Skip to main content

Abstract

A mathematical symbol generally used to denote the imaginary unit, the constant √(−1). Note that some authors use j for this purpose. Although such “imaginary” numbers had been used by the Italian mathematician Girolamo Cardan (1501–1576) in 1545 and other mathematicians subsequently, it was the Swiss mathematician and physicist, Leonhard Paul Euler (1707–1783) who introduced the symbolic notation i (Euler 1748). An example of early use in geophysics is Macelwayne and Sohon (1932). See also: complex conjugate, complex number.

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

Access this chapter

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

  • ABBOTT, G.A. (1925). A chemical investigation of the water of Devil’s Lake, North Dakota. Proceedings of the Indiana Academy of Sciences, 34, 181–184

    Google Scholar 

  • ABRAMOWITZ, M and STEGUN, I.A. (eds.) (1965). Handbook of mathematical functions with formulas, graphs, and mathematical tables. 2nd edn., New York, NY, Dover Publications.

    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 

  • ALAMILLA, J.L., VAI, R. and ESTEVA, L. (2015). Estimating seismic-source rate parameters associated with incomplete catalogues and superimposed Poisson-renewal generating processes. Journal of Seismology, 19, 55–68.

    Article  Google Scholar 

  • ANDERSON, E.M. (1937). The dynamics of the formation of cone-sheets, ring-dykes and caldron-subsidences. Proceedings of the Royal Society of Edinburgh, 56, 128–157.

    Article  Google Scholar 

  • ANONYMOUS (1992b). United States Geological Survey National Mapping Division. Standards for digital elevation models [online: http://nationalmap.gov/standards/ pdf/1DEM0897.PDF; /2DEM0198.PDF; /3DEM0897.PDF; /PDEM0198.PDF].

  • ANSOFF, H.I. (1959). The state of the art in making plans – Some comments on the ill-structured problem. In: STRASSMAN, P.A. (ed.). First Symposium on Corporate Long-range Planning: Proceedings of the College on Planning, Chicago, Illinois, June 6, 1959. Pleasantville, NY, The Institute of Management Sciences, 1–16.

    Google Scholar 

  • ASHENHURST, R.L. and METROPOLIS, N. (1965). Error estimation in computer calculation. The American Mathematical Monthly, 72, 47–58.

    Article  Google Scholar 

  • ASHMEAD, J. and PIPPARD, A.B. (1946). The use of spherical reflectors as microwave scanning aerials. Journal of the Institution of Electrical Engineers – Part IIIA: Radiolocation, 93, 627–632.

    Google Scholar 

  • BACKUS, G.E. (1962). The propagation of short elastic surface waves on a slowly rotating earth. Bulletin of the Seismological Society of America, 52, 823–846.

    Google Scholar 

  • BACKUS, J. (1980). Programming in America in the 1950s – Some personal recollections. In: METROPOLIS, N., HOWLETT, J. and ROTA, G.-C. (eds.). History of computing in the 20th Century. New York, NY, Academic Press, 125–135.

    Chapter  Google Scholar 

  • BAILEY, A.I. (1975). A method of analyzing polymodal distributions in orientation data. Journal of the International Association for Mathematical Geology, 7, 285–294.

    Article  Google Scholar 

  • BARBER, N.F. (1956). A correlation treatment of fading signals. Journal of Atmospheric and Terrestrial Physics, 8, 318–330.

    Article  Google Scholar 

  • BATEMAN, H. (1910). The solution of the integral equation which connects the velocity of propagation of an earthquake wave in the interior of the Earth with the times which the disturbance takes to travel to different stations on the Earth’s surface. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 6, 19, 576–587.

    Article  Google Scholar 

  • BAUER, L.A. (1895). On the secular motion of a free magnetic needle. The Physical Review, ser. 1, 2, 455–465.

    Google Scholar 

  • BAYES, T. (1763). An essay towards solving a problem in the doctrine of chances. By the Late Rev. Mr. Bayes, F.R.S. Communicated by Mr [R.] Price, in a letter to John Canton, A.M. F.R.S. Philosophical Transactions of the Royal Society, London, 53, 370–418.

    Article  Google Scholar 

  • BEATON, A.E. and TUKEY, J.W. (1974). The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics, 16, 147–185.

    Article  Google Scholar 

  • BINGHAM, C., GODFREY, M.D. and TUKEY, J.W. (1967). Modern techniques of power spectrum estimation. IEEE Transactions on Audio and Electroacoustics, AU-15, 56-66.

    Article  Google Scholar 

  • BIVAND, R.S., PEBESMA, E.J. and GÓMEZ-RUBIO, V. (2008). Applied spatial data analysis with R. New York, Springer-Verlag.

    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 

  • BLAIK, M. and DONN, W.L. (1954). Microseism ground motion at Palisades and Weston. Bulletin of the Seismological Society of America, 44, 597–612.

    Google Scholar 

  • BLODGET, L. (1857). Climatology of the United States, and of the temperate latitudes of the North American Continent. Philadelphia, PA, J.B. Lippincott.

    Google Scholar 

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

    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 

  • BOISEN, M.B., Jr. and GIBBS, G.V. (1985). Mathematical crystallography. Reviews in Mineralogy. v. 15. Washington, DC, Mineralogical Society of America.

    Google Scholar 

  • BOND, C.E., PHILO, C. and SHIPTON, Z.K. (2011). When there isn’t a right answer: Interpretation and reasoning, key skills for twenty-first century geoscience. International Journal of Science Education, 33, 629–652.

    Article  Google Scholar 

  • BONHAM-CARTER, G.F. (1988). Numerical procedures and computer program for fitting an Inverted Gaussian Model to vegetation reflectance data. Computers & Geosciences, 14, 339–356.

    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 

  • BREWSTER, D. (1816). On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances by mechanical compression and dilation. Philosophical Transactions of the Royal Society, London, 106, 157–178.

    Google Scholar 

  • BRIGHAM, E.O., SMITH, H.W., BOSTICK, F.X. and DUESTERHOEFT, W.C. (1968). An iterative technique for determining inverse filters. IEEE Transactions on Geoscience Electronics, 6, 86–96.

    Article  Google Scholar 

  • BROADBENT, S.R. and HAMMERSLEY, J.M. (1957). Percolation processes. I. Crystals and mazes. Proceedings of the Cambridge Philosophical Society, 53, 629–641.

    Google Scholar 

  • 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 

  • BUCHHEIM, A. (1884). Proof of Professor Sylvester’s ‘Third Law of Motion’. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 5, 18, 459–460.

    Article  Google Scholar 

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

    Book  Google Scholar 

  • CAERS, J. and HOFFMAN, T. (2006). The probability perturbation method: A new look at Bayesian inverse modelling. Mathematical Geology, 38, 81–100.

    Article  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, K. (1988). Bootstrapped models for intrinsic random functions. Mathematical Geology, 20, 699–715.

    Article  Google Scholar 

  • CAMPBELL, N.A. (1980). Robust procedures in multivariate analysis. Robust covariance estimation. Applied Statistics, 29, 231–237.

    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 

  • CELENK, O., CLARK, A.L, DE VLETTER, D.R, GARRETT, R.G. and VAN STAALDVINEN, C. (1978). Workshop on abundance estimation. Journal of the International Association for Mathematical Geology, 10, 473–480.

    Article  Google Scholar 

  • CHENG, Q., AGTERBERG, F.P. and BALLANTYNE, S.B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109–130.

    Article  Google Scholar 

  • CHIN, S.-T. (1991). Bandwidth selection for kernel density estimation. Annals of Statistics, 19, 1528–1546.

    Article  Google Scholar 

  • CIARAMELLA, A., DE LAURO, E., DE MARTINO, S., DI LIETO, B., FALANGA, M. and TAGLIAFERRI, R. (2004). Characterization of Strombolian events by using independent component analysis. Nonlinear Processes in Geophysics, 11, 453–461.

    Article  Google Scholar 

  • CICCI, D.A. (1992). Improving gravity field determination in ill-conditioned inverse problems. Computers & Geosciences, 18, 509–516.

    Article  Google Scholar 

  • CLAERBOUT, J.F. (1985). Fundamentals of geophysical data processing with applications to petroleum prospecting. 2nd edn., Oxford, Blackwell.

    Google Scholar 

  • COMON, P. (1994). Independent Component Analysis: a new concept? Signal Processing, 36, 287–314.

    Article  Google Scholar 

  • COMON, P. and JUTTEN, C. (2010). Handbook of blind source separation, Independent Component Analysis and applications. Oxford, Academic Press.

    Google Scholar 

  • CONSULTATIVE COMMITTEE FOR SPACE DATA SYSTEMS (2005). Report concerning space data system standards. Image data compression. Blue Book, November 2005. Recommended standard CCSDS 122.0-B-1. Washington, DC, CCSDS Secretariat, National Aeronautics and Space Administration [online: http://public.ccsds.org/publications/archive/122x0b1c3.pdf].

  • CONSULTATIVE COMMITTEE FOR SPACE DATA SYSTEMS (2015). Report concerning space data system standards. Image data compression. Green Book. February 2015. Informational Report CCSDS 120.1-G-2. Washington, DC, CCSDS Secretariat, National Aeronautics and Space Administration [online: http://public.ccsds.org/publications/archive/120x1g2.pdf].

  • CURRIE, J.B., PATNODE, H.W. and TRUMP, R.P. (1962). Development of folds in sedimentary strata. Geological Society of America Bulletin, 73, 655–674.

    Article  Google Scholar 

  • DE BREMAECKER, J.C. (1964). Detection of small arrivals. Bulletin of the Seismological Society of America, 54, 2141–2163.

    Google Scholar 

  • DE MOIVRE, A. (1738). The doctrine of chances: or, a method of calculating the probability of events in play. 2nd edn., London, H. Woodfall.

    Google Scholar 

  • DE MORGAN, A. (1847). Calculus of functions. In: BARLOW, P., PEACOCK, G., LARDNER, D., AIRY, G.B., HAMILTON, H.P., LEVY, A., DEMORGAN, A. and MOSLEY, H. (eds.). The encyclopaedia of pure mathematics [Two volumes as one, II]. London, John Joseph Griffin, 305–392.

    Google Scholar 

  • DEMPSTER, A.P. (1968). A generalization of Bayesian inference. Journal of the Royal Statistical Society, ser. B 30, 205–247.

    Google Scholar 

  • DEUTCH, C.V. and JOURNEL, A.G. (1994). Integrating well test-derived effective absolute permeabilities in geostatistical reservoir modelling. In: YARUS, J.M. and CHAMBERS, R.L. (eds.). Stochastic modelling and geostatistics. Tulsa, OK, American Association of Petroleum Geologists, 131–142.

    Google Scholar 

  • DEVLIN, S.J., GNANADESIKAN, R. and KETTENRING, J.R. (1981). Robust estimation of dispersion matrices and principal components. Journal of the American Statistical Association, 76, 354–362.

    Article  Google Scholar 

  • DICKSON, L.E. (1908). Representations of the general symmetric group as linear groups in finite and infinite fields. Transactions of the American Mathematical Society, 9, 121–148.

    Article  Google Scholar 

  • DIENES, I. and MANN, C.J. (1977). Mathematical formalization of stratigraphic terminology. Journal of the International Association for Mathematical Geology, 9, 587–603.

    Article  Google Scholar 

  • DIRAC, P.A.M. (1930). The principles of quantum mechanics. Oxford, Clarendon Press.

    Google Scholar 

  • DORIAN, J.P. and CLARK, A.L. (1986). Value of tectonic regions in the United States. Mathematical Geology, 18, 375–400.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • DUTKA, J. (1981). The incomplete Beta function – a historical profile. Archive for History of Exact Sciences, 24, 11–29.

    Article  Google Scholar 

  • EDGEWORTH, F.Y. (1896). A defence of index-numbers. The Economic Journal, 6, 132–142.

    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 

  • EISNER, W. and GOODMAN, A.F. (1964). Determination of dominant error sources in an inertial navigation system with iterative weighted least squares. American Institute of Aeronautics and Astronautic Journal, 2, 722–727.

    Article  Google Scholar 

  • ELLMANN, A. (2005). Computation of three stochastic modifications of Stokes’s formula for regional geoid determination. Computers & Geosciences, 31, 742–755.

    Article  Google Scholar 

  • ESKOLA, P. (1922). The mineral facies of rocks. Norsk geologisk Tidsskrift, 6, 143–194.

    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 

  • FABBRI, A.G. (1984). Image processing of geologic data. New York, NY, Van Nostrand Reinhold.

    Google Scholar 

  • FARRINGTON, O.C. (1902). Meteorite studies. I. Field Columbian Museum Publication 64. Geological Studies, 1 (11), 283–315.

    Google Scholar 

  • FAYERS, F.J. and SHELDON, J.W. (1962). The use of a high-speed digital computer in the study of the hydrodynamics of geologic basins. Journal of Geophysical Research, 67, 2421–2431.

    Article  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 

  • FERMAT, P. de (1679). Varia opera mathematica [Various mathematical works]. Toulouse, Johan Pech.

    Google Scholar 

  • FINCH, V.C., TREWARTHA, G.T, ROBINSON, A.H. and HAMMOND, E.H. (1957). Elements of geography: Physical and cultural. New York, NY, McGraw-Hill.

    Google Scholar 

  • FISHER, O. (1881). Physics of the Earth’s crust. London, Macmillan.

    Google Scholar 

  • FISHER, R.A. (1935). The design of experiments. London, Oliver & Boyd.

    Google Scholar 

  • FRANKLIN, S.E. and PEDDLE, D.R. (1987). Texture analysis of digital image data using spatial co-occurrence. Computers & Geosciences, 13, 293–311.

    Article  Google Scholar 

  • GAO, Z., HE, X., ZHANG, G., LI, Y. and WU, X. (1999). Investigation on the relationship between analytical precision and concentration with iteratively reweighted least-squares linear regression method. Talanta, 49, 331–337.

    Article  Google Scholar 

  • GIBBS, J.W. (1876). On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy of Arts and Sciences, 3, 108–248.

    Google Scholar 

  • GILBERT, F. and BACKUS, G. (1965). The rotational splitting of the free oscillations of the Earth, 2. Reviews of Geophysics, 3, 1–9.

    Article  Google Scholar 

  • GOLDBERG, D. (1991). What every computer scientist should know about floating-point arithmetic. Computing Surveys, 23, 5–48.

    Article  Google Scholar 

  • GOLDSTINE, H.H. (1977). A history of numerical analysis from the 16th through the 19th Century. New York, NY, Springer-Verlag.

    Book  Google Scholar 

  • GÓMEZ-HERNÁNDEZ, J.J. and SRIVASTAVA, R.M. (1990). ISIM3D: An ANSI-C three-dimensional multiple indicator conditional simulation program. Computers & Geosciences, 16, 395–440.

    Article  Google Scholar 

  • GOMPERTZ, B. (1871). On one uniform law of mortality from birth to extreme old age, and on the law of sickness. Journal of the Institute of Actuaries and Assurance Magazine, 16, 329–344.

    Article  Google Scholar 

  • GONZALEZ, R.C. and WINTZ, P.A. (1987). Digital image processing. Reading, MS, Addison-Wesley.

    Google Scholar 

  • GOODMAN, A.F. (1971). Extended iterative weighted least squares: Estimation of a linear model in the presence of complications. Naval Research Logistics, 18, 243–276.

    Article  Google Scholar 

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

  • 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 

  • GOUPILLAUD, P.L. (1961). An approach to inverse filtering of near-surface layer effects from seismic records. Geophysics, 26, 754–760.

    Article  Google Scholar 

  • GRANT, J.A. (1986). The isocon diagram; a simple solution to Gresen’s equation for metasomatic alteration. Economic Geology, 81, 1976–1982.

    Article  Google Scholar 

  • GREENBERG, B.G. and SARHAN, A.E. (1959). Matrix inversion, its interest and application in analysis of data. Journal of the American Statistical Association, 54, 755–766.

    Google Scholar 

  • GREENWOOD, H.J. (1975). Thermodynamically valid projections of extensive phase relationships. The American Mineralogist, 60, 1–8.

    Google Scholar 

  • GRESENS, R.L. (1967). Composition-volume relationships of metasomatism. Chemical Geology, 2, 47–55.

    Article  Google Scholar 

  • GREVILLE, T.N.E. (1959). The pseudoinverse of a rectangular or singular matrix and its application to the solution of systems of linear equations. SIAM Review, 1, 38–43.

    Article  Google Scholar 

  • GRIFFITHS, C.M. (1982). A proposed geologically consistent segmentation and reassignment algorithm for petrophysical borehole logs. In: CUBITT, J.M. and REYMENT, R.A. (eds.). Quantitative stratigraphic correlation. Chichester, John Wiley & Sons, 287–298.

    Google Scholar 

  • GRIFFITHS, J.C. (1967a). Unit regional value as basis for decision-making in selecting an exploration strategy [abstract]. AAPG Bulletin, 51, 467.

    Google Scholar 

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

    Book  Google Scholar 

  • GUIRAUD, M. and POWELL, R. (2006). P-V-T relationships and mineral equilibria in inclusions in minerals. Earth and Planetary Science Letters, 244, 683–694.

    Article  Google Scholar 

  • GUNDUZ, O. and ARAL, M.M. (2005). A Dirac Delta function notation for source/sink terms in groundwater flow. Journal of Hydrological Engineering, 10, 420–427.

    Article  Google Scholar 

  • HAMMING, R.W. (1977). Digital filters. Englewood Cliffs, NJ, Prentice-Hall.

    Google Scholar 

  • HANNA, M.T. (2003). Multiple signal extraction by multiple interference attenuation in the presence of random noise in seismic array data. IEEE Transactions on Signal Processing, 51, 1683–1694.

    Article  Google Scholar 

  • HARE, E.W., MILLER, J.R. and EDWARDS, G.R. (1985). Studies of the vegetation red reflectance edge in geobotanical remote sensing. In: TILL, S.M. and BAJZAK, D. (eds.). Proceedings of the 9th Canadian Symposium on Remote Sensing, August 14–17, 1984, St. Johns, Newfoundland. Kanata, ON, Canadian Aeronautics and Space Institute, 433–440.

    Google Scholar 

  • HARFF, J. and MERRIAM, D.F. (eds.) (1993). Computerised basin analysis. New York, NY, Plenum Publishing.

    Google Scholar 

  • HARKRIDER, D.G. and ANDERSON, D.L. (1962). Computation of surface wave dispersion for multilayered anisotropic media. Bulletin of the Seismological Society of America, 52, 321–332.

    Google Scholar 

  • HARRIS, F.J. (1977). Trigonometric transforms: A unique introduction to the FFT. Technical Publication DSP-005, San Diego, CA, Scientific-Atlanta, Spectral Dynamics Division.

    Google Scholar 

  • HASTINGS, N.A.J. and PEACOCK, J.B. (1974). Statistical distributions. New York, NY, John Wiley & Sons.

    Google Scholar 

  • HEALY, M.J.R. (1963). Programming multiple regression. The Computer Journal, 6, 57–61.

    Article  Google Scholar 

  • HEILBRONNER, R. and BARRETT, S. (2014). Image analysis in earth Sciences. Microstructures and textures of earth materials. Berlin, Springer-Verlag.

    Book  Google Scholar 

  • HERBERT SMITH, G.F. (1907). The construction and use of the moriogram. Mineralogical Magazine, 14, 49–53.

    Article  Google Scholar 

  • HERSH, A.H. (1934). Evolutionary relative growth in Titanotheres. American Naturalist, 68, 537–561.

    Article  Google Scholar 

  • HINRICHS, G. (1868). On the composition, valuation and proximate analysis of Iowa coals. In: WHITE, C.A. and HINRICHS, G. (eds.). First and second annual report of progress by the State Geologist and the Assistant and Chemist on the Geological Survey of The State of Iowa also extracts originally contributed to scientific journals as a part of the work of the Survey. Des Moines, IA, F.W. Palmer, 248–268.

    Google Scholar 

  • HOHN, M.E. (1976). Binary coefficients: A theoretical and empirical study. Journal of the International Association for Mathematical Geology, 8, 137–150.

    Article  Google Scholar 

  • HOUSEHOLDER, A.S. (1964). The theory of matrices in numerical analysis. New York, NY, Blaisdell Publishing.

    Google Scholar 

  • HOUTERMANS, F.G. (1946). Die Isotopenhäufigkeiten im natürlichen Blei und das Alter des Urans [The isotopic abundances in natural lead and the age of the uranium]. Naturwissenschaften, 33, 185–186, 219.

    Article  Google Scholar 

  • HOWARTH, R.J. (2003). The J-chart: a simple plot that combines the capabilities of the Shewhart and cusum charts, for use in analytical quality control. Royal Society of Chemistry, AMC Technical Brief no 12 [online: www.rsc.org/lap/rsccom/amc/amc_index.htm].

  • 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 

  • 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 

  • HUXLEY, J. (1932). Problems of relative growth. London, Methuen.

    Google Scholar 

  • HYDE, E.W. (1890). The directional calculus: Based upon the methods of Hermann Grassmann. Boston, MS, Ginn & Co.

    Google Scholar 

  • HYVÄRINEN, A. and OJA, E. (2000). Independent Component Analysis: Algorithms and Applications. Neural Networks, 13, 411–430.

    Article  Google Scholar 

  • INMAN, D.L. (1952). Measures for describing the size distribution of sediments. Journal of Sedimentary Petrology, 22, 125–145.

    Google Scholar 

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

    Google Scholar 

  • JACKSON, P.L. (1963). Signal enhancement through an ensemble presentation. Bulletin of the Seismological Society of America, 53, 585–591.

    Google Scholar 

  • JEFFERSON, C.W. and SPIRITO, W.A. (eds.) (2003). Mineral and energy resource assessment of the Tlogotsho Plateau, Nahanni Karst, Ragged Ranges and adjacent areas under consideration for expansion of Nahanni National Park Reserve, Northwest Territories. Open Files 1686 and 1576 [CD-ROM], Ottawa, ON, Geological Survey of Canada, Mineral Resources Division.

    Google Scholar 

  • JOHNSON, A.K., BREWSTER, D. and BERGHAUS, H.K.W. (1848). The physical atlas. A series of maps and notes. The geographical distribution of natural phenomena. Edinburgh, William Blackwood and Sons.

    Google Scholar 

  • JONES, V.L. (1956). Extrapolation and interpolation formulae adaptable to desk and other types of digital computers. Geophysics, 21, 1047–1054.

    Article  Google Scholar 

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

    Google Scholar 

  • JOURNEL, A.G. (1982). The indicator approach to estimation of spatial distributions. In: Proceedings of the 17th APCOM Symposium, Society of Mining Engineers of the AIMMPE, Port City Press, New York, 793–806.

    Google Scholar 

  • JOURNEL, A.G. (1988). New distance measures: the route towards truly non-Gaussian geostatistics. Mathematical Geology, 20, 459–475.

    Article  Google Scholar 

  • JUTTEN, C. and HÉRAULT, J. (1991). Blind separation of sources. Part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing, 24, 1–10.

    Article  Google Scholar 

  • KAGAN, Y.Y. (1993). Statistics of characteristic earthquakes. Bulletin of the Seismological Society of America, 83, 7–24.

    Google Scholar 

  • KAY, M. (1945). Palaeogeographic and palinspastic maps. Bulletin of the American Association of Petroleum Geologists, 29, 426–450.

    Google Scholar 

  • KELLEY, J.L. (1955). General topology. Princeton, NJ, Van Nostrand Reinhold.

    Google Scholar 

  • KENDALL, M.G. (1969). The early history of index numbers. Review of the International Statistical Institute, 37 (1), 1–12.

    Article  Google Scholar 

  • KENYON, A.M., INGOLD, L. and HEDRICK, E.R. (1913). Trigonometry. New York, NY, Macmillan.

    Google Scholar 

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

    Article  Google Scholar 

  • KING, T. (1996). Quantifying nonlinearity and geometry in time series of climate. Quaternary Science Reviews, 15, 247–266.

    Article  Google Scholar 

  • KLEENE, S.C. (1981). The theory of recursive functions, approaching its centennial. Bulletin of the American Mathematical Society, new ser., 5, 43–61.

    Article  Google Scholar 

  • KOVACH, R.L. and ANDERSON, D.L. (1964). Higher mode surface waves and their bearing on the structure of the earth’s mantle. Bulletin of the Seismological Society of America, 54, 161–182.

    Google Scholar 

  • KRUMBEIN, W.C. (1934b). The probable error of sampling sediments for mechanical analysis. American Journal of Science, ser. 5, 27, 204–214.

    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. (1937). Sediments and exponential curves. The Journal of Geology, 45, 577–601.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1938). Size frequency distributions of sediments and the normal phi curve. Journal of Sedimentary Petrology, 8, 84–90.

    Article  Google Scholar 

  • KRUMBEIN, W.C. (1945). Recent sedimentation and the search for petroleum. AAPG Bulletin, 29, 1233–1261.

    Google Scholar 

  • KRUMBEIN, W.C. and GARRELS, R.M. (1952). Origin and classification of chemical sediments in terms of pH and oxidation reduction potentials. The Journal of Geology, 60, 1–33.

    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 GRIFFITH, J.S. (1938). Beach environment at Little Sister Bay, Wisconsin. Bulletin of the Geological Society of America, 49, 629–652.

    Article  Google Scholar 

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

    Google Scholar 

  • LACROIX, S.F. (1806). Traité élémentaire de calcul différentiel et de calcul intégral [Elementary treatise on differential and integral calculus].. Paris, Courcier.

    Google Scholar 

  • LAMÉ, G. (1852). Leçons sur la théorie mathématique de l’élasticité des corps solides [Lessons on the mathematical theory of the elasticity of solid bodies]. Paris, Bachelier.

    Google Scholar 

  • LAMÉ, G. (1859). Leçons sur les coordonées curvilignes et leurs diverses applications [Lessons on curvilinear coordinates and their various applications]. Paris, Mallet-Bachelier.

    Google Scholar 

  • LATTMAN, L.H. and RAY, R.G. (1965). Aerial photographs in field geology. New York, NY, Holt, Reinhardt & Winston.

    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 

  • LEBEDEV, S. and VAN DER HILST, R.D. (2008). Global upper-mantle tomography with the automated multimode inversion of surface and S-wave forms. Geophysical Journal International, 173, 505–518.

    Article  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 

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

    Article  Google Scholar 

  • LISLE, R.J., MARTÍNEZ, F., BOBILLO-ARES, N., MENÉNDEZ, O., ALLER, J. and BASTIDA, F. (2006). FOLD PROFILER – A MATLAB-based program for fold shape classification. Computers & Geosciences, 32, 102–108.

    Article  Google Scholar 

  • LLOYD, H. (1849). On the mean results of observations. The Transactions of the Royal Irish Academy, 22, 61–73.

    Google Scholar 

  • LONG, L.T. and KAUFMANN, R.D. (2013). Acquisition and analysis of terrestrial gravity data. Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • LUEDER, D.R. (1959). Aerial photographic interpretation. New York, NY, McGraw-Hill Book Co.

    Google Scholar 

  • LUQUE-ESPINAR, J.A., CHICA-OLMO, M. and PARDO-IGÚZQUIA, E. (2008). Climatological cycles in groundwater levels in a detritic aquifer. In: DRAGONI, W. and SUKHIJA, B.S. (eds.). Climate change and groundwater. Geological Society Special Publication 288. London, The Geological Society, 53–62.

    Google Scholar 

  • MACDOUGALL, J.D. (1979). The distribution of total alpha radioactivity in selected manganese nodules from the North Pacific: Implications for growth process. In: BISCHOFF, J.L. and PIPER, D.Z. (eds.). Marine geology and oceanography of the Pacific manganese nodule province. Marine Science v. 9. New York, NY, Plenum Press, 775–789.

    Chapter  Google Scholar 

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

    Google Scholar 

  • MANCEY, S.J. (1982). Cluster analysis in geology. In: HORDER, M.F. and HOWARTH, R.J. (eds.). Computer applications in geology I and II. Miscellaneous Paper no. 14. London, The Geological Society, 89–102.

    Google Scholar 

  • MANDELBROT, B. (1967). How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, new ser., 156, 636–638.

    Google Scholar 

  • MARBLE, J.P. (1936). Lead-Uranium ratio of siliceous pitchblende from Great Bear Lake, N.W.T., Canada, and its possible age. Journal of the American Chemical Society, 58, 434–437.

    Article  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 

  • MARTIN, E.W. (1965). Electronic data processing: an introduction. Homewood, IL, R.D. Irwin.

    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 

  • MATHERON, G. (1967). Kriging or polynomial interpolation procedures? A contribution to polemics in mathematical geology. Canadian Institute of Mining and Metallurgy Transactions, 70, 240–244.

    Google Scholar 

  • McCAMMON, R.B., BOTBOL, J.M., SINDING-LARSEN, R. and BOWEN, R.W. (1984). The New Characteristic Analysis (NCHARAN). United States Geological Survey Bulletin 1621, Washington, DC, United States Government Printing Office.

    Google Scholar 

  • MELBOURNE, A.J. and PUGMIRE, J.M. (1965). A small computer for the direct processing of FORTRAN statements. Computer Journal, 8, 24–27.

    Article  Google Scholar 

  • MERRIMAN, M. (1877). Elements of the method of least squares. London, Macmillan.

    Google Scholar 

  • MILLER, V.C. and MILLER, C.F. (1961). Photogeology. New York, NY, McGraw-Hill Book Co.

    Google Scholar 

  • MOORE, E.H. (1935). Lectures on general analysis. Memoirs of the American Philosophical Society, 1, 197–209.

    Google Scholar 

  • MORAN, J.H., COUFLEAU, M.A., MILLER, G.K. and TIMMONS, J.P. (1962). Automatic computation of dipmeter logs digitally recorded on magnetic tape. Journal of Petroleum Technology, 14, 771–782.

    Article  Google Scholar 

  • NEUMANN, F. (1925). Some remarks on certain earthquakes of 1925. The problem of determining epicentres. Bulletin of the Seismological Society of America, 15, 114–121.

    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 

  • NICHOLS, E.W. (1900). Differential and integral calculus. Boston, MS, D.C. Heath.

    Google Scholar 

  • NÖBELING, G. (1935). Zur Topologie der Mannigfaltigkeiten [On topology of manifolds]. Monatshefte für Mathematik und Physik, 42, 117–152.

    Article  Google Scholar 

  • OHM, G.S. (1839). Bemerkungen über Combinationstöne und Stosse [Remarks on combination tones and pulses]. Poggendorff’s Annalen der Physik und Chemie, 47, 463–466.

    Article  Google Scholar 

  • OLIVER, D.S. (2003). Gaussian cosimulation: Modelling of the cross-covariance. Mathematical Geology, 35, 681–698.

    Article  Google Scholar 

  • OLSEN, E.C. and MILLER, R.L. (1951). Relative growth in palaeontological studies. Journal of Palaeontology, 25, 212–223.

    Google Scholar 

  • OPTNER, S.L. (1965). Systems analysis for business and industrial problem solving. Englewood Cliffs, NJ, Prentice-Hall.

    Google Scholar 

  • OWEN, L. (1923). Notes on the phosphate-deposit of Ocean Island; with remarks on the phosphates of the equatorial belt of the Pacific Ocean. Quarterly Journal of the Geological Society, London, 79, 1–15.

    Article  Google Scholar 

  • PARKER, R.L. (1970). The inverse problem of electrical conductivity in the mantle. Geophysical Journal of the Royal Astronomical Society, 22, 121–138.

    Article  Google Scholar 

  • PARKER, R.L. (1972). Inverse theory with grossly inadequate data. Geophysical Journal of the Royal Astronomical Society, 29, 123–138.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • PARKER, R.L. (1994). Geophysical inverse theory. Princeton, NJ, Princeton University Press.

    Google Scholar 

  • PATTERSON, C. (1956). Age of meteorites and the Earth. Geochimica et Cosmochimica Acta, 10, 230–237.

    Article  Google Scholar 

  • PAUL, M.K. (1961). On computation of second derivatives from gravity data. Pure and Applied Geophysics, 48, 7–15.

    Article  Google Scholar 

  • PEARSON, K. (ed.) (1922). Tables of the incomplete Γ [Gamma] function computed by the staff of the Department of Applied Statistics, University of London, University College. London, His Majesty’s Stationary Office.

    Google Scholar 

  • PEARSON, K. (ed.) (1934). Tables of the incomplete Beta-function. Cambridge, The Trustees of Biometrika.

    Google Scholar 

  • PEIKERT, E.W. (1969). Developments at the man-machine interface. In: MERRIAM, D.F. (ed.). Computer applications in the earth sciences. Proceedings of a conference on the state of the art held on campus at The University of Kansas, Lawrence on 16–18 June 1969. New York, Plenum Press, 1–11.

    Chapter  Google Scholar 

  • PERKINS, E.H., BERMAN, R. and BROWN, T.H. (1986b). Software for the computation and graphical display of intensive variable phase diagrams. In: JACKSON, K.J. and BOURCIER, W.L., (eds.). Proceedings of the Workshop on Geochemical Modelling. September 14–17, 1986. Fallen Leaf Lake, California, Lawrence Livermore National Laboratory, Livermore CA, 176–183.

    Google Scholar 

  • PERKINS, E.H., BROWN, T.H. and BERMAN, R.G. (1986a). PT-SYSTEM, TX-SYSTEM, PX-SYSTEM: Three programs which calculate pressure-temperature-composition phase diagrams. Computers & Geosciences, 12, 749–755.

    Article  Google Scholar 

  • PETERMANN, A. and MILNER, T. (1850). Atlas of physical geography with descriptive letter-press, embracing a general view of the physical phenomena of the Globe. The atlas of physical geography. London, W.S. Orr.

    Google Scholar 

  • PETROU, M. and PETROU, C. (2010). Image processing: The fundamentals. 2nd edn., Chichester, John Wiley & Sons.

    Book  Google Scholar 

  • PIKE, R. (1992). Machine visualization of synoptic topography by digital image processing. 2016,. In: WILTSHIRE, D.A. (ed.). Selected papers in the applied computer sciences. United States Geological Survey Bulletin 2016. Washington, DC, Government Publications Office, B1–B12.

    Google Scholar 

  • PRESS, W.H., FLANNERY, B.P., TEUKOLSKY, S.A. and VETTERLING, W.T. (1992). Backus-Gilbert method. In: PRESS, W.H., TEUKOLSKY, S.A., VETTERLING, W.T. and FLANNERY, B.P. (eds.). Numerical recipes in Fortran 77. The art of scientific computing. 2nd edn., Cambridge, Cambridge University Press, 806–809.

    Google Scholar 

  • RABBANI, M. and JONES, P.W. (1991). Digital image compression techniques. Bellingham, WA, SPIE Optical Engineering Press.

    Book  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 

  • RASHED, T. and WEEKS, J. (2003). Assessing vulnerability to earthquake hazards through spatial multicriteria analysis of urban areas. International Journal of Geographical Information Science, 17, 547–576.

    Article  Google Scholar 

  • REED, J.J. (1964). Machine-punched cards for cataloguing rocks and minerals. New Zealand Journal of Geology and Geophysics, 7, 573–584.

    Article  Google Scholar 

  • RESCHER, N. (1954). Leibniz’s interpretation of his logical calculi. The Journal of Symbolic Logic, 19, 1–13.

    Article  Google Scholar 

  • RIAL, J.A. (2003). Earth’s orbital eccentricity and the rhythm of the Pleistocene ice ages; the concealed pacemaker. Global and Planetary Change, 41, 81–93.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • RILEY, J.D. (1955). Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix. Mathematical Tables and Other Aids to Computation, 9 (51), 96–101.

    Article  Google Scholar 

  • ROBINSON, A.H. (1961). The cartographic representation of the statistical surface. International Yearbook of Cartography, 1, 53–63.

    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 

  • ROERO, C.S. (2005). Gottfried Wilhelm Leibniz first three papers on the calculus (1684, 1686, 1693). In: GRATTAN-GUINNES, I. (ed.). Landmark writings in Western mathematics (1640–1940). Amsterdam, Elsevier, 46–58.

    Chapter  Google Scholar 

  • ROLLINSON, H.R. (1993). Using geochemical data: evaluation, presentation, interpretation. Harlow, Longman.

    Google Scholar 

  • RUTHERFORD, S. and D’HONDT, S. (2000). Early onset and tropical forcing of 100,000-year Pleistocene glacial cycles. Nature, 408, 72–75.

    Article  Google Scholar 

  • SABATIER, P.C. (2009). Inverse problems: anniversary and short review of generalized inverse scattering transforms. Inverse Problems, 25, 1–20.

    Article  Google Scholar 

  • SANDERSON, P.C. (1973). Interactive computing in BASIC. London, Butterworth.

    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 

  • SARMA, D.D. and SELVARAJ, J.B. (1990). Two-dimensional orthonormal trend surfaces for prospecting. Computers & Geosciences, 16, 897–909.

    Article  Google Scholar 

  • SCALES, J.A. (1995). Theory of seismic imaging. Berlin, Springer-Verlag.

    Google Scholar 

  • SHAW, N. (1911). Forecasting weather. London, Constable.

    Google Scholar 

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

    Google Scholar 

  • SHEYNIN, O. (1994). Chebyshev’s lectures on the theory of probability. Archive for History of Exact Sciences, 46, 321–340.

    Article  Google Scholar 

  • SIMON, H.A. (1973). The structure of ill-structured problems. Artificial Intelligence, 4, 181–201.

    Article  Google Scholar 

  • SIMPSON, T. (1743). Mathematical dissertations on a variety of physical and analytical subjects. London, T. Woodward.

    Google Scholar 

  • SMITH, P.F. and GALE, A.S. (1904). The elements of analytic geometry. New York, Ginn.

    Google Scholar 

  • SNEATH, P.H.A. (1968). Vigour and pattern in taxonomy. Journal of General Microbiology, 54, 1–11.

    Article  Google Scholar 

  • SNEATH, P.H.A. (1979). BASIC program for identification of an unknown with presence-absence data against an identification matrix of percent positive characters. Computers & Geosciences, 5, 195–213.

    Article  Google Scholar 

  • SNELL, O. (1892). Die Abhängigkeit des Hirngewichts von dem Körpergewicht und den geistigen Fähigkeiten [The dependence of brain weight on body weight and mental faculties]. Archiv fur Psychiatrie und Nervenkrankheiten, 23, 436–446.

    Article  Google Scholar 

  • SOKAL, R.R. (1961). Distance as a measure of taxonomic similarity. Systematic Zoology, 10, 70–79.

    Article  Google Scholar 

  • SOUTHARD, D.A. (1992). Compression of digitized map images. Computers & Geosciences, 18, 1213–1253.

    Article  Google Scholar 

  • SOUTHWELL, R.V. (1940). Relaxation methods in engineering science: a treatise on approximate computation. Oxford, Clarendon Press.

    Google Scholar 

  • SUTTERLIN, P.G. and VISHER, G.S. (1990). The use of expert systems in identification of siliciclastic depositional systems for hydrocarbon reservoir assessment. In: GAÁL, G. and MERRIAM, D.F. (eds.). Computer applications in resource estimation. Prediction and assessment for metals and petroleum. Computers & Geology, v. 7. Oxford, Pergamon Press, 347–365.

    Chapter  Google Scholar 

  • TANER, M.T., KOEHLER, F. and SHERIFF, R.E. (1979). Complex seismic trace analysis. Geophysics, 44, 1041–1063.

    Article  Google Scholar 

  • TARANIK, J.V. (1978). Principles of computer processing of LANDSAT data for geologic applications. Open File Report 78-117, Sioux Falls, SD, United States Geological Survey.

    Google Scholar 

  • TARANTOLA, A. (2005). Inverse problem theory and methods for model parameter estimation. Philadelphia, PA, Society for Industrial and Applied Mathematics.

    Google Scholar 

  • TARANTOLA, A. and VALETTE, B. (1982). Inverse problems = Quest for information. Journal of Geophysics, 50, 159–170.

    Google Scholar 

  • TARLOWSKI, Z. (1982). Direct and inverse problems in local electromagnetic induction. Surveys in Geophysics, 4, 395–404.

    Article  Google Scholar 

  • TAUBMAN, D.S. and MARCELLIN, M.W. (2001). JPEG 2000: Image compression fundamentals, standards and practice. Norwell, MS, Kluwer Academic Publishers.

    Google Scholar 

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

    Google Scholar 

  • THRALL, R.M. and TORNHEIM, L. (1957). Vector spaces and matrices. London, Chapman & Hall.

    Google Scholar 

  • TODHUNTER, I. and PEARSON, K.P. (1886). A history of the theory of elasticity and of the strength of materials: from Galilei to the present time. Vol. 1. Galilei to Saint-Venant 1639–1850. Cambridge, Cambridge University Press.

    Google Scholar 

  • TUFTE, E.R. (2001). Envisioning information. 2nd edn., Cheshire, CT, Graphics Press.

    Google Scholar 

  • TURING, A.M. (1948). Rounding-off errors in matrix processes. Quarterly Journal of Mechanics and Applied Mathematics, 1, 287–308.

    Article  Google Scholar 

  • TUSKA, C.D. (1944). Historical notes on the determination of distance by timed radio waves. Journal of the Franklin Institute, 237, 1–20.

    Article  Google Scholar 

  • UNITED STATES DEPARTMENT OF DEFENSE (1961). COBOL. Report to Conference on Data Systems Languages including initial specifications for a Common Business Oriented Language (COBOL) for programming electronic digital computers. Washington, DC, United States Government Printing Office.

    Google Scholar 

  • van der BAAN, M. (2006). PP/PS Wavefield separation by independent component analysis. Geophysical Journal International, 166, 339–348.

    Article  Google Scholar 

  • VASCO, D.W. (1986). Extremal inversion of travel-time residuals. Bulletin of the Seismological Society of America, 76, 1828–1845.

    Google Scholar 

  • VERMA, S.P. and RIVERA-GÓMEZ, M.A. (2013). Computer programs for the classification and nomenclature of igneous rocks. Episodes, 36, 115–124.

    Google Scholar 

  • VISTELIUS, A.B. (1964a). Informational characteristic of frequency distributions in geochemistry. Nature, 202, 1206.

    Article  Google Scholar 

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

    Google Scholar 

  • VOLGER, G.H.O. (1856). Untersuchungen über das letztjährige Erdbeben in Central-Europa [Investigations into last year’s earthquake in Central Europe]. Petermann’s Geographische Mittheilungen, 2, 85–102.

    Google Scholar 

  • von HUMBOLDT, A. and BONPLAND, A. (1825). Relation historique du voyage aux régions équinoxiales du Nouveau Continent, fait en [Personal narrative of travels to the equatorial regions of the New Continent (America), made in] 1799, 1800, 1801, 1802, 1803 et 1804. v. 10. Paris, J. Smith and Gide.

    Google Scholar 

  • WADELL, H. (1936). Volume, shape, and shape-position of rock fragments in open-work gravel. Geographiska Annaler, 18, 74–92.

    Article  Google Scholar 

  • WALLIS, J. (1656). Arithmetica Infinitorum [The arithmetic of infinitesimals]. Oxford, Leon Lichfield.

    Google Scholar 

  • WALSH, J.L. (1923). A closed set of normal orthogonal functions. American Journal of Mathematics, 45, 5–24.

    Article  Google Scholar 

  • WATSON, H.W. and GALTON, F. (1875). On the probability of the extinction of families. Journal of the Anthropological Institute of Great Britain, 4, 138–144.

    Article  Google Scholar 

  • WEBB, J.S., THORNTON, I., THOMPSON, M., HOWARTH, R.J. and LOWENSTEIN, P.L. (1978). The Wolfson geochemical atlas of England and Wales. Oxford, Clarendon Press.

    Google Scholar 

  • WEBER, H.C. (1939). Thermodynamics for chemical engineers. New York, NY, John Wiley & Sons.

    Google Scholar 

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

    Book  Google Scholar 

  • WEEDON, G.P., COE, A.L. and GALLOIS, R.W. (2004). Cyclostratigraphy, orbital tuning and inferred productivity for the type Kimmeridge Clay (Late Jurassic), Southern England. Journal of the Geological Society, 161, 655–666.

    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 

  • WILLCOX, W.R., LAPAGE, S.P., BASCOMB, S. and CURTIS, M.A. (1973). Identification of Bacteria by Computer: Theory and Programming. Journal of General Microbiology. 77, 317–330.

    Article  Google Scholar 

  • WOLLASTON, W.H. (1809). Description of a reflective goniometer. Philosophical Transactions of the Royal Society, London, 99, 253–258.

    Article  Google Scholar 

  • WOODWARD, P.M. (1953). Probability and information theory, with applications to radar. London, Pergamon.

    Google Scholar 

  • WORONOW, A. and BUTLER, J.C. (1986). Complete subcompositional independence testing of closed arrays. Computers & Geosciences, 12, 267–279.

    Article  Google Scholar 

  • WRINCH, D.M. and JEFFREYS, H. (1919). On some aspects of the theory of probability. Philosophical Magazine, ser. 6, 38, 715–731.

    Article  Google Scholar 

  • YOUNG, D.M. (1954). Iterative methods for solving partial difference equations of the elliptic type. Transactions of the American Mathematical Society, 76, 92–111.

    Article  Google Scholar 

  • YOUNG, D.M. (1989). A historical review of iterative methods. In: NASH, S.G. (ed.). A history of scientific computation. Reading, MA, Addison-Wesley, 180–194.

    Google Scholar 

  • YOUNG, J.R. (1833). The elements of analytical geometry. London, John Souter.

    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 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Howarth, R.J. (2017). I. In: Dictionary of Mathematical Geosciences . Springer, Cham. https://doi.org/10.1007/978-3-319-57315-1_9

Download citation

Publish with us

Policies and ethics