403–410.

    Article  Google Scholar 

  • BARBIER, J. (1979). Images geochimiques du socle hercynien dans le Massif central français. Bulletin de recherche géologique et minière, ser. 2, 2 (2–3), 175–194.

    Google Scholar 

  • BARR, D.R. and SHERRILL, E.T. (1999). Mean and variance of truncated normal distributions. The American Statistician, 53, 357–361.

    Google Scholar 

  • BARRY, D.A. (1990). Supercomputers and their use in modeling subsurface solute transport. Reviews of Geophysics, 28, 277–295.

    Article  Google Scholar 

  • BARTELS, J. (1946). Geomagnetic data on variations of solar radiation. Part I. Wave-radiation. Journal of Geophysical Research, 51, 181–242.

    Article  Google Scholar 

  • BARTLETT, M.S. (1948). Smoothing periodograms from time series with continuous spectra. Nature, 161, 686–687.

    Article  Google Scholar 

  • BARTLETT, M.S. (1950). Periodogram analysis and continuous spectra. Biometrika, 37, 1–16.

    Article  Google Scholar 

  • BEAR, J. and CHENG, A.H.-D. (2010). Modeling groundwater flow and contaminant transport. Theory and applications of transport in porous media, v. 23. Dordrecht, Springer.

    Book  Google Scholar 

  • BEARD, C.N. (1959). Quantitative study of columnar jointing. Bulletin of the Geological Society of America, 70, 379–382.

    Article  Google Scholar 

  • BECKE, F. (1896). Gesteine der Columbretes [Rocks of the Columbretes]. Tschermak’s Mineralogische und petrographische Mittheilungen, 16, 308–336.

    Google Scholar 

  • BENDAT, J.S. and PIERSOL, A.G. (1971). Random data. Analysis and measurement procedures. New York, NY. Wiley-Interscience.

    Google Scholar 

  • BENDER, R., BELLMAN, S. H. and GORDON, R. (1970). ART and the ribosome: A preliminary report on the three-dimensional structure of individual ribosomes determined by an algebraic reconstruction technique. Journal of Theoretical Biology, 29, 483–487.

    Article  Google Scholar 

  • BENNETT, A.A. (1921). Some algebraic analogies in matric theory. Annals of mathematics, ser. 2, 23, 91–96.

    Article  Google Scholar 

  • BERNŠTEIN, S.N. (1926a). Sur l’extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes [On the extension of the limit theorem of probability to sums of dependent quantities]. Mathematische Annalen, 97, 1–59.

    Article  Google Scholar 

  • BEZVODA, V., JEŽEK, J. and SEGETH, K. (1990). FREDPACK – A program package for linear filtering in the frequency domain. Computers & Geosciences, 16, 1123–1154.

    Article  Google Scholar 

  • BI, G. and ZENG, Y. (2004). Transforms and fast algorithms for signal analysis and representations. Boston, Birkhäuser.

    Book  Google Scholar 

  • BIRKS, H.J.B. (1995). Quantitative palaeoenvironmental reconstructions. In: MADDY, D. and BREW, J.S. (eds.). Statistical modelling of Quaternary Science data. Technical Guide 5. Cambridge, Quaternary Research Association, 161-254.

    Google Scholar 

  • BIVAND, R.S., PEBESMA, E. and GÓMEZ-RUBIO, V. (2013). Applied spatial data analysis with R. 2nd edn., New York, NY, Springer-Verlag.

    Book  Google Scholar 

  • BLACKMAN, R.B. and TUKEY, J.W. (1958). The measurement of power spectra from the point of view of communications engineering. Bell System Technical Journal, 37, 185–282, 485–569.

    Article  Google Scholar 

  • BLAKE, A. (1941). Progress-report on periodicity and time-series. EoS, Transactions of the American Geophysical Union, 22, 407–408.

    Article  Google Scholar 

  • BLANDER, M. (1968). The topology of phase diagrams of ternary molten salt systems. Chemical Geology, 3, 33–58

    Article  Google Scholar 

  • BLOOMFIELD, P. (1976). Fourier analysis of time series: An introduction. New York, John Wiley & Sons.

    Google Scholar 

  • BODE, H.W. (1934). A general theory of electric wave filters. Journal of Mathematical Physics, 13, 275–362.

    Article  Google Scholar 

  • BOOLE, G. (1854). An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. London, Walton and Maberly.

    Book  Google Scholar 

  • BOOTS, B.N. and JONES, D.J. (1983). The spatial arrangement of random Voronoï polygons. Computers & Geosciences, 9, 351–365.

    Article  Google Scholar 

  • BORDLEY, R.F. (1982). A multiplicative formula for aggregating probability assessments. Management Science, 28, 1137–1148.

    Article  Google Scholar 

  • BOSWELL, P.G.H. (1915). The stratigraphy and petrology of the Lower Eocene deposits of the north-eastern part of the London Basin. Quarterly Journal of the Geological Society, London, 71, 536–591.

    Article  Google Scholar 

  • BOSWELL, P.G.H. (1961). The case against a Lower Palaeozoic geosyncline in Wales. Geological Journal, 2, 612–625.

    Article  Google Scholar 

  • BOTBOL, J.M. (1970). A model way to analyse the mineralogy of base metal mining districts. Mining Engineering, 22 (3), 56–59.

    Google Scholar 

  • BREIMAN, L., FRIEDMAN, J.H., OLSHEN, R. and STONE, C.J. (1984). Classification and regression trees. Belmont, CA, Wadsworth.

    Google Scholar 

  • BREITENBERGER, E. (1999). Johann Benedikt Listing. In: JAMES, I.M. (ed.). History of topology. Amsterdam, North-Holland, 909–924.

    Chapter  Google Scholar 

  • BUCCIANTI, A., MATEU-FIGUERAS, G. and PAWLOWSKY-GLAHN, V. (eds.) (2006). Compositional data analysis in the geosciences: From theory to practice. London, The Geological Society.

    Google Scholar 

  • BURNS, K.L. (1975). Analysis of geological events. Journal of the International Association for Mathematical Geology, 7, 295–321.

    Article  Google Scholar 

  • BUTTKUS, B. (1991). Spektralanalyse und Filtertheorie in der angewandten Geophysik. Berlin, Springer-Verlag.

    Book  Google Scholar 

  • BUTTKUS, B. (2000). Spectral analysis and filter theory in applied geophysics [translated by C NEWCOMB].. Berlin, Springer-Verlag.

    Google Scholar 

  • CAMINA, A.R. and JANACEK, G.J. (1984). Mathematics for seismic data processing and interpretation. London, Graham and Trotman.

    Book  Google Scholar 

  • CAMPBELL, G.A. (1922). Physical theory of the electric wave-filter. Bell System Technical Journal, 1 (2), 1–32.

    Article  Google Scholar 

  • CARLE, S.F. and FOGG, G.E. (1996). Transition probability-based indicator geostatistics. Mathematical Geology, 28, 453–476.

    Article  Google Scholar 

  • CAUCHY, A.-L. (1823). Recherches sur l'equilibre et le mouvement intérieur des corps solides ou fluides, élastiques ou non-élastiques [Researches on the equilibrium and interior movement of solid, fluid, elastic or inelastic bodies]. Bulletin des sciences par la Société Philomatique de Paris, new ser., 1823, 9–13.

    Google Scholar 

  • CAYLEY, A. (1858). A memoir on the theory of matrices. Philosophical Transactions of the Royal Society, London, 148, 17–37.

    Article  Google Scholar 

  • CHAMBERLIN, A.C. and TURNER, F.M. (1952). Errors and variations in white cell counts. Biometrika, 8, 55–65.

    Article  Google Scholar 

  • CHATFIELD, C. and PEPPER, M.P.G. (1971). Time-series analysis: An example from geophysical data. Journal of the Royal Statistical Society. ser. C. Applied statistics, 20, 217–238.

    Google Scholar 

  • CHENG, R. T.-S. and HODGE, D.S. (1976). Finite-element method in modeling geologic transport processes. Journal of the International Association for Mathematical Geology, 8, 43–56.

    Article  Google Scholar 

  • CHIU, W.K. and LEUNG, M.P. (1981). A graphical method for estimating the parameters of a truncated normal distribution. Journal of Quality Technology, 13, 42–45.

    Google Scholar 

  • COHEN, A.C. (1959). Simplified estimators for the normal distribution when samples are singly censored or truncated. Technometrics, 1, 217–237.

    Article  Google Scholar 

  • COX, K.G., BELL, J.D. and PANKHURST, R.J. (1979). The interpretation of igneous rocks. London, George, Allen and Unwin.

    Book  Google Scholar 

  • CRAIN, I.K. (1976). Statistical analysis of geotectonics. In: MERRIAM, D.F. (ed.). Random processes in geology. Berlin, Springer-Verlag, 3–15.

    Chapter  Google Scholar 

  • CRANDALL, I.B. (1926). Theory of vibrating systems and sound. New York, NY, Van Nostrand.

    Google Scholar 

  • DACEY, M.F. and KRUMBEIN, W.C. (1970). Markovian models in stratigraphic analysis. Journal of the International Association for Mathematical Geology, 2, 175–191.

    Article  Google Scholar 

  • DACEY, M.F. and KRUMBEIN, W.C. (1976). Topological properties of disjoint channel networks within enclosed regions. Journal of the International Association for Mathematical Geology, 8, 429–462.

    Article  Google Scholar 

  • DAGBERT, M. (1981). Simulation and mapping of space-dependent data in geology. Bulletin of Canadian Petroleum Geology, 29, 267–276.

    Google Scholar 

  • DAVIS, J.C. and SAMPSON, R.J. (1973). Statistics and data analysis in geology. New York, NY, John Wiley & Sons.

    Google Scholar 

  • DAVIS, M. (1987a). Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Mathematical Geology, 19, 91–98.

    Article  Google Scholar 

  • DAVIS, M.W. (1987b). Generating large stochastic simulations – The matrix polynomial approximation method. Mathematical Geology, 19, 99–107.

    Article  Google Scholar 

  • DE GEER, G. (1910). Excursion 82. Phenomènes quaternaires de Stockholm,19 Août. v. 2. In: Compte Rendu de la XI e session, Congrès géologique international, Nordstet, Stockholm, 1290–1292.

    Google Scholar 

  • DEAN, J.M. and KEMP, A.E.S. (2004). A 2100 year BP record of the Pacific Decadal Oscillation, El Niño Southern Oscillation and Quasi-biennial Oscillation in marine production and fluvial input from Saanich Inlet, British Columbia. Palaeogeography, Palaeoclimatology, Palaeogeography, 213, 207–229.

    Article  Google Scholar 

  • DEUTSCH, C.V. and JOURNEL, A.G. (1992). GSLIB. Geostatistical software library and user’s guide. Oxford, Oxford University Press.

    Google Scholar 

  • DIMITRIJEVIČ, M.D. (1971). Analysis of statistical diagrams of folded surfaces. II. Scalar descriptors of the fold form. Neues Jahrbuch für Geologie und Paläontologie, Monatshefte, 1971 (7), 385–397.

    Google Scholar 

  • DIRICHLET, G.L. (1850). Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen [On the reduction of positive quadratic forms with three undetermined integers]. Journal für die reine und angewandte Mathematik, 40, 209–234.

    Article  Google Scholar 

  • DONNAY, J.D.H. (1943). Resetting a triclinic unit-cell in the conventional orientation. American Mineralogist, 28, 507–511.

    Google Scholar 

  • DOUGLAS, J. (1958). The application of stability analysis in the numerical solution of quasi-linear parabolic difference equations. Transactions of the American Mathematical Society, 89, 484–518.

    Article  Google Scholar 

  • DOWD, P.A. (1991). A review of recent developments in geostatistics. Computers & Geosciences, 17, 1481–1500.

    Article  Google Scholar 

  • DYER, B.C. and WORTHINGTON, M.H. (1988). Seismic reflection tomography: a case study. First Break, 6, 354–366.

    Article  Google Scholar 

  • EBERHART-PHILLIPS, D. (1986). Three-dimensional velocity structure in northern California Coast Ranges from inversion of local earthquake travel times. Bulletin of the Seismological Society of America, 76, 1025–1052.

    Google Scholar 

  • EINSTEIN, A. (1902). Kinetische Theorie des Wannegleichgewichtes und des zweiten Hauptsotzes der Thermodynamik [Kinetic theory of equilibrium and the two principles of thermodynamics]. Annalen der Physik, 9, 417–433.

    Article  Google Scholar 

  • EINSTEIN, A. (1903). Eine Theorie der Grundlagen der Thermodynamik [A theory on the foundations of thermodynamics]. Annalen der Physik, 11, 170–187.

    Article  Google Scholar 

  • EVANS, D.G. and JONES, S.M. (1987). Detecting Voronoï (area-of-influence) polygons. Mathematical Geology, 19, 523–537.

    Article  Google Scholar 

  • FEJÉR, L. (1904). Untersuchungen über Fouriersche Reihen [Studies on Fourier series]. Mathematische Annalen, 58, 501–569.

    Google Scholar 

  • FISHER, R.A. (1925a). Statistical methods for research workers. Edinburgh, Oliver and Boyd.

    Google Scholar 

  • FISHER, R.A. (1925b). Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society, 22, 700–725.

    Google Scholar 

  • FISHER, R.A. (1931). The sampling error of estimated deviates, together with other illustrations of the properties and applications of the integrals and derivatives of the normal error function. In: Mathematical tables, v. 1. London, British Association for the Advancement of Science, 26–35.

    Google Scholar 

  • FLINN, D. (1978). Construction and computation of three-dimensional progressive deformations. Quarterly Journal of the Geological Society, London, 135, 291–305.

    Article  Google Scholar 

  • FLINN, D. (1979). The deformation matrix and the deformation ellipsoid. Journal of Structural Geology, 1, 299–307.

    Article  Google Scholar 

  • FOLK, R.L. (1955). Student operator error in determination of roundness, sphericity, and grain-size. Journal of Sedimentary Petrography, 25, 297–301.

    Google Scholar 

  • FRIESE, K.-I., CICHY, S.B., WOLTER, F.-E. and BOTCHARNIKOV, R.E. (2013). Analysis of tomographic mineralogical data using YaDiV – Overview and practical case study. Computers & Geosciences, 56, 92–103.

    Article  Google Scholar 

  • GENTLEMAN, W.M. and SANDE, G. (1966). Fast Fourier Transforms – for fun and profit. In: American Federation of Information Processing Societies: Proceedings of the AFIPS ’66 Fall Joint Computer Conference, November 7–10, 1966, San Francisco, California, USA. AFIPS Conference Proceedings 29, Spartan Books, Washington, DC, 563–578.

    Google Scholar 

  • GIBBONS, R.D. (1994). Statistical methods for groundwater monitoring. New York, NY, John Wiley & Sons.

    Book  Google Scholar 

  • GIBBS, J.W. (1902). Elementary principles in statistical mechanics. Developed with special reference to the rational foundation of thermodynamics. New York, NY, Charles Scribner’s sons.

    Google Scholar 

  • GIBSON, G.A. and PINKERTON, P.W. (1929). Elements of analytical geometry: Graphs and curve tracing. London, Macmillan.

    Google Scholar 

  • GILBERT, E.N. (1962). Random subdivisions of space into crystals. The Annals of Mathematical Statistics, 33, 958–972.

    Article  Google Scholar 

  • GOOGLE RESEARCH (2012). Google Books Ngram Viewer (v. 2.0) [online: https://books.google.com/ ngrams/info].

  • GORDON, R., BENDER, R. and HERMAN, G.T. (1970). Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology, 29, 471–481.

    Article  Google Scholar 

  • GORELICK, S.M. (1985). Contaminant transport models for groundwater quality simulation. IAHS Publication 154. In: DOWNING, R.A. and JONES, G.P. (eds.). Hydrogeology in the service of man. Proceedings of a symposium held at Cambridge, UK, 8–13 Sept. 1985. Wallingford, International Association of Hydrological Sciences, 239–249.

    Google Scholar 

  • GRADSTEIN, F.M. and AGTERBERG, F.P. (1982). Models of Cenozoic foraminiferal stratigraphy – Northwestern Atlantic margin. In: CUBITT, J.M. and REYMENT, R.A. (eds.). Quantitative stratigraphic correlation. Chichester, John Wiley & Sons, 119–173.

    Google Scholar 

  • GRANT, F. (1957). A problem in the analysis of geophysical data. Geophysics, 22, 309–344.

    Article  Google Scholar 

  • GRAY, N.H., ANDERSON, J.B., DEVINE, J.D. and KWASNIK, J.M. (1976). Topological properties of random crack networks. Journal of the International Association for Mathematical Geology, 8, 617–626.

    Article  Google Scholar 

  • GRENANDER, V. and SZEGÖ, G. (1984). Toeplitz forms and their applications. New York, NY, Chelsea Publishing.

    Google Scholar 

  • GUBBINS, D. (2004). Time series analysis and inverse theory for geophysicists. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • HAHN, G.J. and MEEKER, W.Q. (1991). Statistical Intervals. New York, NY, John Wiley & Sons.

    Book  Google Scholar 

  • HALD, A. (1949). Maximum likelihood estimation of the parameters of a normal distribution which is truncated at a known point. Skandinavisk Actuarietidskrift, 32, 119–134.

    Google Scholar 

  • HARDING, J.E. (1920). Calculation of ore tonnage and grade from drill-hole samples. Transactions of the American Institute of Mining Engineers, 66, 117–126.

    Google Scholar 

  • HARDING, J.E. (1923). How to calculate tonnage and grade of an ore-body. Engineering and Mining Journal-Press, 116, 445–448.

    Google Scholar 

  • HARRIS, F.J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66, 51–83.

    Google Scholar 

  • HARTSHORNE, C. and WEISS, P. (eds). Collected papers of Charles Sanders Pierce. vol. III. Exact logic. Cambridge, MA, Harvard University Press.

    Google Scholar 

  • HAUSMAN, L.F. and SCHWARZSCHILD, M. (1947). Automatic integration of linear sixth-order differential equations by means of punched-card machines. Review of Scientific Instruments, 18, 877–883.

    Article  Google Scholar 

  • HAVILAND, E.K. (1935). On the inversion formula for Fourier-Stieltjes transforms for more than one dimension. II. American Journal of Mathematics, 57, 382–388.

    Article  Google Scholar 

  • HAWKES, H.E. (1957). Principles of geochemical prospecting. United States Geological Survey Bulletin 1000-F, Washington, DC, United States Government Printing Office. p. 225–355.

    Google Scholar 

  • HEALEY, M.J.R. and BOGERT, B.P. (1963). FORTRAN subroutines for time series analysis. Communications of the ACM, 6, 32–34.

    Article  Google Scholar 

  • HELSEL, D.R. (2005). Nondetects and data analysis. Hoboken, NJ, Wiley-Interscience.

    Google Scholar 

  • HENDERSON, R.G. (1960). A comprehensive system of automatic computation in magnetic and gravity interpretation. Geophysics, 25, 569–585.

    Article  Google Scholar 

  • HOLZBECHER, E. and SOREK, S. (2005). Numerical models of groundwater flow and transport. In: ANDERSON, M.G. (ed.). Encyclopaedia of hydrological sciences. Part 13, v. 4. Chichester, John Wiley & Sons, 2001–2044.

    Google Scholar 

  • HORTON, R.E. (1917). Rational study of rainfall data makes possible better estimates of water yield. Engineering News-Record, 211–213.

    Google Scholar 

  • HOUGHTON, J.C. (1988). Use of the truncated shifted Pareto Distribution in assessing size distributions of oil and gas fields. Mathematical Geology, 20, 907–937.

    Article  Google Scholar 

  • HOWARTH, R.J. (1973b). Preliminary assessment of a nonlinear mapping algorithm in a geological context. Journal of the International Association for Mathematical Geology, 5, 39–57.

    Article  Google Scholar 

  • HOWARTH, R.J. (1996a). Sources for the history of the ternary diagram. British Journal for the History of Science, 29, 337–356.

    Article  Google Scholar 

  • HOWARTH, R.J. (2001a). A history of regression and related model-fitting in the earth sciences (1636?–2000). Natural Resources Research, 10, 241–286.

    Article  Google Scholar 

  • HOWARTH, R.J. and LOWENSTEIN, P.L. (1976). Three-component colour maps from lineprinter output. Transactions of the Institution of Mining and Metallurgy, London, sec. B, 85, 234–237.

    Google Scholar 

  • HOWARTH, R.J. and THOMPSON, M. (1976). Duplicate analysis in practice. Part 2. Examination of proposed method and examples of its use. The Analyst, 101, 699–709.

    Article  Google Scholar 

  • HUDSON, C.B. and AGTERBERG, F. (1982). Paired comparison models in biostratigraphy. Journal of the International Association for Mathematical Geology, 14, 141–159.

    Article  Google Scholar 

  • HULL, E. (1862). On iso-diametric lines, as a means of representing the distribution of sedimentary clay and sandy strata, as distinguished from calcareous strata, with special reference to the Carboniferous rocks of Britain. Quarterly Journal of the Geological Society of London, 18, 127–146.

    Article  Google Scholar 

  • HUTCHINSON, G.E. (1949). A note on two aspects of the geochemistry of carbon. American Journal of Science, 247, 27–82.

    Article  Google Scholar 

  • INOUE, Y. and KAUFMAN, W.J. (1963). Prediction of movement of radionuclides in solution through porous media. Health Physics, 9, 705–715.

    Article  Google Scholar 

  • ISAAKS, E.H. and SRIVASTAVA, R.M. (1989). Applied geostatistics. Oxford, Oxford University Press.

    Google Scholar 

  • IYER, H.M. and HIRAHARA, K. (eds.) (1993). Seismic Tomography – Theory and Practice. London, Chapman and Hall.

    Google Scholar 

  • JACOBSEN, B.H. and PEDERSEN, L.B. (1980). Interpretation of the magnetic field from a sphere in the wavenumber domain. Pure and Applied Geophysics, 118, 1155–1169.

    Article  Google Scholar 

  • JEFFREYS, H. (1939). Theory of probability. Oxford, Clarendon Press.

    Google Scholar 

  • JENKINS, G.M. (1961). General considerations in the analysis of spectra. Technometrics, 3, 133–166.

    Article  Google Scholar 

  • JENKINS, G.M. (1963). An example of the estimation of a linear open loop transfer function. Technometrics, 5, 227–245.

    Article  Google Scholar 

  • JOHANNSEN, A. (1917). Suggestions for a quantitative mineralogical classification of igneous rocks. Journal of Geology, 25, 63–97.

    Article  Google Scholar 

  • JOHANNSEN, A. (1920). A quantitative mineralogical classification of igneous rocks: Revised. Journal of Geology, 28, 60–83.

    Google Scholar 

  • JOHNSON, N.L. and KOTZ, S. (1999). Non-smooth sailing or triangular distributions revisited after some 50 years. The Statistician, 48, 179–187.

    Google Scholar 

  • JOURNEL, A.G. (1974). Geostatistics for conditional simulation of ore bodies. Economic Geology, 69, 673–687.

    Article  Google Scholar 

  • KALBFLEISCH, J.D. and LAWLESS, J.F. (1992). Some useful statistical methods for truncated data. Journal of Quality Technology, 24, 145–152.

    Google Scholar 

  • KANAL, L. and CHANDRASEKARAN, B. (1968). On dimensionality and sample size in statistical pattern classification. In: Proceedings of the 24th National Electronics Conference, December 9–11, 1968, Chicago, Illinois, National Electronics Conference Inc., Oak Brook, IL, 2–7.

    Google Scholar 

  • KARLIN, S. (1966). A first course in stochastic processes. New York, NY, Academic Press.

    Google Scholar 

  • KERSEY, J. (1741). The elements of that mathematical art commonly called algebra. To which is added lectures read in the School of Geometry in Oxford by Dr. Edmund Halley. London, W. Mount and T. Page.

    Google Scholar 

  • KHEIR, R.B., WILSON, J. and DENG, Y. (2007). Use of terrain variables for mapping gully erosion susceptibility in Lebanon. Earth Surface Processes and Landforms, 32, 1770–1782.

    Article  Google Scholar 

  • KING, W.I. (1912). The elements of statistical method. London, Macmillan.

    Google Scholar 

  • KOOPMANS, T.C. (1937). Linear regression analysis of economic time series. Haarlem, De erven F. Bohn.

    Google Scholar 

  • KOPPELT, U. and ROJAS, J. (1994). Backus-Gilbert inversion of potential field data in the frequency domain and its application to real and synthetic data. Geofisica Internacional, 33, 531–539.

    Google Scholar 

  • KORMYLO, J. and JAIN, V. (1974). Two-pass recursive digital filter with zero phase shift. IEEE Transactions on Acoustics, Speech and Signal Processing, 22, 384–387.

    Article  Google Scholar 

  • KOTOV, S. and BERENDSEN, P. (2002). Statistical characteristics of xenoliths in the Antioch kimberlite pipe, Marshall County, Northeastern Kansas. Natural Resources Research, 11, 289–297.

    Article  Google Scholar 

  • KRISHNAN, S. (2008). The tau model for data redundancy and information combination in earth sciences: Theory and application. Mathematical Geosciences, 40, 705–727.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1954). The tetrahedron as a facies mapping device. Journal of Sedimentary Petrology, 24, 3–19.

    Google Scholar 

  • KRUMBEIN, W.C. (1959b). Trend surface analysis of contour-type maps with irregular control-point spacing. Journal of Geophysical Research, 64,823–834.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1960b). The ‘geological population’ as a framework for analysing numerical data in geology. Liverpool and Manchester Geological Journal, 2, 341–368.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1963b). Confidence intervals on low-order polynomial trend-surfaces. Journal of Geophysical Research, 68, 5869–5878.

    Article  Google Scholar 

  • KRUMBEIN, W.C. and DACEY, M.F. (1969). Markov chains and embedded Markov chains in geology. Journal of the International Association for Mathematical Geology, 1, 79–96.

    Article  Google Scholar 

  • KRUMBEIN, W.C. and GRAYBILL, F.A. (1965). An introduction to statistical models in geology. New York, NY, McGraw-Hill.

    Google Scholar 

  • KRUMBEIN, W.C. and PETTIJOHN, F.J. (1938). Manual of sedimentary petrography.. New York, NY, NY, Appleton-Century.

    Google Scholar 

  • KUNO, H. (1968). Differentiation of basalt magmas. In: HESS, H.H. and POLDERVAART, A. (eds.). Basalts. The Poldervaart treatise on rocks of basaltic composition. Vol 2. New York, Interscience, 623–688.

    Google Scholar 

  • KUZNETS, S. (1928). On the analysis of time series. Journal of the American Statistical Association, 23, 398–410.

    Article  Google Scholar 

  • LACHENBRUCH, A.H. (1962). Mechanics of thermal contraction cracks and ice-wedge polygons in permafrost. Geological Society of America, Special Paper, 70, 1–66.

    Article  Google Scholar 

  • LANGHEINRICH, G. (1967). Die Bestimmung der tektonischen Gesteins deformation mit Hilfe deformierter Ammoniten: mit zwei Beispielen aus den Allgaü-Schichten (Jura-Fleckenmergeln) Oberbayerns und Tirols [Determination of tectonic rock deformation with the aid of deformed ammonites: with two examples from the Allgaü-Schichten (Jura-Fleckenmergeln) of Upper Bavaria and Tyrol]. Neues Jahrbuch für Geologie und Paläontologie. Abhandlungen, 128, 275–293.

    Google Scholar 

  • Le MAITRE, R.W., BATEMAN, P., DUDEK, A., KELLER, J., LAMEYRE, J., LE BAS, M.J., SABINE, P.A., SCHMID, R., SORENSEN, H., STRECKEISEN, A., WOOLLEY, A.R. and ZANETTIN, B. (1989). A classification of igneous rocks and glossary of terms. Oxford, Blackwell.

    Google Scholar 

  • LEE, W. (1943). The stratigraphy and structural development of the Forest City Basin in Kansas. Kansas Geological Survey Bulletin, 51.

    Google Scholar 

  • LEES, J.M. and PARK, J. (1995). Multi-taper spectral analysis: A stand-alone C-subroutine. Computers & Geosciences, 21, 199–236.

    Article  Google Scholar 

  • LEIBNIZ, G.W. (1684). Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus [A new method for maxima and minima as well as tangents, which is neither impeded by fractional nor irrational quantities, and a remarkable type of calculus for them]. Acta Eruditorum, 3, 467–473 [partial English translation in STRUIK (1986), 271–280; see also PARMENTIER (1995), 96–117].

    Google Scholar 

  • LEVORSEN, A.I. (1927). Convergence studies in the mid-continent region. Bulletin of the American Association of Petroleum Geologists, 11, 657–682.

    Article  Google Scholar 

  • LI, C. and YAN, M. (1983). A matrix analysis of the rotation in crystals. Materials Science and Engineering, 57, 143–147.

    Article  Google Scholar 

  • LI, W. (2006). Transiogram: A spatial relationship measure for categorical data. International Journal of Geographical Information Science, 20, 693–699.

    Article  Google Scholar 

  • LI, W. (2007a). Markov chain random fields for estimation of categorical variables. Mathematical Geology, 39, 321–335.

    Article  Google Scholar 

  • LI, W. (2007b). Transiograms for characterizing spatial variability of soil classes. Soil Science Society of America Journal, 71, 881–893.

    Article  Google Scholar 

  • LI, W. and ZHANG, C. (2012). Linear interpolation and joint model fitting of experimental transiograms for Markov chain simulation of categorical spatial variables. International Journal of Geographical Information Science, 26, 599–620.

    Article  Google Scholar 

  • LI, W., ZHANG, C. and DEY, D.K. (2012). Modeling experimental cross-transiograms of neighboring landscape categories with the gamma distribution. International Journal of Geographical Information Science, 26, 599–620.

    Article  Google Scholar 

  • LI, W., ZHANG, C., WILLIG, M.R., DEY, D.K., WANG, G. and YOU, L. (2015). Bayesian Markov chain random field cosimulation for improving land cover classification accuracy. Mathematical Geosciences, 47, 123–148.

    Article  Google Scholar 

  • LIEBERMAN, D.S. and ZIRINSKY, S. (1956). A simplified calculation for the elastic constants of arbitrarily oriented single crystals. Acta Crystallographica, 9, 431–436.

    Article  Google Scholar 

  • LISTING, J.B. (1847). Vorstudien zur Topologie [Initial studies in topology]. Göttinger Studien, 2, 811–875.

    Google Scholar 

  • LORENZ, E.N. (1963). Deterministic non-periodic flow. Journal of Atmospheric Science, 20, 130–141.

    Article  Google Scholar 

  • LOU, J. (1996). Transition probability approach to statistical analysis of spatial qualitative variables in geology. In: FORSTER, A. and MERRIAM, D.F. (eds.). Geologic modeling and mapping (Proceedings of the 25th Anniversary Meeting of the International Association for Mathematical Geology, October 10–14, 1993, Prague, Czech Republic). New York, NY, Plenum Press, 281–299.

    Google Scholar 

  • LOW, J. (1950). Subsurface maps and illustrations. In: LEROY, L.W. (ed.). Subsurface geologic methods. (A symposium). 2nd edn. Golden, CO, Colorado School of Mines, 894–968.

    Google Scholar 

  • LOWENSTEIN, P.L. and HOWARTH, R.J. (1973). Automated colour-mapping of three-component systems and its application to regional geochemical reconnaissance. In: JONES, M.J. (ed.). Geochemical Exploration 1972. Proceedings of the Fourth International Geochemical Exploration Symposium. London, Institution of Mining and Metallurgy, 297–304.

    Google Scholar 

  • MACELWANE, J.B. 1932. Introduction to theoretical seismology. Part 1. Geodynamics. Saint Louis, MO, St. Louis University.

    Google Scholar 

  • MACLAURIN, C. (1742). A treatise of fluxions in two books. Edinburgh, T.W. and T. Ruddimans.

    Google Scholar 

  • MALLAT, S.G. (1999). A wavelet tour of signal processing. New York, NY, Academic Press.

    Google Scholar 

  • MANTOGLOU, A. and WILSON, J.L. (1982). The turning bands methods for simulation of random fields using line generation by the spectral method. Water Resources Research, 18, 1379–1394.

    Article  Google Scholar 

  • MARCOTTE, D. (2016). Spatial turning bands simulation of anisotropic non-linear models of coregionalization with symmetric cross-covariances. Computers & Geosciences, 89, 232–238.

    Article  Google Scholar 

  • MARKOV, A.A. (1906). Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga [Extension of the law of large numbers to events dependant one on the other]. Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, ser. 2, 15, 135–156.

    Google Scholar 

  • MATHERON, G. (1972). The turning bands: a method for simulating random functions in ℝn. Technical Report N-303, Paris, Centre de Morphologie Mathématique, École des Mines de Paris.

    Google Scholar 

  • MATHERON, G. (1973a). Le krigage disjonctif [Disjunctive kriging]. Note interne N-360, Fontainebleau, Centre de Géostatistique, École des Mines de Paris.

    Google Scholar 

  • MENKE, W. (1989). Geophysical data analysis: Discrete inverse theory. San Diego, CA, Academic Press.

    Google Scholar 

  • MENKE, W. (2012). Geophysical data analysis: Discrete inverse theory. MATLAB edition. Waltham, MA, Academic Press.

    Google Scholar 

  • MERTENS, M., NESTLER, I. and HUWE, B. (2002). GIS-based regionalization of soil profiles with Classification and Regression Trees. Journal of Plant Nutrition and Soil Science, 165, 39–43.

    Article  Google Scholar 

  • MILLER, J. (ed.) (2015a). Earliest known uses of some of the words of mathematics [online: http://jeff560.tripod.com/mathword.html].

  • MILLER, R.L. (1956). Trend surfaces: their application to analysis and description of environments of sedimentation. I. The relation of sediment-size parameters to current-wave systems and physiography. Journal of Geology, 64, 425–446.

    Google Scholar 

  • MILLER, R.L. and KAHN, J.S. (1962). Statistical analysis in the geological sciences. New York, John Wiley & Sons.

    Google Scholar 

  • NEUMANN-DENZAU, G. and BEHRENS, J. (1984). Inversion of seismic data using tomographical reconstruction techniques for investigations of laterally inhomogeneous media. Geophysical Journal of the Royal Astronomical Society, 79, 305–315.

    Article  Google Scholar 

  • NEWENDORP, P.D. (1975). Decision analysis for petroleum exploration. Tulsa, OK, PennWell.

    Google Scholar 

  • NEYMAN, J. and PEARSON, E.S. (1928). On the use and Interpretation of certain test criteria for purposes of statistical inference [Parts I and II]. Biometrika, 20A, 175–240, 263–294.

    Google Scholar 

  • NEYMAN, J. and PEARSON, E.S. (1933a). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society, London, ser. A, 231, 289–337.

    Google Scholar 

  • NEYMAN, J. and PEARSON, E.S. (1933b). The testing of statistical hypotheses in relation to probabilities a priori. Proceedings of the Cambridge Philosophical Society, 24, 492–510.

    Google Scholar 

  • NG, M.K. (2004). Iterative methods for Toeplitz systems. Oxford, Oxford University Press.

    Google Scholar 

  • NOWAK, R.L. (1990). Tomography and the Herglotz-Wiechert inverse formulation. Pure and Applied Geophysics, 133, 305–315.

    Article  Google Scholar 

  • OKABE, A., BOOTS, B., SUGIHARA, K. and CHIU, S.N. (2000). Spatial tessellations: Concepts and applications of Voronoï diagrams. 2nd edn., Chichester, John Wiley & Sons.

    Book  Google Scholar 

  • ORFORD, J.D. (1978). A comment on the derivation of conditional vector entropy from lithologic transition tally matrices. Journal of the International Association for Mathematical Geology, 10, 97–102.

    Article  Google Scholar 

  • PARK, J. and HERBERT, T.D. (1987). Hunting for periodicities in a geologic time series with an uncertain time scale. Journal of Geophysical Research, 92, 14027–14040.

    Article  Google Scholar 

  • PARKER, R.L. (1977). Understanding inverse theory. Annual Review of Earth and Planetary Sciences, 5, 35–64.

    Article  Google Scholar 

  • PATIL, S.B. and CHORE, H.S. (2014). Contaminant transport through porous media: An overview of experimental and numerical studies. Advances in Environmental Research, 3, 45–69.

    Article  Google Scholar 

  • PAYO, G., CORCHETE, V., BADAL, J., SERON, F., CANAS, J.A. and PUJADES, L. (1992). First two-station Rayleigh-wave velocity measurements for the northern Iberian region. Bulletin of the Seismological Society of America, 82, 1434–1452.

    Google Scholar 

  • PEARSON, K. (1920). Notes on the history of correlation. Biometrika, 13, 25–45.

    Article  Google Scholar 

  • PERCIVAL, D.B. and WALDEN, A.T. (1993). Spectral analysis for physical applications. Multitaper and conventional univariate techniques. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • PERSONS, W.M. (1910). The correlation of economic statistics. Publications of the American Statistical Association, 12, 287–322.

    Article  Google Scholar 

  • PETTIJOHN, F.J. (1949). Sedimentary rocks. New York, NY, Harper and Borthers.

    Google Scholar 

  • POINCARÉ, H. (1881). Mémoire sur les courbes définies par une équation différentielle [Memoir on curves defined by a differential equation]. I. Journal de Mathématiques Pures et Appliquées, ser. 3, 7, 375–442.

    Google Scholar 

  • POINCARÉ, H. (1882). Mémoire sur les courbes définies par une équation différentielle [Memoir on curves defined by a differential equation]. II. Journal de Mathématiques Pures et Appliquées, ser. 3, 8, 251–296.

    Google Scholar 

  • POPOFF, C.C. (1966). Computing reserves of mineral deposits: Principles and conventional methods. Bureau of Mines Information Circular 8283. Washington, DC, United States Department of the Interior.

    Google Scholar 

  • PRANDTL, L. and BUSEMANN, A. (1929). Näherungsverfahren zur zeichnerischen Ermittlung von ebenen Strömungen mit Überschallgeschwindigkeit [Proximity method for the graphic determination of plane flows with a supersonic velocity]. Zürich, Stodola Festschrift.

    Google Scholar 

  • QUENOUILLE, M.H. (1949b). Problems in plane sampling. The Annals of Mathematical Statistics, 20, 355–375.

    Article  Google Scholar 

  • RADON, J. (1917). Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten [On the determination of functions by their integral values along certain manifolds]. Berichte Sächsische Akademie der Wissenschaften, Leipzig, Mathematisch-physikalische Klasse, 69, 262–267.

    Google Scholar 

  • RAMSAY, J.G. (1967). Folding and fracturing of rocks. New York, McGraw-Hill.

    Google Scholar 

  • RAMSAY, J.G. and HUBER, M.I. (1983). The techniques of modern structural geology. Vol. 1: Strain analysis. London, Academic Press.

    Google Scholar 

  • RAO, K.R. (1969). Discrete transforms and their applications. New York, NY, Van Nostrand Reinhold.

    Google Scholar 

  • REIMANN, C., FILZMOSER, P. and GARRETT, R.G. (2005). Background and threshold: critical comparison of methods of determination. Science of the Total Environment, 346, 1–16.

    Article  Google Scholar 

  • REIMANN, C., FILZMOSER, P., GARRETT, R.G. and DUTTER, R. (2008). Statistical data analysis explained. Applied environmental statistics with R. Chichester, John Wiley & Sons.

    Chapter  Google Scholar 

  • RITZI, R.W. (2000). Behavior of indicator variograms and transition probabilities in relation to the variance in lengths of hydrofacies. Water Resources Research, 36, 3375–3381.

    Article  Google Scholar 

  • ROBINSON, E.A. (1966a). Collection of FORTRAN II programs for filtering and spectral analysis of single-channel time series. Geophysical Prospecting, 14, 2–52.

    Article  Google Scholar 

  • ROBINSON, E.A. (1967a) Predictive decomposition of time series with application to seismic exploration. Geophysics, 32, 418–484.

    Article  Google Scholar 

  • ROBINSON, E.A. (1967b). Statistical communication and detection with special reference to digital signal processing of radar and seismic signals. London, Griffin.

    Google Scholar 

  • ROBINSON, E.A. and TREITEL, S. (1964). Principals of digital filtering. Geophysics, 29, 395–404.

    Article  Google Scholar 

  • ROOZEBOOM, H.W.B. (1894). Graphische Darstellung der heterogenen Systeme aus ein bis vier Stoffen, mit Einschluss der chemischen Umsetzung [Graphical representation of heterogeneous systems from one to four substances, including chemical conversion]. Zeitschrift fur physikalische Chemie, 15, 145–158.

    Article  Google Scholar 

  • ROSS, B. and KOPLIK, C.M. (1978). A statistical approach to modeling transport of pollutants in ground water. Journal of the International Association for Mathematical Geology, 10, 657–672.

    Article  Google Scholar 

  • ROY, K.K. and NAIDU, P.S. (1970). Computation of telluric field and apparent resistivity over an anticline. Pure and Applied Geophysics, 80, 205–217.

    Article  Google Scholar 

  • SABINE, E. (1822). The Bakerian Lecture: An account of experiments to determine the amount of the dip of the magnetic needle in London, in August 1821; with remarks on the instruments which are usually employed in such determinations. Philosophical Tranactions of the Royal Society, London, 112, 1–21.

    Article  Google Scholar 

  • SABINE, P.A. and HOWARTH, R.J. (1998). The role of ternary projections in colour displays for geochemical maps and in economic mineralogy and petrology. Journal of Geochemical Exploration, 63, 123–144.

    Article  Google Scholar 

  • SCHEIDEGGER, A.E. (1967). The topology of river nets. Water Resources Research, 3, 103–106.

    Article  Google Scholar 

  • SCHMID, K. (1934). Biometrische Untersuchungen an Foriniferen aus dem Phacen von Ceram [Biometric studies of foraminifera from the Stages of Ceram]. Eclogae Geologicae Helvetiae, 27, 46–128.

    Google Scholar 

  • SCHWARZACHER, W. (1969). The use of Markov chains in the study of sedimentary cycles. Journal of the International Association for Mathematical Geology, 1, 17–39.

    Article  Google Scholar 

  • SEAVER, D.A. (1978). Assessing probability with multiple individuals: Group interaction versus mathematical aggregation. Social Science Research Institute, SSRI Research Report 78-3. Los Angeles, CA, University of Southern California.

    Google Scholar 

  • SHARMA, P.V. (1997). Environmental and engineering geophysics. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • SHERIFF, R.E.(1984). Encyclopedic dictionary of exploration geophysics. 2nd edn., Tulsa, Society of Exploration Geophysicists.

    Google Scholar 

  • SHOSKY, J. (1997). Russell’s use of truth tables. Russell, new ser., 17, 11–26.

    Google Scholar 

  • SHREVE, R.L. (1966). Statistical law of stream numbers. The Journal of Geology, 74, 17–37.

    Article  Google Scholar 

  • SIMPSON, T. (1755). A letter to the Right Honorable George Earl of Macclesfield, President of the Royal Society, on the advantage of taking the mean of a number of observations, in practical astronomy. Philosophical Transactions of the Royal Society, London, 49, 82–93.

    Article  Google Scholar 

  • SMART, J.S. (1969). Topological properties of channel networks. Geological Society of America Bulletin, 80, 1757–1774.

    Article  Google Scholar 

  • SMIRNOV, V.I., PROKOF’YEV, A.P. and BORZUNOV V.M. (1960). Podsčet zapasov mestoroždenij poleznyh iskopaemyh [Calculation of reserves of commercial mineral deposits]. Moscow, GosGeolTechizdat.

    Google Scholar 

  • SMITH, D.E. (1923–5). History of mathematics (2 vols.). Boston, MS, Glinn & Co [reprinted: Dover Publications, New York, NY, 1958].

    Google Scholar 

  • SMITH, D.G. (1994). Cyclicity or chaos? Orbital forcing versus non-linear dynamics. In: DE BOER, P.L. and SMITH, D.G. (eds.). Orbital forcing and cyclic sequences. International Association of Sedimentologists Special Publication 19. Oxford, Blackwell Scientific, 531–544.

    Google Scholar 

  • SMITH, J.V. (1970). Physical properties of order-disorder structures with especial reference to feldspar minerals. Lithos, 3, 145–160.

    Article  Google Scholar 

  • SMITH, P.J. and BUCKEE, J.W. (1985). Paper SPE 13776. Calculating in-place and recoverable hydrocarbons: A comparison of alternative methods. In:. Proceedings 1985 SPE Hydrocarbon Economics and Evaluation Symposium. March 14–15, 1985, Dallas, Texas. Richardson, TX, Society of Petroleum Engineers of AIME [online: http://dx.doi.org/10.2118/13776-MS].

  • SNIEDER, R. (1991). An extension of the Backus-Gilbert theory to nonlinear inverse problems. Inverse Problems, 7, 409–433.

    Article  Google Scholar 

  • SPRUILL, T.B., SHOWERS, W.J. and HOWE, S.S. (2002). Application of classification-tree methods to identify nitrate sources in ground water. Journal of Environmental Quality, 31, 1538–1549.

    Article  Google Scholar 

  • STANLEY, C.R. (2003b). THPLOT.M: A MATLAB function to implement generalized Thompson–Howarth error analysis using replicate data. Computers & Geosciences, 29, 225–237.

    Article  Google Scholar 

  • STANLEY, C.R. (2006a). Numerical transformation of geochemical data: 1. Maximizing geochemical contrast to facilitate information extraction and improve data presentation. Geochemistry: Exploration, Environment, Analysis, 6, 69–78.

    Google Scholar 

  • STANLEY, C.R. (2006c). On the special application of Thompson-Howarth error analysis to geochemical variables exhibiting a nugget effect. Geochemistry, Exploration, Environment, Analysis, 6, 357–368.

    Article  Google Scholar 

  • STANLEY, C.R. and LAWIE, D. (2007). Thomson-Howarth error analysis: unbiased alternatives to the large-sample method for assessing non-normally distributed measurement error in geochemical samples. Geochemistry, Exploration, Environment, Analysis, 7, 1–10.

    Google Scholar 

  • STAUFFER, F., KINZELBACH, W., KOVAR, K. and HOEHN, E. (eds.) (2000). Calibration and reliability in groundwater modelling: Coping with uncertainty. Proceedings of the ModelCARE’99 Conference, Zurich, Switzerland, 20–23 Sept. 1999. IAHS Publication 265. Wallingford, International Association of Hydrological Sciences.

    Google Scholar 

  • STEVENS, W.L. (1937). The truncated normal distribution. Annals of Applied Biology, 24, 815–852.

    Google Scholar 

  • STEWART, R.R. (1991). Exploration seismic tomography. Fundamentals. Course Notes, ser. 3. Tulsa, OK, Society of Exploration Geophysicists.

    Book  Google Scholar 

  • STRATTON, E.F. and HAMILTON, R.G. (1950). Application of dipmeter surveys. In: LEROY, L.W. (ed.). Subsurface geologic methods (a symposium). Golden, CO, Colorado School of Mines, 625–643.

    Google Scholar 

  • STRUIK, D.J. (ed.) (1986). A source book in mathematics, 1200–1800. Princeton, NJ, Princeton University Press.

    Google Scholar 

  • TAIT, P.G. (1867). An elementary treatise on quaternions. Oxford, Clarendon Press.

    Google Scholar 

  • TALL, D. (1985). Chords, tangents and the Leibniz notation. Mathematics Teaching, 112, 48–52.

    Google Scholar 

  • TAN, B.K. (1973). Determination of strain ellipses from deformed ammonites. Tectonophysics, 16, 89–101.

    Article  Google Scholar 

  • TANNER, W.F. (1966). The surf “break”: Key to paleogeography? Sedimentology, 7, 203–210.

    Article  Google Scholar 

  • TARANTOLA, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259–1266.

    Article  Google Scholar 

  • TAYLOR, B. (1715). Methodus incrementorum directa et inversa [A method for direct and inverse increments]. London, William Innes.

    Google Scholar 

  • TEMPFLI, K. and MAKAROVIC, B. (1979). Transfer-functions of interpolation methods. Geo-Processing, 1, 1–26.

    Google Scholar 

  • ter BRAAK, C.J.F. and JUGGINS, S. (1993). Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages. Hydrobiologia, 269, 485–502.

    Article  Google Scholar 

  • THIESSEN, A.H. (1911). Precipitation averages for large areas. Monthly Weather Review, 39, 1082–1084.

    Article  Google Scholar 

  • THOMPSON, M. (1988). Variation of precision with concentration in an analytical system. The Analyst, 113, 1579–1587.

    Article  Google Scholar 

  • THOMPSON, M.. and HOWARTH, R.J. (1973). The rapid estimation and control of precision by duplicate determinations. The Analyst, 98, 153–160.

    Article  Google Scholar 

  • THOMPSON, M.. and HOWARTH, R.J. (1976). Duplicate analysis in practice. Part 1. Theoretical approach and estimation of analytical reproducibility. The Analyst, 101, 690–698.

    Article  Google Scholar 

  • THOMPSON, M.. and HOWARTH, R.J. (1978). A new approach to the estimation of analytical precision. Journal of Geochemical Exploration, 9, 23–30.

    Article  Google Scholar 

  • THOMSON, D.J. (1982). Spectrum estimation and harmonic analysis. IEEE Proceedings, 70, 1055–1096.

    Google Scholar 

  • TRASK, P.D. (1930). Mechanical analysis of sediments by centrifuge. Economic Geology, 25, 581–599.

    Article  Google Scholar 

  • TRASK, P.D. (1932a). Origin and environment of source sediments of petroleum. Houston, TX, Gulf Publishing.

    Google Scholar 

  • TUKEY, J.W. (1950). The sampling theory of power spectrum estimates. In: Symposium on applications of autocorrelation analysis to physical problems. NAVEXOS P-735, Washington, DC, United States Office of Naval Research, 47–67 [reprinted in: BRILLINGER, D.R. (ed.) The collected works of John W. Tukey. Vol. 1. Time series: 1949–1964. Wadsworth, Pacific Grove, CA., 129–160].

    Google Scholar 

  • TUKEY, J.W. (1958a). Bias and confidence in not-quite large samples [abstract]. The Annals of Mathematical Statistics, 29, 614.

    Article  Google Scholar 

  • TUKEY, J.W. (1959b). An introduction to the measurement of spectra. In: GRENANDER, U. (ed.). Probability and statistics. The Harald Cramér volume. New York, NY, John Wiley & Sons, 300–330.

    Google Scholar 

  • TUKEY, J.W., (1965). The future of processes of data analysis. Proceedings of the Tenth Conference on the Design of Experiments in Army Research. Development and Testing. ARO-D Report 65-3. Durham, NC, United States Army Research Office, 691–729 [Reprinted in: BRILLINGER, D.R. (ed.) (1984): The Collected Works of John W. Tukey. Vol. IV. Philosophy: 1965–1986. Monterey, CA, Wadsworth, 517–549].

    Google Scholar 

  • TUKEY, J.W. and HAMMING, R. W. (1949). Measuring noise color. I. Memorandum MM-49-110-119, 1 December 1949, Murray Hill, NJ, Bell Telephone Laboratory, 1–120 [Reprinted in: BRILLINGER, D.R. (ed.) (1984). The collected works of John W. Tukey. Vol. 1. Time series: 1949–1964. Wadsworth, Pacific Grove, CA, 1–127].

    Google Scholar 

  • TURCOTTE, D.L. (1997). Fractals and chaos in geology and geophysics. 2nd edn., Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • TUSTIN, A. (1947). A method of analysing the behaviour of linear system in terms of time series. Journal of the Institute of Electrical Engineers, 94 (Part IIA), 130–142.

    Google Scholar 

  • VAUGHAN, S., BAILEY, R.J. and SMITH, D.G. 2015. Cyclostratigraphy: Data filtering as a source of spurious spectral peaks. In: SMITH, D.G., BAILEY, R.J., BURGESS, P.M. and FRASER, A.J. Strata and time: Probing our gaps in our understanding. London, The Geological Society, 151–156.

    Google Scholar 

  • VERSTER, A., de WAAL, D., SCHALL, R. and PRINS, C. (2012). A truncated Pareto model to estimate the under recovery of large diamonds. Mathematical Geosciences, 44, 91–100.

    Article  Google Scholar 

  • VISTELIUS, A.B. (1966). Ob obrazovanii granodioritov g. Belayna Kamchatke [Formation of the Mt. Belaya granodiorite, Kamchatka]. Doklady Akademiya Nauk SSSR, 167, 1115–1118.

    Google Scholar 

  • VISTELIUS, A.B. (1980). Osnovy matematičeskoj geologii [Essential mathematical geology]. Leningrad, AN SSSR Izdatel’stvo nauk.

    Google Scholar 

  • VISTELIUS, A.B. (1992). Principles of mathematical geology [translated by S.N. BANERGEE]. Dordrecht, Kluwer.

    Google Scholar 

  • VISTELIUS, A.B. and YANOVSKAYA, T.B. (1963). Programmirovaniye geologicheskikh i geokhimicheskikh problem dlya vsekh universal’nykh elektronnykh vychislitel’nykh mashin [The programming of geological and geochemical problems for all-purpose electronic computers]. Geologiya Rudnykh Mestorozhdenii, 3, 34–48 [English translation in: VISTELIUS (1967), 29–40].

    Google Scholar 

  • VOIGT, W. (1900). L’etat actuel de nos connaissances sur l'élasticité des cristaux [The current state of our knowledge of the elasticity of crystals]. Rapport présenté au Congress International de Physique, Paris, 1900, sous les auspices de la Société française de Physique. Paris, Gauthier-Villars.

    Google Scholar 

  • VORONOÏ, G. (1909). Nouvelles applications des paramètres continus à la théorie des formes quadratiques. II. Recherches sur les parallélloèdres primitifs II [New applications of continuous parameters to theory of quadratic forms II. Research on primitive parallelohedra. II]. Journal für die reine und angewandte Mathematik, 136, 67–179.

    Google Scholar 

  • WATSON, G.S. and NGUYEN, H. (1985). A confidence region in a ternary diagram from point counts. Journal of the International Association for Mathematical Geology, 17, 209–213.

    Article  Google Scholar 

  • WEEDON, G.P. (2003). Time series analysis and cyclostratigraphy. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • WEISSMANN, G.S. and FOGG, G.E. (1999). Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework. Journal of Hydrology, 226, 48–65.

    Article  Google Scholar 

  • WELTJE, G.J. (2002). Quantitative analysis of detrital modes: statistically rigorous confidence regions in ternary diagrams and their use in sedimentary petrology. Earth Science Reviews, 57, 211–253.

    Article  Google Scholar 

  • WHITTEN, E.H.T. (1959). Composition trends in a granite: Modal variation and ghost stratigraphy in part of the Donegal Granite, Eire. Journal of Geophysical Research, 64, 835–848.

    Article  Google Scholar 

  • WIENER, N. (1926). The harmonic analysis of irregular motion. Journal of Mathematics and Physics, 5, 99–121, 158–189.

    Article  Google Scholar 

  • WIENER, N. (1930). Generalised harmonic analysis. Acta Mathematica, 55, 117–258.

    Article  Google Scholar 

  • WIENER, N. (1949). Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications. Cambridge, MA, Technology Press, Massachusetts Institute of Technology.

    Google Scholar 

  • WILSON, M. (1989). Igneous petrogenesis. London, Unwin Hyman.

    Book  Google Scholar 

  • WORTHINGTON, M.H. (1984). An introduction to geophysical tomography. First Break, 2 (11), 20–26.

    Google Scholar 

  • WORTHINGTON, M.H., MASON, I.M. and WHELLER, P.M. (1983). Application of seismic tomography in mineral exploration. Applied Earth Science, ser. B, 92, 209–212.

    Google Scholar 

  • WURTELE, M.G. (1961). On the problem of truncation error. Tellus, 13, 379–391.

    Article  Google Scholar 

  • ZHU, A.-Z. (2008). Rule-based mapping. In: WILSON, J.P. and FOTHERINGHAM, A.S. (eds.). The handbook of geographic information science. Oxford, John Wiley & Sons, 273–291.

    Google Scholar 

  • ZIMMIE, T.F. and RIGGS, C.O. (eds.) (1981). Permeability and groundwater contaminant transport. A symposium sponsored by ASTM Committee D-18 on Rock and Soil for Engineering Purposes. Philadelphia, Pa. 17–23 June 1979. Special Technical Publication 7. Philadelphia, PA, American Society for Testing materials.

    Google Scholar 

  • ZMUDA, A.J. (1957). Extrapolation of geomagnetic field components along a radius from the center of the Earth. Eos, Transactions American Geophysical Union, 38, 306–307.

    Article  Google Scholar 

  • ZOBEL, O.J. (1923a). Electrical wave filter. United States Patent Office, Patent number 1,615,212 [filed 1923, granted 1927].

    Google Scholar 

  • ZOBEL, O.J. (1923b). Theory and design of uniform and composite electric wave filters. Bell Systems Technical Journal, 2, 1–46.

    Article  Google Scholar 

  • ZOBEL, O.J. (1923c). Transmission characteristics of electric wave filters. Bell System Technical Journal, 2, 567–620.

    Article  Google Scholar 

  • ZYGMUND, A. (1932). Trigonometrical series. Seria Monografie Matematyczne 5. Warsaw, Instytut Matematyczny Polskiej Akademii Nauk.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth Sciences, University College London, London, UK

    Richard J. Howarth

Authors
  1. Richard J. Howarth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Howarth, R.J. (2017). T. In: Dictionary of Mathematical Geosciences . Springer, Cham. https://doi.org/10.1007/978-3-319-57315-1_20

Download citation

Publish with us

Policies and ethics

Search

Navigation