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Popperian geophysics and tunnelling algorithm

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Abstract

Parasnis has observed in a presidential address that geophysics is not a Popperian science in a major way. That is, hypotheses are not consciously put forth in a falsifiable format and much of the effort goes in seeking supporting evidence for favoured hypotheses. Parker evolved a parameter extremization strategy, initially to tackle the problem of non-uniqueness in geophysical inference. Later he based a hypothesis testing proposal on it, which is refreshingly Popperian. It has not been adopted widely, partly because it requires global extrema, and not local and this has been regarded as a problem with no solution. Attention is drawn towards tunnelling algorithm, which solves the problem of global optimization successfully, makes Parker’s Popperian proposal practical and extends the range of Popperian geophysics.

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References

  • Ander M E and Huestis S P 1987 Gravity ideal bodies;Geophysics 52 1265–1278

    Article  Google Scholar 

  • Aoki M 1971Introduction to optimization techniques (New York: Macmillan) pp 146–163

    Google Scholar 

  • Backus G E and Gilbert J F 1970 Uniqueness in the inversion of inaccurate gross earth data;Philos. Trans. R. Soc. London A266 123–192

    Google Scholar 

  • Bellman R E 1961Adaptive control processes (Princeton: University Press)

    Google Scholar 

  • Benvenuto N and Marchesi M 1989 Digital filter design by simulated annealing;IEEE Trans. Circuits System 36 459–460

    Article  Google Scholar 

  • Bohachevsky I, Johnson M and Stein M 1986 Generalized simulated annealing for function optimization;Technometrics 28 209–217

    Article  Google Scholar 

  • Brush S G 1974 Should the history of science be rated X?;Science 183 1164–1172

    Article  Google Scholar 

  • Burley D M 1974Studies in optimization (Norfolk: Intertext Books)

    Google Scholar 

  • Cabrielli C A 1984 Minimum entropy deconvolution and simplicity: a noniterative algorithm;Geophysics 50 394–413

    Article  Google Scholar 

  • Curry H B 1965 The relation of logic to science; InInformation and prediction in science (eds) S Dockx and P Bernays (New York: Academic Press) pp 79–97

    Google Scholar 

  • Dennis Jr J E and Schnabel R B 1983Numerical methods for unconstrained optimization and nonlinear equations (Englewood Cliffs: Prentice Hall) pp 147–152

    Google Scholar 

  • Donoho D 1980 On minimum entropy deconvolution; In:Applied time-series II (ed.) D Findley (New York: Academic Press)

    Google Scholar 

  • Dosso S E and Oldenburg D W 1991 Magnetotelluric appraisal using simulated annealing;Geophys. J. Int. 106 379–385

    Article  Google Scholar 

  • Farhat N H and Bai B 1987 Phased-array antenna pattern synthesis by simulated annealing;Proc. IEEE 75 842–844

    Google Scholar 

  • Goldstein A A and Price J F 1971 On descent from local minima;Math. Comput. 25 569–575

    Article  Google Scholar 

  • Gomez S and Levy A V 1982 The tunnelling method for solving the constrained global optimization problems with several non-connected feasible regions; In:Numerical analysis (ed.) J P Hennart (Berlin; Springer-Verlag) pp 34–37

    Chapter  Google Scholar 

  • Gray W C 1979Variable norm dec (involution; Ph. D Thesis, Stanford Univ.

  • Gubbins D 1975 Can the earth’s magnetic field be sustained by core oscillations?;Geophys. Res. Lett. 2 409–412

    Article  Google Scholar 

  • Halstead B 1980 Karl Popper: good philosophy, bad science;New Sci. 87 215–217

    Google Scholar 

  • Hesse M B 1964 Francis Bacon; In: A critical history of western philosophy (ed.) D J O’Connor (London: The Free Press of Glencoe) pp 145

    Google Scholar 

  • Johnson D S, Aragon C R, McGeoch L A and Schevon C 1989 Optimization by simulated annealing; an experimental evaluation: Part I: Graph partitioning:Oper. Res. 37 865–892

    Article  Google Scholar 

  • Jacoby S L S, Kowalik J S and Pizzo J T 1972Iterative methods for nonlinear optimization problems (Englewood Cliffs: Prentice-Hall) pp 13–25

    Google Scholar 

  • Jordan T H 1975 The continental tectosphere;Rev. Geophys. Space Phys. 13 1–12

    Article  Google Scholar 

  • Khattri K N, Mohan C and Shanker K 1987 A random search technique of nonlinear optimization for the inversion of gravity data; Sixth Indian Geol. Cong. Roorkee: MG-8

  • Kirkpatrick S, Galatt R C D and Vecchi M P 1983 Optimization by simulated annealing;Science 220 671–680

    Article  Google Scholar 

  • Kuhn T S 1970The structure of scientific revolutions (Chicago: The Univ. Chicago Press) 210 pp

    Google Scholar 

  • Lakatos I 1978The methodology of scientific research programmes (London: Cambridge Univ. Press) 45 pp

    Google Scholar 

  • Landa E, Beydoun W and Tarantola A 1989 Reference velocity model estimation from prestacked waveforms: Coherency optimization by simulated annealing;Geophys. 54 984–990

    Article  Google Scholar 

  • Laudan L 1977Progress and its problems: towards a theory of scientific growth (Berkeley: University of California Press)

    Google Scholar 

  • Laudan L 1984Science and values: the aims of science and their role in scientific debate (Berkeley: University of California Press)

    Google Scholar 

  • Le Grand H E 1988Drifting continents and shifting theories (Cambridge: University Press) 313 pp

    Google Scholar 

  • Levy A V and Gomez S 1980 The tunnelling gradient restoration algorithm for the global minimization of nonlinear functions subject to nonlinear inequality constraints, IIMAS-UNAM rep. no. 231

  • Levy A V and Gomez S 1985 The tunnelling method applied to global optimization; In:Numerical optimization (eds) P T Boggs, R H Byrd and R B Schnabel (Philadelphia: Soc. Indust. App. Math.) pp 213–244

    Google Scholar 

  • Levy A V and Montalvo A 1977 The tunnelling algorithm for the global optimization of functions (Dundee: Dundee Bienn. Conf. Numer. Anal.)

  • Levy A V and Montalvo A 1985 The tunnelling algorithm for the global minimization of functions;Soc. Ind. Appl. Math. J. Stat. Comput. 6 15–29

    Google Scholar 

  • Levy A V, Montalvo A, Gomez S and Calderon A 1982 Topics in global optimization; In:Numerical analysis (eds) A Dold and B Eckman (Berlin: Springer-Verlag) pp 18–33

    Chapter  Google Scholar 

  • Menke W 1989Geophysical data analysis: discrete inverse theory (San Diego: Academic Press) pp 155–156

    Google Scholar 

  • Moharir P S 1988A priori information, In (ed.) Murthy Y S (Waltair: Souvenir 14th Ann. Conv. AEG) 67–72

  • Moharir P S 1990 Inversion of potential field data;Proc. Indian Acad. Sci. (Earth. Planet. Sci.) 99 473–514

    Google Scholar 

  • Moharir P S 1992a History syndrome;Proc. Indian Acad. Sci. (Earth Planet. Sci.)

  • Moharir P S 1992b Informative scientific ordination; Geos. (to appear)

  • Montalvo A 1979Desarrollo de un nuevo algoritmo para la minimizacion global de funciones, Ph. D thesis, National Autonomous Univ. Mexico

  • Mora P 1989 Inversion = migration + tomography;Geophysics 54 1575–1586

    Article  Google Scholar 

  • Ooe M and Ulrych T J 1979 Minimum entropy deconvolution with an exponential transformation;Geophys. Prospect. 27 458–473

    Article  Google Scholar 

  • Oldroyd D R 1990The Highlands controversy (Chicago: The University of Chicago Press) 438 p

    Google Scholar 

  • Parasnis D S 1980 A Popperian look at geophysics: Presidential address;Geophys. Prospect. 28 667–673

    Article  Google Scholar 

  • Pardalos P M and Rosen J B 1986 Methods for global concave minimization: a bibliographic survey;SIAM Rev. 28 367–379

    Article  Google Scholar 

  • Pardalos P M and Rosen J B 1987Constrained global optimization: algorithms and applications (Berlin: Springer-Verlag) 143 pp

    Google Scholar 

  • Parker R L 1974 Best bounds on density and depth from gravity data;Geophysics 39 644–649

    Article  Google Scholar 

  • Parker R L 1975 The theory of ideal bodies for gravity interpretation; Geophys;J. R. Astron. Soc. 42 315–334

    Google Scholar 

  • Parker R L 1977 Understanding inverse theory, In:Annu. Rev. Earth Planet. Sci. (eds) F A Donath, F G Stehli, and G W Wetherill5 (Palo Alto: Annual Reviews Inc.) pp 35–64

    Google Scholar 

  • Peirce C S 1957Essays in the philosophy of science (Indianapolis: Bobbs-Merrill) pp 191–192

    Google Scholar 

  • Popper K R 1968The logic of scientific discovery (New York: Harper Torchbooks) 480 pp

    Google Scholar 

  • Popper K R 1984Conjectures and refutations: the growth of scientific knowledge (London: Routledge and Kegan Paul) pp 251–292, 385–413

    Google Scholar 

  • Powell M J D 1982Nonlinear optimization (London: Academic Press) pp 319–335

    Google Scholar 

  • Price W L 1978 A controlled random search procedure for global optimization; In:Towards global optimization 2 (eds) L C W Dixon and G P Szego (Amsterdam: North Holland) pp 71–84

    Google Scholar 

  • Quinton A M 1964 Contemporary British philosophers; In:A critical history of western philosophy (London: The Free Press of Glencoe) 552

    Google Scholar 

  • Ray W H and Szekely J 1973Process optimization (New York: John Wiley) pp 243–244

    Google Scholar 

  • Rothman D H 1985 Nonlinear inversion, statistical mechanics and residual statics estimation;Geophysics 50 2784–2796

    Article  Google Scholar 

  • Rudwick M 1985The great Devonian controversy (Chicago: University Press)

    Google Scholar 

  • Runge R J and Runge K J 1991 Obtaining lumped (blocked) well logs by simulated annealing;Log. Anal. 32 371–377

    Google Scholar 

  • Sastry R G S and Moharir P S 1990 Regularizing tunnelling algorithm in nonlinear gravity problem—a numerical study,IAG Symp. 103 Gravity, gradiometry and gravimetry (eds) R Rummel and R G Hipkin (New York: Springer-Verlag) pp 171–179

    Google Scholar 

  • Schneider Jr W W and Whitman W W 1990 Dipmeter analysis by a Monte Carlo technique;Geophysics 55 320–326

    Article  Google Scholar 

  • Secord J 1986Controversy in Victorian geology (Princeton: University Press)

    Google Scholar 

  • Szu H H and Hartley R L 1987 Nonconvex optimization by fast simulated annealing;Proc. IEEE 75 1538–1540

    Google Scholar 

  • Teotia S S 1985Simple structure deconvolution scheme of seismograms; M. Tech. dissertation (Roorkee: University of Roorkee)

    Google Scholar 

  • Treccani G 1978 A global descent optimization strategy, In:Towards global optimization 2 (eds) L C W Dixon and G P Szego (Amsterdam: North Holland) pp 165–177

    Google Scholar 

  • Wiggins R 1978 Minimum entropy deconvolution;Geoexploration 16 21–35

    Article  Google Scholar 

  • Wiggins R 1985 Entropy guided deconvolution;Geophysics 50 2720–2726

    Article  Google Scholar 

  • Yao Y 1989 Dynamic tunnelling algorithm for global optimization;IEEE Trans. Syst. Man Cybern. 19 1222–1230

    Article  Google Scholar 

Download references

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  1. National Geophysical Research Institute, Uppal Road, 500 007, Hyderabad, India

    P. S. Moharir

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Moharir, P.S. Popperian geophysics and tunnelling algorithm. Proc. Indian Acad. Sci. (Earth Planet Sci.) 101, 1–11 (1992). https://doi.org/10.1007/BF02839168

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