Skip to main content
SpringerLink
Log in

L

  • Chapter
  • First Online:
Dictionary of Mathematical Geosciences

  • 1060 Accesses

Abstract

Consider a system in which the input is described by a set of M parameters m, and the prescribed output of the system by a linear transform on m, A m, where A is an M × N matrix. The objective is to minimize the difference, specified by the 2-norm ‖A m − d‖2, between the expected output from the system and the observed data d (e.g. grey scale values for each cell in a rasterized image). The estimated (least squares) solution is given by: \( {\boldsymbol{m}}_{est}=\frac{1}{{\mathbf{A}}^{\mathrm{T}}\mathbf{A}}{\mathbf{A}}^{\mathrm{T}}\boldsymbol{d} \), where T represents matrix transposition. However, because in practice, real data contains errors, the matrix A is often ill-conditioned, and an optimum solution has to be sought for using the technique of regularization. The objective function is:

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

Access this chapter

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

Institutional subscriptions

Bibliography

  • ADRAIN, R. (1818). Investigation of the Figure of the Earth and of gravity in different latitudes. Transactions of the American Philosophical Society, 1, 119–135.

    Article  Google Scholar 

  • AGOCS, W.B. (1951). Least squares residual anomaly determination. Geophysics, 16, 686–696.

    Article  Google Scholar 

  • AGTERBERG, F.P. (1974). Automatic contouring of geological maps to detect target areas for mineral exploration. Journal of the International Association for Mathematical Geology, 6, 373–395.

    Article  Google Scholar 

  • AGTERBERG, F.P. (1989). LOGDIA – FORTRAN77 program for logistic regression with diagnostics. Computers & Geosciences, 15, 599–614.

    Article  Google Scholar 

  • AGTERBERG, F.P., BONHAM-CARTER, G.F., CHENG, Q. and WRIGHT, D.F. (1993). Weights of evidence modeling and weighted logistic regression for mineral potential mapping. In: DAVIS, J. and HERZFELD, J.C. (eds.). Computers in geology – 25 years of progress. Oxford, Oxford University Press, 13–32.

    Google Scholar 

  • AHRENS, L.H. (1954a). The lognormal distribution of the elements (A fundamental law of geochemistry and its subsidiary). I. Geochimica et Cosmochimica Acta, 5, 49–73.

    Article  Google Scholar 

  • AHRENS, L.H. (1954b). The lognormal distribution of the elements (A fundamental law of geochemistry and its subsidiary). II. Geochimica et Cosmochimica Acta, 6, 121–131.

    Article  Google Scholar 

  • AITCHISON, J. (1981). A new approach to null correlation of proportions. Journal of the International Association for Mathematical Geology, 13, 175–189.

    Article  Google Scholar 

  • AITCHISON, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society, ser. B, 44, 139–177.

    Google Scholar 

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

    Book  Google Scholar 

  • AITCHISON, J. (2003). The statistical analysis of compositional data. 2nd edn., London, Chapman and Hall.

    Google Scholar 

  • AITCHISON, J. and BROWN, J.A.C. (1957). The lognormal distribution with special reference to its uses in economics. Cambridge, Cambridge University Press.

    Google Scholar 

  • AITCHISON, J. and SHEN, S.M. (1980). Logistic-normal distributions: some properties and uses. Biometrika, 67 (2), 261–272.

    Article  Google Scholar 

  • ALABERT, F.G. (1987). The practice of fast conditional simulations through the LU decomposition of the covariance matrix. Mathematical Geology, 19, 369–386.

    Article  Google Scholar 

  • AL-AHMADI, K., AL-AHMADI, S. and AL-AMRI, A. (2014). Exploring the association between the occurrence of earthquakes and the geologic-tectonic variables in the Red Sea using logistic regression and GIS. Arab Journal of Earth sciences, 7, 3871–3879.

    Google Scholar 

  • AL-SADI, H.N. (1980). Seismic exploration. Technique and Processing. Astronomisch-geophysikalische Reihe, v. 7. Basel, Birkhliuser Verlag.

    Google Scholar 

  • ALPER, A.M. and POLDERVAART, A. (1957). Zircons from the Animas stock and associated rocks, New Mexico. Economic Geology, 52, 952–971.

    Article  Google Scholar 

  • ANALYTICAL METHODS COMMITTEE (1987). Recommendations for the definition, estimation and use of the detection limit. The Analyst, 112, 199–204.

    Article  Google Scholar 

  • ANALYTICAL METHODS COMMITTEE (2001). Measurement of near zero concentrations: recording and reporting results that fall close to or below the detection limit. The Analyst, 126, 256–259.

    Article  Google Scholar 

  • ANDREWS, D.F., BICKEL, P.J., HAMPEL, F.R., HUBER, P.J., ROGERS, W.H. and TUKEY, J.W. (1972). Robust estimates of location: Survey and advances. Princeton, NJ, Princeton University Press.

    Google Scholar 

  • ASTER, R.C., BORCHERS, B. and THURBER, C.H. (2013). Parameter estimation and inverse problems. 2nd edn., Kidlington, Academic Press.

    Google Scholar 

  • AZZALINI, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.

    Google Scholar 

  • AZZALINI, A., DAL CAPPELLO, T. and KOTZ, S. (2003). Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution, 11, 12–20.

    Google Scholar 

  • BAGNOLD, R.A. and BARNDORFF-NIELSEN, O. (1980). The pattern of natural size distribution. Sedimentology, 27, 199–207.

    Article  Google Scholar 

  • BANKS, R. (1979). The use of linear programming in the analysis of petrological mixing problems. Contributions to Mineralogy and Petrology, 70, 237–244.

    Article  Google Scholar 

  • BARNARD, G.A. (1949). Statistical inference. Journal of the Royal Statistical Society, ser. B, 11, 115–149.

    Google Scholar 

  • BARNES, J.A. and MOCKLER, R.C. (1960). The power spectrum and its importance in precise frequency measurements. IRE Transactions on Instrumentation, I-9 (2), 149–155.

    Article  Google Scholar 

  • BARNES, S.J. (1988). Automated plotting of geochemical data using the LOTUS Symphony package. Computers & Geosciences, 14, 409–411.

    Article  Google Scholar 

  • BARNETT, C.T. and WILLIAMS, P.M. (2006). Mineral exploration using modern data mining techniques. In: DOGGETT, M.E. and PARRY, J.R. (eds.). Wealth creation in the minerals industry: Integrating science, business and education. Society of Economic Geologists Special Publication 12. Littleton, CO, Society of Economic Geologists, 295–310.

    Google Scholar 

  • BARTELS, R.H. and GOLUB, G.H. (1969). The simplex method of linear programming using LU decomposition. Communications of the ACM, 12, 266–268.

    Article  Google Scholar 

  • BARTLETT, M.S. (1946). On the theoretical specification and sampling properties of autocorrelated time-series. Journal of the Royal Statistical Society, Supplement, 8, 27–41, 85–97.

    Google Scholar 

  • BARTLETT, M.S. (1947). The use of transformations. Biometrics, 3, 39–52.

    Article  Google Scholar 

  • BELSLEY, D.A., KUH, E. and WELSCH, R.E. (1980). Regression diagnostics. New York, NY, John Wiley & Sons

    Book  Google Scholar 

  • BENEDEK, G. and GREYTAK, T. (1965). Brillouin scattering in liquids. Proceedings of the IEEE, 53, 1623–1629.

    Google Scholar 

  • BERKSON, J. (1944). Application of the logistic function to bio-assay. Journal of the American Statistical Association, 39, 357–365.

    Google Scholar 

  • BICKEL, P.J. and BÜHLMANN, P. (1996). What is a linear process? Proceedings of the National Academy of Sciences of the United States of America, 93, 12128–12131.

    Google Scholar 

  • BIRCH, F. and BANCROFT, D. (1938). Elasticity and internal friction in a long column of granite. Bulletin of the Seismological Society of America, 28, 243-254.

    Google Scholar 

  • BIRD, D.N. (1982). A linear programming approach to time-term analysis. Bulletin of the Seismological Society of America, 72, 2171-2180.

    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 

  • 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 

  • BOGERT, B.P., HEALY, M.J.R. and TUKEY, J.W. (1963). The quefrency alanysis of time series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum and saphe-cracking. In: ROSENBLATT, M. (ed.). Proceedings of the symposium on time series analysis. New York, John Wiley & Sons, 209–243.

    Google Scholar 

  • BOOLE, G. (1843). Exposition of a general theory of linear transformations, Parts I and II. Cambridge mathematical Journal, 3, 1–20, 106–119.

    Google Scholar 

  • BOOLE, G. (1844). On a general method in analysis. Philosophical Transaction of the Royal Society, London, 134, 225–282.

    Article  Google Scholar 

  • BORN, M. (1936). On the linearization of the energy density of the electromagnetic field. Mathematical Proceedings of the Cambridge Philosophical Society, 32, 102–107.

    Google Scholar 

  • BOS, H.J.M. (1974). Differentials, higher-order differentials and the derivative in Leibnizian calculus. Archive for the History of Exact Sciences, 14, 1–90.

    Article  Google Scholar 

  • BOWKER, A.H. (1947). On the norm of a matrix. Annals of Mathematical Statistics, 18, 285–288.

    Article  Google Scholar 

  • BRIANCHON, C.-J. (1817). Mémoire sur les lignes du second ordre [Memoir on lines of the second order]. Paris, Bachelier.

    Google Scholar 

  • BRIGGS, H. (1617). Logarithmorum chilias prima [The first thousand logarithms]. London, Unknown.

    Google Scholar 

  • BRIGGS, H. (1624). Arithmética logarithmica [Logarithmical arithmetic]. London, William Jones.

    Google Scholar 

  • BRIGGS, H. (1631). Logarithmicall arithmetike. Or tables of logarithmes for absolute numbers from an unite to 100,000: as also for sines, tangentes and secantes for every minute of a quadrant with a plaine description of their use in arithmetike, geometrie, geographie, &c. London, George Miller.

    Google Scholar 

  • BRUCE, I. (2012). John Napier: Mirifici Logarithmorum Canonis Descriptio – & Constructio [translated and annotated by I. Bruce; online: http://www.17centurymaths.com/contents/napiercontents.html].

  • BRUTSAERT, W. (1968). The permeability of a porous medium determined from certain probability laws for pore size distribution. Water Resources Research, 4, 425–434.

    Article  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 

  • BURG, J.P. (1967). Maximum entropy spectral analysis. Proceedings of the 37th Meeting of the Society of Exploration Geophysicists, Oklahoma City, Oklahoma, 31 October 1967, pp. 34–41. In: CHILDERS, D.G. (ed.). (1978). Modern spectrum analysis. New York, NY, IEEE Press, 34–39.

    Google Scholar 

  • BURG, J.P. (1968). A new analysis technique for time series data. Paper given at: NATO Advanced Study Institute on signal processing with emphasis on underwater acoustics, 12–23 August 1968, Twente Institute of Technology, Enschede, The Netherlands. In: CHILDERS, D.G. (ed.). (1978). Modern spectrum analysis. New York, NY, IEEE Press, 42–48.

    Google Scholar 

  • BURG, J.P. (1975). Maximum entropy spectral analysis. Doctoral dissertation. Stanford Exploration Project Report no. 6, Stanford, CA, Stanford Exploration Project, Stanford University (online: http://sepwww.stanford.edu/data/media/public/oldreports/sep06/).

  • BURK, F. (1988). Lebesgue measure and integration. An introduction. New York, NY, John Wiley & Sons.

    Google Scholar 

  • BURK, F.E. (2007). A garden of integrals. The Dolciani Mathematical Expositions v. 31. Washington, DC, The Mathematical Association of America.

    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 

  • CALTENCO, J.H., LÓPEZ-BONILLA, J., MORALES, J. and PÉREZ-TERUEL, G.R. (2014). Polynomial solutions of differential equations. The SciTech, International Journal of Engineering Sciences, 2, 73–79.

    Google Scholar 

  • CAMERON, G.W., ELLIOTT, B.E. and RICHARDSON, K.A. (1976). Effects of line spacing on contoured airborne Gamma-ray spectrometry data. In: Exploration for uranium ore deposits. Proceedings of a symposium: Vienna, 29 March–2 April, 1976. Vienna, International Atomic Energy Agency, 81–92.

    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 

  • CAUCHY, A.-L. (1843). Rapport sur un memoir de M. Laurent qui a pour titre: Extension du théorème de M. Cauchy relatif à la convergence du développement d'une fonction suivant les puissances ascendantes de la variable x [Report on a memoir by M. Laurent]. Comptes rendus hebdomadaires des Séances de l’Académie des Sciences, Paris, 17, 938–940.

    Google Scholar 

  • CHATTERJEE, S. and HADI, A.S. (1986). Influential observations, high leverage points, and outliers in regression. Statistical Science, 1, 379–416.

    Article  Google Scholar 

  • CHENG, Q. (1997). Multifractal modelling and lacunarity analysis. Mathematical Geology, 29, 919–932.

    Article  Google Scholar 

  • CHILD, J.M. (1920). The early mathematical manuscripts of Leibniz, translated from the Latin texts published by Carl Immanuel Gerhardt with critical and historical notes. London, Open Court Publishing.

    Google Scholar 

  • CHORK, C.Y. (1991). An assessment of Least Median Squares regression in exploration geochemistry. Journal of Geochemical Exploration, 41, 325–340.

    Article  Google Scholar 

  • CHORK, C.Y. and ROUSSEEUW, P.J. (1992). Integrating a high-breakdown option into discriminant analysis in exploration geochemistry. Journal of Geochemical Exploration, 43, 191–203.

    Article  Google Scholar 

  • CHRISTIANSEN, C., BLAESILD, P. and DALSGAARD, K. (1984). Re-interpreting ‘segmented’ grain-size curves. Geological Magazine, 121, 47–51.

    Article  Google Scholar 

  • CLAERBOUT, J.F. (1986). A canonical program library. Stanford Exploration Project Report SEP-50, Stanford, CA, Geophysics Department, Stanford University, 281–289.

    Google Scholar 

  • CLAERBOUT, J.F. (1992). Earth soundings analysis: Processing versus inversion. London, Blackwell Scientific Publications.

    Google Scholar 

  • CLARK, D.A. (1981). A system for regional lithofacies mapping. Bulletin of Canadian Petroleum Geology, 20, 197–208.

    Google Scholar 

  • COHEN, T.J. (1970). Source-depth determinations using spectral, pseudo-autocorrelation and cepstral analysis. Geophysical Journal International, 20, 223–231.

    Article  Google Scholar 

  • COLLINS, F. and LEE, C.C. (1956). Seismic wave attenuation characteristics from pulse experiments. Geophysics, 21, 16–40.

    Article  Google Scholar 

  • CONNOLLY, J.A.D. (2005). Computation of phase equilibria by linear programming: A tool for geodynamic modelling and its application to subduction zone decarbonation. Earth and Planetary Science Letters, 236, 524–541.

    Article  Google Scholar 

  • CONNOR, C.B., SPARKS, R.S.J., MASON, R.M., BONADONNA, C. and YOUNG, S.R.A. (2003). Exploring links between physical and probabilistic models of volcanic eruptions: The Soufrière Hills, Montserrat. Geophysical Research Letters, 30, 1701–1708 [http://dx.doi.org/10.1029/2003GL017384].

    Article  Google Scholar 

  • COOK, R.D. and WEISBERG, S. (1982). Residuals and influence in regression. London, Chapman and Hall.

    Google Scholar 

  • CORTINI, M. and BARTON, C.C. (1994). Chaos in geomagnetic reversal records: A comparison between Earth’s magnetic field data and model disk dynamo data. Journal of Geophysical research: Solid Earth, 99 (B9), 18021–18033.

    Article  Google Scholar 

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

    Google Scholar 

  • CURRIE, L.A. (1995). Nomenclature in evaluation of analytical methods including detection and quantification capabilities. Pure and Applied Chemistry, 67, 1699–1723.

    Article  Google Scholar 

  • CURRIE, L.A. (2004). Uncertainty in measurements close to detection limits: Detection and quantification capabilities. In: Quantifying uncertainty in nuclear analytical measurements. IAEA-TECDOC-1401. Vienna, International Atomic Energy Agency, 9–33.

    Google Scholar 

  • CURRIE, R.G. (1973). Geomagnetic line spectra – 2 to 70 years. 21,. Astrophysics and Space Science, 21, 425–438.

    Article  Google Scholar 

  • DAHL, P.S. (1990). A PC- and LOTUS-based data acquisition/reduction system for an ICP spectrometer. Computers & Geosciences, 16, 881–896.

    Article  Google Scholar 

  • DANTZIG, G.B. (1949). Programming in a linear structure [abstract]. Econometrica, 17, 73–74.

    Article  Google Scholar 

  • DAVID, M. (1977). Geostatistical ore reserve estimation. Developments in geomathematics 2. Amsterdam, Elsevier Scientific.

    Google Scholar 

  • DAVIS, J.C. (1986). Statistics and data analysis in geology. 2nd edn., 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.D. and DAVID, M. (1978). The numerical calculation of integrals of an isotropic variogram function on hypercubes. Journal of the International Association for Mathematical Geology, 10, 311–314.

    Article  Google Scholar 

  • DEAKIN, M.A.B. (1981). The development of the Laplace transform, 1737–1937. I. Euler to Spitzer, 1737–1880. Archive for History of the Exact Sciences, 25, 343–390.

    Article  Google Scholar 

  • DEAKIN, M.A.B. (1982). The development of the Laplace transform, 1737–1937. II. Poincaré to Doetsch, 1880–1937. Archive for History of the Exact Sciences, 26, 351–381.

    Article  Google Scholar 

  • DeMERS, M.N. (1990). SEDRULE: a rule-based system for interpreting some major sedimentary environments. Computers & Geosciences, 16, 833–846.

    Article  Google Scholar 

  • DIELMAN, T.E. (1984). Least absolute value estimation in regression models: an annotated bibliography. Communications in Statistics – Theory and Methods, 13, 513–541.

    Article  Google Scholar 

  • DODGE, Y. (1987). Statistical data analysis based on the L 1 norm and related methods. Amsterdam, North-Holland.

    Google Scholar 

  • DODSON, J. (1742). The anti-Logarithmic canon. Being a table of numbers, consisting of eleven places of figures, corresponding to all Logarithms under 100000 London, James Dodson.

    Google Scholar 

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

    Article  Google Scholar 

  • DURBIN, J. (1960). The fitting of time-series models. Review of the International Statistical Institute, 28, 233–243.

    Article  Google Scholar 

  • DUTKA, J. (1996). On Gauss’ priority in the discovery of the method of least squares. Archive for the History of Exact Sciences, 49, 355–370.

    Article  Google Scholar 

  • EGOZCUE, J.J., PAWLOWSKY-GLAHN, V., MATEU-FIGUERAS, G. and BARCELÓ-VIDAL, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35, 279–300.

    Article  Google Scholar 

  • EISENHART, C. (1935). A test for the significance of lithological variations. Journal of Sedimentary Petrology, 5, 137–145.

    Google Scholar 

  • EMICH, F. and FEIGEL, F. (1932). Microchemical laboratory manual. London, Chapman and Hall.

    Google Scholar 

  • ENCKE, J.F. (1841). On the method of least squares. In: TAYLOR, R. (ed.). Scientific memoirs, selected from the transactions of Foreign Academies of Science and Learned Societies, and from foreign journals. Vol. 2. London, Richard and John E. Taylor, 317–369.

    Google Scholar 

  • EYNATTEN, H. von, BARCELO-VIDAL, C. and PAWLOWSKY-GLAN, V. (2003). Modelling compositional change: The example of chemical weathering of granitoid rocks. Mathematical Geology, 35, 231–252.

    Article  Google Scholar 

  • EZEKIEL, M. and FOX, K.A. (1930). Methods of correlation and regression analysis, linear and curvilinear. New York, NY, John Wiley & Sons.

    Google Scholar 

  • FERBER, R.-G. (1984). Stabilization of normal-incidence seismogram inversion removing the noise-induced bias. Geophysical Prospecting, 33, 212–233.

    Article  Google Scholar 

  • FISHER, R.A. (1921). On the ‘probable error’ of a coefficient of correlation deduced from a small sample. Metron, 1, 3–32.

    Google Scholar 

  • FISHER, A. (1923). Mathematical theory of probabilities. 2nd edn., New York, NY, Macmillan.

    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. (1934). Two new properties of mathematical likelihood. Proceedings of the Royal Society, London. ser. A, 144, 285–307.

    Google Scholar 

  • FITCH, T.J., McCOWAN, D.W. and SHIELDS, M.W. (1980). Estimation of the seismic moment tensor from teleseismic body wave data with applications to intraplate and mantle earthquakes. Journal of Geophysical Research – Solid Earth, ser. B, 85, 3817–3828.

    Google Scholar 

  • FLINN, D. (1962). On folding during three-dimensional progressive deformation. Quarterly Journal of the Geological Society, London, 118, 385–433.

    Article  Google Scholar 

  • FOUGERE, P.F. (1985). A review of the problem of spontaneous line splitting in maximum entropy power spectral analysis. In: SMITH, C.R. and GRANDY, W.T. Jr. (eds.). Minimum-entropy and Bayesian methods in inverse problems. Fundamental Theories of Physics volume 14. Dordrecht, D. Reidel, 303–315.

    Chapter  Google Scholar 

  • FRÉCHET, M. (1906). Sur quelques points du calcul fonctionnel [On several points of functional calculus; Doctoral dissertation, Paris, 1905]. Rendiconti del Circolo Matematico di Palermo, 22, 1–74.

    Article  Google Scholar 

  • FRIBERG, L.M. (1989). Garnet stoichiometry program using a LOTUS 1-2-3 spreadsheet. Computers & Geosciences, 15, 1169–1172.

    Article  Google Scholar 

  • GADDUM, J.H. (1945). Lognormal distributions. Nature,, 156, 463–466.

    Article  Google Scholar 

  • GAUSS, C.F. (1809a). Theoria motus corporum coelestium in sectionibus conicis solem ambientium [Theory of the motion of the heavenly bodies moving about the Sun in conic sections]. Hamburg, F. Perthes and I.H. Besser.

    Google Scholar 

  • GAUSS, C.F. (1809b [1857]). Determination of an orbit satisfying as nearly as possible any number of observations whatever. In: Theory of the motion of the heavenly bodies moving about the Sun in conic sections [translated from Latin by C.H. DAVIS]. Boston, MS, Little, Brown & Co, 249–273.

    Google Scholar 

  • GELLIBRAND, H. (1635). A discourse mathematical on the variation of the magneticall needle. Together with its admirable diminution discovered. London, William Jones.

    Google Scholar 

  • GIBRAT, R. (1931). Lés inégalités economiques [Economic inequalities]. Paris, Recueil Sirey.

    Google Scholar 

  • GOGORZA, C.S.G., SINITO, A.M., DI TOMMASO, I., VILAS, J.F., CREER, K.M. and NUÑEZ, H. (1999). Holocene geomagnetic secular variations recorded by sediments from Escondido Lake (south Argentina). Earth, Planets and Space, 51, 93–106.

    Article  Google Scholar 

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

  • GREENHALGH, S.A., ZHOU, B. and GREEN, A. (2006). Solutions, algorithms and inter-relations for local minimization search geophysical inversion. Journal of Geophysics and Engineering, 3, 101–113.

    Article  Google Scholar 

  • GREENWOOD, H.J. (1967). The N-dimensional tie-line problem. Geochimica et Cosmochimica Acta, 31, 465–490.

    Article  Google Scholar 

  • GRIFFITHS, L.J. (1975). Rapid measurement of digital instantaneous frequency. IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-23, 207–222.

    Article  Google Scholar 

  • GRIFFITHS, L.J. and PRIETO-DIAZ, R. (1977). Spectral analysis of natural seismic events using autoregressive techniques. IEEE Transactions on Geoscience Electronics, GE-15, 13–25.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • HAMILTON, W.R. (1848). Researches concerning quaternions. First series. Transactions of the Royal Irish Academy, 21 (1), 199–296.

    Google Scholar 

  • HAMON, B.V. and HANNAN, E.J. (1963). Estimating relations between time series. Journal of Geophysical Research, 68, 6033–6041.

    Article  Google Scholar 

  • HANNAN, E.J. (1966). Spectral analysis for geophysical data. Geophysical Journal International, 11, 225–236.

    Article  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 

  • HARRISON, P.W. (1957). New technique for three-dimensional fabric analysis of till and englacial debris containing particles from 3 to 40 mm in size. Journal of Geology, 65, 98–105.

    Article  Google Scholar 

  • HARVEY, G. (1822). On the method of minimum squares, employed in the reduction of experiments, being a translation of the appendix to an essay of Legendre’s entitled, “Nouvelles methodes pour la determination des orbites des cometes,” with remarks. The Edinburgh Philosophical Journal, 7, 292–301.

    Google Scholar 

  • HEAVISIDE, O. ( 1892b). Electrical papers. v. 1. London, Macmillan.

    Google Scholar 

  • HEAVISIDE, O. (1892c). On operators in physical mathematics. Part I. Proceedings of the Royal Society, London, 52, 504–529.

    Google Scholar 

  • HEAVISIDE, O. (1893). On operators in physical mathematics. Part II. Proceedings of the Royal Society, London, 54, 105–142.

    Google Scholar 

  • HEAVISIDE, O. (1899). Generalised differentiation and divergent series. In: Electromagnetic theory. London, The Electrician Printing and Publishing Co., 434–492.

    Google Scholar 

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

    Google Scholar 

  • HELSEL, D.R. and HIRSCH, R.M. (1992). Statistical methods in water resources. Amsterdam, Elsevier.

    Google Scholar 

  • HERRING, R. (1980). The cause of line splitting in Burg maximum-entropy spectral analysis. IEEE Transactions on Acoustics, Speech and Signal Processing, 28, 692–701.

    Article  Google Scholar 

  • HOAGLIN, D.C. and WELSCH, R.E. (1978). The Hat matrix in regression and ANOVA. The American Statistician, 32, 17–22.

    Google Scholar 

  • HOOKER, R.H. (1901). Correlations of the marriage rate with trade. Journal of the Royal Statistical Society, London, 64, 485–492.

    Google Scholar 

  • HOSSACK, J.R. (1968). Pebble deformation and thrusting in the Bygdin area (S. Norway). Tectonophysics, 5, 315–339.

    Article  Google Scholar 

  • HOWARTH, R.J. (1973a). The pattern recognition problem in applied geochemistry. In: JONES, M.J. (ed.). Geochemical Exploration 1972. Institution of Mining and Metallurgy, London, p. 259–273.

    Google Scholar 

  • HOWARTH, R.J. (1984). Statistical applications in geochemical prospecting: A survey of recent methods. Journal of Geochemical Exploration, 21, 41–61.

    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. (1996b). History of the stereographic projection and its early use in geology. Terra Nova, 8, 499–513.

    Article  Google Scholar 

  • HOWARTH, R.J. (1999). Measurement, portrayal and analysis of orientation data in structural geology (1670–1967). Proceedings of the Geologists’ Association, 110, 273–309.

    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. (2001b). Measurement, portrayal and analysis of orientation data in structural geology (1670–1967): Corrections and additions. Proceedings of the Geologists' Association, 112, 187–190.

    Google Scholar 

  • HOWARTH, R.J. and MCARTHUR, J.M. (1997). Statistics for Strontium isotope stratigraphy: A robust LOWESS fit to the marine Sr-isotope curve for 0 to 206 Ma, with look-up table for derivation of numerical age. The Journal of Geology, 105, 441–456.

    Article  Google Scholar 

  • HUBAUX, A. and SMIRIGA-SNOECK, N. (1964). On the limit of sensitivity and the analytical error. Geochimica et Cosmochimica Acta, 28, 1199–1216.

    Article  Google Scholar 

  • HUBBERT, A.M.K. (1948). Line-integral method of computing the gravimetric effects of two-dimensional masses. Geophysics, 13, 215–225.

    Article  Google Scholar 

  • HUBBERT, M.K. (1959). Techniques of prediction with application to the petroleum industry. Preprint for presentation at the 44th Annual Meeting of the American Association of Petroleum Geologists, Dallas, Texas, Tuesday, March 17, 1959. Publication 204, Houston, TX, Shell Development Company, Exploration and Production Research Division.

    Google Scholar 

  • IMBRIE, J. (1963). Factor and vector analysis programs for analyzing geologic data. United States Office of Naval Research, Geography Branch, Technical Report 6, ONR Task No. 389-135 [AD0420466], Evanston, IL, Northwestern University.

    Google Scholar 

  • IMBRIE, J. and PURDY, E.G. (1962). Classification of modern Bahamian carbonate sediments. In: HAM, W.E. (ed.). Classification of carbonate rocks: A symposium arranged by the Research Committee of the American Association of Petroleum Geologists. Including papers presented orally at Denver, Colorado, April 27, 1961. AAPG Memoir 1. Tulsa, OK, The American Association of Petroleum Geologists, 253–272.

    Google Scholar 

  • IMBRIE, J. and VAN ANDEL, T.H. (1964). Vector analysis of heavy-mineral data. Bulletin of the Geological Society of America, 75, 1131–1156.

    Article  Google Scholar 

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

    Google Scholar 

  • JENSEN, J.L. (1988). Maximum-likelihood estimation of the hyperbolic parameters from grouped observations. Computers & Geosciences, 14, 389–408.

    Article  Google Scholar 

  • JOHNSON, D.S. and NURMINEN, J. (2007). The history of seafaring: navigating the World oceans. London, Conway.

    Google Scholar 

  • JONES, H.E. (1937). Some geometrical considerations in the general theory of fitting lines and planes. Metron, 13, 21–30.

    Google Scholar 

  • JÖRESKOG, K.G., KLOVAN, J.E. and REYMENT, R. (1976). Geological factor analysis. Amsterdam, Elsevier.

    Google Scholar 

  • KAILATH, T. (1974). A view of three decades of linear filtering theory. IEEE Transactions on Information Theory, IT-20, 146–181.

    Article  Google Scholar 

  • KAISER, H. (1947). Die Berechnung der Nachweisempfindlichkeit [The calculation of detection sensitivity]. Spectrochimica Acta, 3, 40–67.

    Article  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 

  • KANTOROVICH, L. (1939). Mathematicheskie metody organizatsii i planirovania proizvodstva [Mathematical methods of organization and planning production]. Leningrad, Leningrad State University Publishers.

    Google Scholar 

  • KANTOROVICH, L.V. (1960). Mathematical methods of organizing and planning production. Management Science, 6, 363–422.

    Article  Google Scholar 

  • KAY, S.M. and MARPLE, S.L., Jr. (1979). Sources of and remedies for spectral line splitting in autoregressive spectrum analysis. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal processing, Washington, DC, Institute of Electrical and Electronic Engineers, New York, NY, [IEEE/IEE Electronic Library. 4, 151–154].

    Google Scholar 

  • KERMACK, K.A. (1954). A biometrical study of Micraster coranginum and M. (isomicraster) senonensis. Philosophical Transactions of the Royal Society, London, ser. B, 237, 375–428.

    Google Scholar 

  • KERMACK, K.A. and HALDANE, J.B.S. (1950). Organic correlation and allometry. Biometrika, 37, 30–41.

    Article  Google Scholar 

  • KIJKO, A. (1994). Seismological outliers: L1 or adaptive Lp norm application., 84. Bulletin of the Seismological Society of America, 84, 473–477.

    Google Scholar 

  • KIRCHHOFF, G and BUNSEN, R. (1860). Chemische Analyse durch Spectralbeobachtungen [Chemical analysis by observation of spectra]. Annalen der Physik und Chemie, 110 (6), 161–189.

    Article  Google Scholar 

  • KLEINECKE, D. (1971). Use of linear programming for estimating geohydrologic parameters of groundwater basins. Water Resources Research, 7, 367–374.

    Article  Google Scholar 

  • KOCH, G.S. and LINK, R.F. (1970–71). Statistical analysis of geological data. v. 2. New York, NY, John Wiley & Sons.

    Google Scholar 

  • KOCH, G.S., Jr. (ed.) (1990). Geological problem solving with Lotus 1-2-3 for exploration and mining geology. Computer methods in the earth sciences volume 8. Oxford, Pergamon Press.

    Google Scholar 

  • KRIGE, D.G. (1960). On the departure of ore value distributions from the lognormal model in South African gold mines. Journal of the South African Institute of Mining and Metallurgy, 61, 231–244.

    Google Scholar 

  • KRUHL, J.H. (ed.) (1994). Fractals and dynamical systems in earth science. Berlin, Springer-Verlag.

    Google Scholar 

  • KRUMBEIN, W.C. (1934a). Size frequency distributions of sediments. Journal of Sedimentary Petrology, 4, 65–77.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1936a). Application of logarithmic moments to size frequency distributions of sediments. Journal of Sedimentary Petrology, 6, 35–47.

    Google Scholar 

  • KRUMBEIN, W.C. (1936b). The use of quartile measures in describing and comparing sediments. American Journal of Science, ser. 5, 32, 98–111.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1939). Preferred orientation of pebbles in sedimentary deposits. Journal of Geology, 47, 673–706.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1948). Lithofacies maps and regional sedimentary-stratigraphic analysis. Bulletin of the American Association of Petroleum Geologists, 32, 1909–1923.

    Google Scholar 

  • KRUMBEIN, W.C. (1952). Principles of facies map interpretation. Journal of Sedimentary Petrology, 22, 200–211.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1955a). Composite end members in facies mapping. Journal of Sedimentary Petrology, 25, 115–122.

    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 

  • KRUMBEIN, W.C. and SLOSS, L.L. (1951). Stratigraphy and sedimentation. San Francisco, CA, W.H. Freeman.

    Google Scholar 

  • KRUSKAL, W.H. (1953). On the uniqueness of the line of organic correlation. Biometrics, 9, 47–58.

    Article  Google Scholar 

  • KYRIAKIDIS, P.C. (2005). Sequential spatial simulation using Latin hypercube sampling. v. 1. In: LEUANGTHONG, O. and DEUTCH, C.V. (eds.). Geostatistics Banff 2004: Seventh International Geostatistics Congress, Quantitative Geology and Geostatistics. Dordrecht, Kluwer, 65–74.

    Google Scholar 

  • LAGRANGE, J.-L. (1788). Méchanique analytique [Analytical mechanics]. Paris, Desaint.

    Google Scholar 

  • LAGRANGE, J.-L. (1795 [1877]). Leçons élémentaires sur les mathématiques données a l’École Normale [Elementary mathematics lessons taught at the Normal School], v. 7. In: SERRET, J.-A. (ed.). Œuvres de Lagrange. Paris, Gauthier-Villars, 183–287.

    Google Scholar 

  • LAGRANGE, J.-L. (1797). Théorie de fonctions analytiques contenant les principes du calcul différentiel [Theory of analytic functions, containing the principles of differential calculus]. Paris, L’Imprimerie de la République.

    Google Scholar 

  • LAMBERT, J.H. (1772). Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten [Notes and comments on the composition of Terrestrial and Celestial maps]. In: Beiträge zur Gebrauch der Mathematik und deren Anwendung [Contribution to the use of mathematics and its application]. v. III. Berlin, Verlage des Buchladens der Königliche Realschule, 105–199.

    Google Scholar 

  • LANCASTER-JONES, E. (1929). The computation of gravitational effects due to irregular mass distributions. Geophysical Journal International, 2 (Supplement s3), 121–140.

    Google Scholar 

  • LANCZOS, C. (1938). Trigonometric interpolation of empirical and analytic functions. Journal of Mathematics and Physics, 17, 123–199.

    Article  Google Scholar 

  • LANCZOS, C. (1956). Applied analysis. New York, Prentice-Hall.

    Google Scholar 

  • LANCZOS, C. (1961). Linear differential operators. New York, NY, Van Nostrand.

    Google Scholar 

  • LANGELIER, W.F. and LUDWIG, H.F. (1942). Graphical methods for indicating the mineral character of natural waters. Journal of the American Water Works Association, 34, 335–352.

    Google Scholar 

  • LAPLACE, P.-S. (1782 [1785]). Théorie des attractions des sphéroides et de la figure des planètes [Theory of the attraction of spheroids and the figure of the planets]. Histoire de l’Académie Royale des Sciences année 1782 avec les Mémoires de Mathématique & de Physique, pour la même année 1782: tirés des registres de cette Académie, for 1782, 113–196.

    Google Scholar 

  • LAPLACE, P.-S. (1798a). Traité Méchanique Céleste [Treatise on celestial mechanics]. v. II. Paris, Crapelet.

    Google Scholar 

  • LAPLACE, P.-S. (1798b). Exposition du système du monde [Explanation of the system of the World]. 2nd edn., Paris, Crapelet.

    Google Scholar 

  • LAPLACE, P.-S. (1809). The system of the World [translated from French by J. POND]. London, Richard Phillips.

    Google Scholar 

  • LAPLACE, P.-S. (1812). Théorie analytique des probabilités [Analytical probability theory.]. Paris, Mme. Ve. Courcier.

    Google Scholar 

  • LAU, Y.-S., HUSSAIN, Z.M. and HARRIS, R. (2004). A time-dependent LMS algorithm for adaptive filtering. WSEAS Transactions on Circuits and Systems, 3, 35–42.

    Google Scholar 

  • LAURENT, P.-A. (1843). Extension du théorème de M. Cauchy relatif à la convergence du développement d'une fonction suivant les puissances ascendantes de la variable x [Extension of Cauchy's theorem on the convergent expansion of a function according to ascending powers of x]. Comptes rendus hebdomadaires des Séances de l’Académie des Sciences, Paris, 17, 348–349.

    Google Scholar 

  • LAW, J. (1944). A statistical approach to the interstitial heterogeneity of sand reservoirs. Transactions of the American Institute of Mining and Metallurgical Engineers, 155, 202–222.

    Google Scholar 

  • Le MAITRE, R.W. (1982). Numerical petrology. Statistical interpretation of geochemical data. Developments in petrology 8. Amsterdam, Elsevier Scientific Publishing.

    Google Scholar 

  • Le ROUX, J.P. and RUST, I.C. (1989). Composite facies maps: a new aid to palaeo-environmental reconstruction. South African Journal of Geology, 92, 436–443.

    Google Scholar 

  • LEATHEM, J.G. (1905). Volume and surface integrals used in physics. Cambridge, Cambridge University Press.

    Google Scholar 

  • LEBAILLY, J., MARTIN-CLOUAIRE, R. and PRADE, A. (1987). Use of fuzzy logic in a rule-based system in petroleum geology. In: SANCHEZ, E. and ZADEH, L. (eds.). Approximate reasoning in intelligent systems, decision and control. Oxford, Pergamon Press, 125–144.

    Chapter  Google Scholar 

  • LEBESGUE, H. (1902). Intégrale, longueur, aire [Integral, length, area]. Doctoral dissertation, University of Paris. Milan, Bernandon de C. Rebeschini]. Annali di Mathematica Pura ed Applicata, 7, 231–359.

    Google Scholar 

  • LEBESGUE, H. (1904). Leçons sur l’intégration et la recherche des fonctions primitives [Lessons on integration and investigating primitive functions]. Paris, Gauthier-Villars.

    Google Scholar 

  • LEGENDRE, A.-M. (1785). Recherches sur l’attraction des sphéroïdes homogènes [Researches on the attraction of homogeneous spheroids]. Mémoires de Mathématiques et de Physique, présentés à l’Académie Royale des Sciences, par divers savans, et lus dans ses Assemblées, Paris, 10, 411–435.

    Google Scholar 

  • LEGENDRE, A.-M. (1805). Appendice sur la méthode des moindres quarrés [Appendix on the method of minimum squares]. In: Nouvelles méthodes pour la détermination des orbites des comètes [New methods for the determination of the orbits of comets]. Paris, Courcier, 72–80.

    Google Scholar 

  • LEGGE, J.A. and RUPNIK, J.J. (1943). Least squares determination of the velocity function V = V 0 + kz for any set of time depth data. Geophysics, 8, 356–361.

    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 

  • LEIBNIZ, G.W. (1710). Symbolismus memorabilis calculi algebraici et infinitesimalis, in comparatione potentiarum et differentiarum; et de lege homogeneorum transcendentali [The remarkable symbolic algebraic calculus, infinitesimals; the transcendental law of homogeneity]. Miscellanea Berolinensia ad incrementum scientiarum, 1, 160–165.

    Google Scholar 

  • LEVENBERG, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2, 164–168.

    Article  Google Scholar 

  • LEVINSON, N. (1947). The Wiener RMS (root mean square) error criterion in filter design and prediction. Journal of Mathematics and Physics, 25, 261–278.

    Article  Google Scholar 

  • LINDSEY, J.P. (1960). Elimination of seismic ghost reflections by means of a linear filter. Geophysics, 25, 130–140.

    Article  Google Scholar 

  • LINK, R.F. and KOCH, G.S. (1975). Some consequences of applying lognormal theory to pseudolognormal distributions. Journal of the International Association for Mathematical Geology, 7, 117–128.

    Article  Google Scholar 

  • LODE, W. ( 1925). Versuche über den Einfluß der mittleren Hauptspannung auf die Fließgrenze [Experiments on the influence of the average major strain on the yield point]. Zeitschrift für angewandte Mathematik und Mechanik, 5, 142–144.

    Google Scholar 

  • LODE, W. (1926). Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen des Metalle, Eisen, Kupfer, und Nickel [Experiments on the influence of the average major strain on the flow of the metals, iron, copper, and nickel]. Zeitschrift für Physik, 36, 913–939.

    Google Scholar 

  • LOMB, N.R. (1976). Least squares frequency analysis of unequally-spaced data. Astrophysics and Space Science, 39, 447–462.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • LOUIS, H. (1907). On a deficiency in the nomenclature of mineral deposits. Transactions of the Institution of Mining Engineers, 34, 286–287.

    Google Scholar 

  • MAGIDIN, A. (2010). Lebesque integral basics [online: http://math.stackexchange.com/questions/7436/lebesgue-integral-basics].

  • MAIRE, C. and BOSCOVICH, R.J. (1755). De litteraria expeditione per pontificam ditionem ad dimetiendos duos meridiani gradus et corrigendam mappam geographicam. Jussu, et auspiciis Benedicti XIV, Pont. Max [An account of an expedition to measure two degrees of the meridian]. Rome, Nicolaus & Marcus Palearini.

    Google Scholar 

  • MAIRE, C. and BOSCOVICH, R.J. (1770). Voyage astronomique et geographique, dans l’état de l’eglise, entrepris par l’ordre et sous l’auspices du Pape Beniot XIV, pour mesurer deux dégrés du méridien, and corriger la Carte de l’Etat ecclésiastique [Astronomical and geographical travel in the state of the Church, undertaken by the order and under the auspices of Pope Benedict XIV, to measure two degrees of the meridian, and to correct the map of the ecclesiastical state]. Paris, N.M. Tillard.

    Google Scholar 

  • MANDELBROT, B. (1975a). Les objects fractales: Forme, hasard, et dimension [Fractals: Form, chance and dimension]. Paris, Flammarion.

    Google Scholar 

  • MANDELBROT, B.B. (1982). The fractal geometry of nature. San Francisco, CA, W.H. Freeman.

    Google Scholar 

  • MANDELBROT, B.B. (1995). Measures of fractal lacunarity: Minkowski content and alternatives. In: BANDT, C., GRAF, S. and ZÄHLE, M. (eds.). Fractal geometry and stochastics. Basel, Birkhäuser Verlag, 15–42.

    Chapter  Google Scholar 

  • MANN, C.J. (1987). Misuses of linear regression in the earth sciences. In: SIZE, W.B. (ed.). Use and abuse of statistical methods in the earth sciences. Oxford, Oxford University Press, 74–108.

    Google Scholar 

  • MARK, D.M. and CHURCH, M. (1977). On the misuse of regression in earth science. Journal of the International Association for Mathematical Geology, 9, 63–77.

    Article  Google Scholar 

  • MARQUARDT, D.W. (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics, 11, 431–441.

    Article  Google Scholar 

  • MARTÍN-FERNÁNDEZ, J.A. and THIO-HENESTROSA, S. (2006). Rounded zeros: some practical aspects for compositional data. In: BUCCIANTI, A., MATEU-FIGUERAS, G. and PAWLOWSKY-GLAHN, V. (eds.). Compositional data analysis in the geosciences: From theory to practice. London, The Geological Society, 191–202.

    Google Scholar 

  • MARTÍN-FERNÁNDEZ, J.A., BARCELÓ-VIDAL, C. and PAWLOWSKY-GLAHN, V. (2003). Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology, 35, 253–278.

    Article  Google Scholar 

  • MATEU-FIGUERAS, G. (2003). Models de distribució sobre el símplex [Distribution models on the simplex]. Doctoral dissertation, Catalunya, Universitat Politècnica de Catalunya.

    Google Scholar 

  • MATHESON, I.B.C. (1990). A critical comparison of least absolute deviation fitting (robust) and least squares fitting: the importance of error distributions. Computers and Chemistry, 14, 49–57.

    Article  Google Scholar 

  • MAXWELL, J.C. (1873). A treatise on electricity and magnetism. 2 vols. Oxford, Clarendon Press.

    Google Scholar 

  • MAY, R.M. (1972). Limit-cycles in predator-prey communities. Science, 177, 900–902.

    Article  Google Scholar 

  • McALISTER, D. (1879). The law of the geometric mean. Proceedings of the Royal Society, London, 29, 367–376.

    Google Scholar 

  • McARTHUR, J.M., HOWARTH, R.J. and SHIELDS, G.A. (2012). Strontium isotope stratigraphy. In: GRADSTEIN, F., OGG, J., SCHMITZ, M. and OGG, G. (eds.). The geologic timescale 2012. Vol. 1. Oxford, Elsevier, 127–144.

    Google Scholar 

  • McCARN, D.W. and CARR, J.R. (1992). Influence of numerical precision and equation solution algorithm on computation of kriging weights. Computers & Geosciences, 18, 1127–1167.

    Article  Google Scholar 

  • McCARTHY, J. (1960). Recursive functions of symbolic expressions and their computation by machine, Part I. Communications of the ACM, 3, 184–195.

    Article  Google Scholar 

  • McKAY, M.D., BECKMAN, R.J. and CONOVER, W.J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239–245.

    Google Scholar 

  • McWILLIAMS, T.P. (1986). Sensitivity analysis of geologic computer models: A formal procedure based on Latin hypercube sampling. Mathematical Geology, 19, 81–90.

    Google Scholar 

  • MEIJERING, E. (2002). A chronology of interpolation. From ancient astronomy to modern signal and image processing. Proceedings of the IEEE, 90, 319–342.

    Google Scholar 

  • MENDEZ, L.A. (2016). A practical introduction to fuzzy logic using LISP. Studies in fuzziness and soft computing 327. Cham, Springer International Publishing.

    Book  Google Scholar 

  • MIESCH, A.T. (1976b). Q-mode factor analysis of geochemical and petrologic data matrices with constant row-sums. United States Geological Survey Professional Paper 574-G, Washington, DC, United States Government Printing Office.

    Google Scholar 

  • MIESCH, A.T. and CHAPMAN, R.P. (1977). Logtransformations in geochemistry. Journal of the International Association for Mathematical Geology, 9, 191–198.

    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, J. (2015c). Legendre functions of the first and second kind [online: http://www.solitaryroad.com/c679.html].

  • MILLER, R.L. (1949). An application of the analysis of variance to paleontology. Journal of Paleontology, 23, 635–640.

    Google Scholar 

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

    Google Scholar 

  • MINASAY, B. and MCBRATNEY, A.B. (2002). Uncertainty analysis for pedotransfer functions. European Journal of Soil Science, 53, 417–430.

    Article  Google Scholar 

  • MINASAY, B. and MCBRATNEY, A.B. (2006). A conditioned Latin hypercube method for sampling in the presence of ancillary information. Computers & Geosciences, 32, 1378–1388.

    Article  Google Scholar 

  • MITKIN, V.N., ZAYAKINA, S.B. and ANOSHIN, G.N. (2003). New technique for the determination of trace noble metal content in geological and process materials. Spectrochimica Acta Part B: Atomic Spectroscopy, 58, 311–328.

    Article  Google Scholar 

  • MITRA, S. (1976). A quantitative study of deformation mechanisms and finite strain in quartzites. Contributions to Mineralogy and Petrology, 59, 203–226.

    Article  Google Scholar 

  • MONTA, P. (2015). Analysis of Briggs’ first logarithm table of 1617, Logarithmorum Chilias Prima [online: http://www.pmonta.com/tables/logarithmorum-chilias-prima/index.html].

  • MOOKERJEE, M. and PEEK, S. (2014). Evaluating the effectiveness of Flinn’s k-value versus Lode’s ratio. Journal of Structural Geology, 68 (Part A), 33–43.

    Google Scholar 

  • MOORE, R.C. (1949). Meaning of facies. In: MOORE, R.C. (ed.). Sedimentary facies in geological history. Memoir 39. Washington, DC, Geological Society of America, 1–34.

    Google Scholar 

  • MORTON, N.E. (1995). LODs [logarithms of odds] past and present. Genetics, 140 (May), 7–12.

    Google Scholar 

  • MULLER, H.-G. (1987). Weighted local regression and kernel methods for nonparametric curve-fitting. Journal of the American Statistical Association, 82, 231–238.

    Google Scholar 

  • NÁDAI, A. (1927). Der bildsame Zustand der Werkstoffe [The plastic state of materials]. Berlin, Springer-Verlag.

    Google Scholar 

  • NÁDAI, A. (1931). Plasticity. A mechanics of the plastic state of matter [translated by A.M. WAHL]. Engineering Societies Monograph. New York, NY, McGraw-Hill.

    Google Scholar 

  • NAPIER, J. (1614). Mirifici logarithmorum canonis descriptio [A description of the wonderful canon of logarithms]. Edinburgh, Andrew Hart.

    Google Scholar 

  • NAPIER, J. and BRIGGS, H. (1618). A description of the admirable table of logarithmes: with a declaration of the most plentifull, easie, and speedy use thereof in both kinds of trigonometry, as also in all mathematicall calculations [translated from Latin by E. WRIGHT]. London,. Simon Waterson.

    Google Scholar 

  • NAPIER, J. and MACDONALD, W.R. (1889). The construction of the wonderful canon of logarithms by John Napier [translated from Latin into English with notes and a catalogue of the various editions of Napier’s works by W.R. MACDONALD]. Edinburgh, William Blackwood.

    Google Scholar 

  • NELDER, J. and MEAD, R. (1965). A simplex method for function minimisation. Computer Journal, 7, 308–313.

    Article  Google Scholar 

  • OMER, G.C.O. (1947). Differential-motion seismographs. Bulletin of the Seismological Society of America, 37, 197–215.

    Google Scholar 

  • OPPENHEIM, A.V. and SCHAFER, R.W. (2004). From frequency to quefrency: a history of the cepstrum. IEEE Signal Processing Magazine, 21 (5), 95–106.

    Article  Google Scholar 

  • ORTIZ, E.L. (1969). The tau method. SIAM Journal on Numerical Analysis, 6, 480–492.

    Article  Google Scholar 

  • ORTIZ, E.L. (1994). The tau method and the numerical solution of differential equations: Past and present research. In: BROWN, J.D., CHU, M.T., ELLISON, D.C. and PLEMMONS, R.J. (eds.). Proceedings of the Cornelius Lanczos International Centenary Conference. SIAM Proceedings Series. Philadelphia, PA, Society for Industrial and Applied Mathematics, 77–82.

    Google Scholar 

  • PARKS, J.M. (1966). Cluster analysis applied to multivariate geological problems. The Journal of Geology, 74, 703–715.

    Article  Google Scholar 

  • PEARSON, K. (1898). Mathematical contributions to the theory of evolution. V. On the reconstruction of the stature of prehistoric races. Philosophical Transactions of the Royal Society, London, Series A, 192, 169–244.

    Google Scholar 

  • PEBESMA, E.J. and HEUVELINK, G.B.M. (1999). Latin hypercube sampling of Gaussian random fields. Technometrics, 41, 303–312.

    Article  Google Scholar 

  • PERUGINI, D., POLI, G. and VALENTINI, L. (2004). Strange attractors in plagioclase oscillatory zoning: petrological implications. Contributions to Mineralogy and Petrology, 149, 482–497.

    Article  Google Scholar 

  • PHILLIPS, F.C. (1954). The use of the stereographic projection in structural geology. London, Edward Arnold.

    Google Scholar 

  • PITMAN, E.J.G. (1939). Tests of hypotheses concerning location and scale parameters. Biometrika, 31, 200–215.

    Article  Google Scholar 

  • PODKOVYROV, V.N., GRAUNOV, O.V. and CULLERS, R.L. (2003). A linear programming approach to determine the normative composition of sedimentary rocks. Mathematical Geology, 35, 459–476.

    Article  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 

  • POISSON, S.-D. (1835). Recherches sur la probabilité des jugements, principalement en matière criminelle [Research on the probability of judgements, mainly in criminal matters]. Comptes rendus hebdomadaires des Séances de l’Académie des Sciences, Paris, 1, 473–494.

    Google Scholar 

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

    Article  Google Scholar 

  • RADNER, R. (1959). The application of linear programming to team decision problems. Management Science, 5, 143–150.

    Article  Google Scholar 

  • RAMBERG, H. (1959). Evolution of ptygmatic folding. Norsk geologisk Tidsskrift, 39, 99–152.

    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 

  • RAZUMOVSKY, N.K. (1941). On the role of the logarithmically normal law of frequency distribution in petrology and geochemistry. Comptes Rendus (Doklady) de l’Academie des Sciences de l’URSS, 33, 48–49.

    Google Scholar 

  • REED, G.W. (1959). Activation analysis applied to geochemical problems. In: ABELSON, P.H. (ed.). Researches in Geochemistry. New York, NY, John Wiley & Sons, 458–475.

    Google Scholar 

  • REHDER, S. and FRANKE, D. (2012). How to include ignorance into hydrocarbon-resource assessments? A case study applied to the presence of source rock at the Argentine Deep Water Margin. Natural Resources Research, 21, 301–309.

    Article  Google Scholar 

  • REICHE, P. (1938). An analysis of cross-lamination. The Coconino sandstone. Journal of Geology, 46, 905–932.

    Google Scholar 

  • REIMANN, C. and FILZMOSER, P. (2000). Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data. Environmental Geology, 39, 1001–1014.

    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 

  • REITER, D. and STROUJKOVA, A. (2005). Improved depth-phase detection at regional distances. In: PATTERSON, E., (ed.). Proceedings of the 27th Seismic Research Review: Ground-based nuclear explosion monitoring techniques, Rancho Mirage, California, 20–22 September 2005, United States Department of Energy, Oak Ridge, TN, 403–412.

    Google Scholar 

  • RENDU, J.-M.M. (1988). Applications in geology. In: CROW, E.L. and SHIMIZU, K. (eds.). Lognormal distributions. Theory and applications. Statistics textbooks and monographs.v. 88. New York, Marcel Dekker, 357–366.

    Google Scholar 

  • REYMENT, R.A., BLACKITH, R.E and CAMPBELL, N.A. (1984). Multivariate morphometrics. 2nd edn., London, Academic Press.

    Google Scholar 

  • REYMENT, R.A. and SAVAZZI, E. (1999). Aspects of multivariate statistical analysis in geology. Amsterdam, Elsevier.

    Google Scholar 

  • RICE, J.R. and WHITE, J.S. (1964). Norms for smoothing and estimation. SIAM Review, 6, 243–256.

    Article  Google Scholar 

  • RICE, R.B. (1962). Inverse convolution filters. Geophysics, 27, 4–18.

    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 

  • RODRIGUEZ-ITURBE, I. and NORDIN, C.F. (1968). Time series analyses of water and sediment discharges. Hydrological Sciences Journal, 13, 69–84.

    Google Scholar 

  • RUTHERFORD, E. (1937). The search for isotopes of hydrogen and helium of mass 3. Nature, 140, 303–305.

    Article  Google Scholar 

  • RUTHERFORD, E. and GEIGER, H. (1908). An electrical method of counting the number of α-particles from radioactive substances. Proceedings of the Royal Society, London, ser. A, A81, 141–161.

    Google Scholar 

  • SABINE, E. (1841). Contributions to terrestrial magnetism. No. II. Philosophical Transactions of the Royal Society, London, 131, 11–35.

    Article  Google Scholar 

  • SANDER, B. (1930). Gefügekunde der Gesteine mit besonderer Berücksichtigung der Tektonite [Microstructure of rocks with special emphasis on tectonite]. Vienna, Springer.

    Google Scholar 

  • SANDRI, M. (1996). Numerical calculation of Lyapunov exponents. The Mathematica Journal, 6 (3), 78–84.

    Google Scholar 

  • SANTOS, E.T.F. and BASSREI, A. (2007). L- and θ-curve approaches for the selection of regularization parameter in geophysical diffraction tomography. Computers & Geosciences, 33, 618–629.

    Article  Google Scholar 

  • SAUVAGEAU, M. and KUMRAL, M. (2015). Analysis of mining engineering data using robust estimators in the presence of outliers. Natural Resources Research, 24, 305–316.

    Article  Google Scholar 

  • SCARGLE, J.D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal, 263, 835–853.

    Article  Google Scholar 

  • SCARGLE, J.D. (1989). Studies in astronomical time series analysis. III. Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data. The Astrophysical Journal, 343, 874–887.

    Article  Google Scholar 

  • SCHMIDT, W. (1925). Gefugestatistik [Microstructural (petrofabric) statistics]. Tschermak’s Mineralogische und Petrographische Mitteilungen, 38, 392–423.

    Google Scholar 

  • SCHUENEMEYER, J.H. and DREW, L.J. (1983). A procedure to estimate the parent populastion of the size of oil and gas fields as revealed by a study of economic truncation. Journal of the International Association for Mathematical Geology, 15, 145–162.

    Article  Google Scholar 

  • SCHULZ, M. and STATTEGGER, K. (1997). SPECTRUM: Spectral analysis of unevenly spaced paleoclimatic time series. Computers & Geosciences, 23, 929–945.

    Article  Google Scholar 

  • SCHWARZACHER, W. (1964). An application of statistical time-series analysis of a limestone-shale sequence. Journal of Geology, 72, 195–213.

    Article  Google Scholar 

  • SCHWERDTFEGER, H. (1950). Introduction to linear algebra and the theory of matrices. Groningen, P. Noordhoff.

    Google Scholar 

  • SEYEDGHASEMIPOUR, S.J. and BHATTACHARYYA, B.B. (1990). The loghyperbolic: An alternative to the lognormal for modelling oil field size distribution. Mathematical Geology, 22, 557–571.

    Article  Google Scholar 

  • SHAH, B.K. and DAVE, P.H. (1963). A note on log-logistic distribution. Journal of the Maharaja Sayajirao University of Baroda, 12 (2–3), 15–20.

    Google Scholar 

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

    Google Scholar 

  • SICHEL, H.S. (1947). 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, 56, 403–474.

    Google Scholar 

  • SIMPSON, S.M. (1954). Least squares polynomial fitting to gravitational data and density plotting by digital computer. Geophysics, 19, 255–269.

    Article  Google Scholar 

  • SIMPSON, S.M., Jr. (1955). Similarity of output traces as a seismic operator criterion. Geophysics, 20, 254–269.

    Article  Google Scholar 

  • SOBEL, D. (1995). Longitude: the true story of a lone genius who solved the greatest scientific problem of his time. New York, NY, Walker.

    Google Scholar 

  • SORNETTE, D. and SAMMIS, G.C. (1995). Complex critical exponents from renormalisation group theory of earthquakes: Implications for earthquake predictions. Journal de Physique. ser. 1, 5, 607–619.

    Google Scholar 

  • SPEARMAN, C.E. (1904b). ‘General intelligence’ objectively determined and measured. American Journal of Psychology, 15, 201–293.

    Article  Google Scholar 

  • SPEIDELL, J. (1619). New logarithmes. London, John Speidell.

    Google Scholar 

  • SPROTT, J.C. (2009). Simplifications of the Lorenz Attractor. Nonlinear Dynamics, Psychology, and Life Sciences, 13, 271–278.

    Google Scholar 

  • STARK, C.P. and HOVIUS, N. (2001). The characterisation of landslide size distributions. Geophysical Research Letters, 28, 1091–1094.

    Article  Google Scholar 

  • STOICA, P. (1993). List of references on spectral line analysis. Signal Processing, 31, 329–340.

    Article  Google Scholar 

  • STRINGHAM, I. (1893). Uniplanar algebra. Berkley, CA, The Berkley Press.

    Google Scholar 

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

    Google Scholar 

  • SWAIN, J.J. (1990). Nonlinear regression. In: WADSWORTH, H.M. (ed.). Handbook of statistical methods for engineers and scientists. 2nd edn., New York, NY, McGraw-Hill, 18.1–18.31.

    Google Scholar 

  • SYLVESTER, J.J. (1883a). Lectures on the principles of universal algebra. American Journal of Mathematics, 6, 270–286.

    Article  Google Scholar 

  • SYLVESTER, J.J. (1883b). On the equation to secular inequalities in the planetary theory. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 5, 16, 267–629.

    Article  Google Scholar 

  • TAYLOR, H.L. (1981). The L1 norm in seismic data processing. Developments in Geophysical Exploration, 2, 53–76.

    Article  Google Scholar 

  • TCHÉBYCHEF, P.-L. (1867). Des valeurs moyennes [translated from Russian by N. DE KHANIKOV]. Journal de mathématiques pures et appliquées. ser. 2, 12, 177–184.

    Google Scholar 

  • TEISSIER, G. (1948). La relation d’allometrie sa signification statistique et biologique [The allometric relationship: its statistical and biological significance]. Biometrics, 4, 14–53.

    Article  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 

  • THANASSOULAS, C., TSELENTIS, G.-A. and DIMITRIADIS, K. (1987). Gravity inversion of a fault by Marquardt’s method. Computers & Geosciences, 13, 399–404.

    Article  Google Scholar 

  • THOMPSON, G.T. (1992). The grand unified theory of least squares: f2(N) = f (2N). Computers & Geosciences, 18, 815–822.

    Article  Google Scholar 

  • THOMPSON, S.E. and KATUL, G.G. (2012). Multiple mechanisms generate Lorentzian and 1/f^α power spectra in daily stream-flow time series. Advances in Water Resources, 37, 94–103.

    Article  Google Scholar 

  • THOMSON, W. [Lord Kelvin] (1847). On a mechanical representation of electric, magnetic and galvanic forces. Cambridge and Dublin Mathematical Journal, new ser., 2, 61–64.

    Google Scholar 

  • THOMSON, W. [Lord Kelvin] (1899). On the reflexion and refraction of solitary plane waves at a plane interface between two isotropic elastic mediums – fluid, solid or ether. London and Edinburgh Philosphical Magazine, ser. 5., 47, 179–191.

    Google Scholar 

  • THURSTONE, L.L. (1931). Multiple factor analysis. Psychological Revue, 38, 406–427.

    Article  Google Scholar 

  • TODHUNTER, I. (1873). A history of the mathematical theories of attraction and the Figure of the Earth. From the time of Newton to that of Laplace. London, Macmillan.

    Google Scholar 

  • TROUTMAN, B.M. and WILLIAMS, G.P. (1987). Fitting straight lines in the earth sciences. In: SIZE, W.B. (ed.). Use and abuse of statistical methods in the earth sciences. Oxford, Oxford University Press, 107–128.

    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 

  • ULRYCH, T.J. (1972). Maximum entropy power spectrum of truncated sinusoids. Journal of Geophysical Research, 77, 1396–1400.

    Article  Google Scholar 

  • ULRYCH, T.J. and OOE, M. (1979). Autoregressive and mixed autoregressive-moving average models and spectra. In: HAYKIN, S. (ed.). Nonlinear methods of spectral analysis. Berlin, Springer-Verlag, 73–125.

    Chapter  Google Scholar 

  • ULRYCH, T.J., SMYLIE, D.E., JENSEN, O.G. and CLARKE, G.K.C. (1973). Predictive filtering and smoothing of short records by using maximum entropy. Journal of Geophysical Research, 78, 4959–4964.

    Article  Google Scholar 

  • UNWIN, D.J. and WRIGLEY, N. (1987). Towards a general theory of control point distribution effects in trend-surface models. Computers & Geosciences, 13, 351–355.

    Article  Google Scholar 

  • van der POL, B. (1926). On relaxation-oscillations. Philosophical Magazine, ser. 7, 2, 978–992.

    Google Scholar 

  • van der POL, B. and van der MARK, J. (1927). Frequency demultiplication. Nature, 120, 363–364.

    Article  Google Scholar 

  • VAUGHAN, S., BAILEY, R.J. and SMITH, D.G. 2011. Detecting cycles in stratigraphic data: Spectral analysis in the presence of red noise. Paleogeography, 26, PA4211 [online: http://dx.doi.org/10.1029/ 2011PA002195].

  • VERHULST, P.-F. (1845). Recherches mathématiques sur la loi d’accroissement de la population [Mathematical research on the law of population growth]. Nouveaux Mémoires de l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 18, 1–32.

    Google Scholar 

  • VISTELIUS, A.B. (1961). Sedimentation time trend functions and their application for correlation of sedimentary deposits. Journal of Geology, 69, 703–728.

    Article  Google Scholar 

  • VISTELIUS, A.B. (ed.) (1967). Studies in mathematical geology. New York, NY, Consultants Bureau (Plenum Press).

    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 

  • WALKER, M.R. and JACKSON, A. (2000). Robust modelling of the Earth’s magnetic field. Geophysical Journal International, 143, 1353–1368.

    Article  Google Scholar 

  • WALTER, É. (2014). Numerical methods and optimization. A consumer guide. Cham, Springer International.

    Book  Google Scholar 

  • WARING, E. (1779). Problems concerning interpolations. Philosophical Transactions of the Royal Society, London, 69, 59–67.

    Article  Google Scholar 

  • WATTIMENA, R.K. (2013). Predicting probability stability of rock slopes using logistic regression. International Journal of the Japanese Committee for Rock Mechanics, 9, 1–6.

    Google Scholar 

  • WEBSTER, R. (1997). Regression and functional relations. European Journal of Soil Science, 48, 557–566.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • WEISSTEIN, E.W. (ed.) (2015). MathWorld – A Wolfram web resource [online: http://mathworld.wolfram.com].

  • WESSON, R.L. (1970). A time integration method for computation of the intensities of seismic rays. Bulletin of the Seismological Society of America, 60, 307–316.

    Google Scholar 

  • WIDROW, B. and HOFF, M.E. (1960). Adaptive switching circuits. In: IRE WESCON Convention Record: at the Western Electronic Show and Convention, Los Angeles, California, August 23–26, 1960, Institute of Radio Engineers, 96–104.

    Google Scholar 

  • WIDROW, B. and STEARNS, S.D. (1985). Adaptive signal processing. Englewood Cliffs, NJ, Prentice-Hall.

    Google Scholar 

  • WIENER, N. (1942). The extrapolation, interpolation and smoothing of stationary time series with engineering applications. D.I.C. Contract 6037, A research pursued on behalf of the National Defence Research Council (Section D) February 1, 1942. Cambridge, MA, The Massachusetts Institute of Technology.

    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 

  • WILCZYNSKI, E.J. (1911). One-parameter families and nets of plane curves. Transactions of the American Mathematical Society, 12, 473–510.

    Article  Google Scholar 

  • WILSON, E.B. and LUYTEN, W.J. (1925). The frequency distribution of some measured parallaxes and of the parallaxes themselves. Proceedings of the National Academy of Sciences of the United States of America, 11, 270–274.

    Google Scholar 

  • WILSON, E.B. and WORCESTER, J. (1945). The normal logarithmic transform. The Review of Economics and Statistics, 27, 17–22.

    Article  Google Scholar 

  • WINSTON, P.H. and HORN, B.K.P. (1981). LISP. Reading, MS., Addison-Wesley.

    Google Scholar 

  • WRIGHT, C.J., MCCARTHY, T.S. and CAWTHORN, R.G. (1983). Numerical modelling of trace element fractionation during diffusion controlled crystallization. Computers & Geosciences, 9, 367–389.

    Article  Google Scholar 

  • YAGER, R.M. (1998). Detecting influential observations in nonlinear regression modelling of groundwater flow. Water Resources Research, 34, 1623–1633.

    Article  Google Scholar 

  • YANG, C.-S. and KOUWE, W.F.P. (1995). Wireline log-cyclicity analysis as a tool for dating and correlating barren strata: an example from the Upper Rotliegend of The Netherlands. In: DUNAY, R.E. and HAILWOOD, E.A. (eds.). Non-biostratigraphical methods of dating and correlation. Special Publication 89. London, The Geological Society, 237–259.

    Google Scholar 

  • YUEN, D.A. (ed.) (1992). Chaotic processes in the geological sciences. The IMA Volumes in Mathematics and its Applications. 41. New York, NY, Springer-Verlag.

    Google Scholar 

  • ZEEMAN, P. (1896). Over den invloed eener magnetisatie op den aard van het door een stof uitgezonden licht [On the influence of magnetism on the nature of the light emitted by a substance]. Amsterdam, Koninklijke Akademie van Wetenschappen te Amsterdam.

    Google Scholar 

  • ZHDANOV, M.S. (2002). Geophysical inverse theory and regularization problems. Methods in geochemistry and geophysics 36. Amsterdam, Elsevier.

    Google Scholar 

  • ZHOU, D., CHEN, H. and LOU, Y. (1991). The logratio approach to the classification of modern sediments and sedimentary environments in northern South China Sea. Mathematical Geology, 23, 157–165.

    Article  Google Scholar 

  • ZITKOVIC, G. (2013). The Lebesgue integral [online: https://www.ma.utexas.edu/users/gordanz/notes/lebesgue_integration.pdf].

  • 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 

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). L. In: Dictionary of Mathematical Geosciences . Springer, Cham. https://doi.org/10.1007/978-3-319-57315-1_12

Download citation

Publish with us

Policies and ethics

Search

Navigation