History of the Wave Equation and Transforms in Engineering

  • Enders A. Robinson
Part of the Review of Progress in Quantitative Nondestructive Evaluation book series


Using Newton’s recently formulated laws of motion, Brook Taylor (1685–1721) discovered the wave equation by means of physical insight alone [1]. Daniel Bernouli (1700–1782) showed that an infinite summation of sinusoids can represent the general solution of the wave equation with given initial conditions [2]. Finally Jean Baptiste Joseph Fourier (1768–1830) showed that such an infinite sum, a Fourier series, can represent any discontinuous function under general conditions [3]. From this early work connecting the wave equation and the Fourier transform, much of engineering mathematics of wave motion and transformations has been developed.


Wave Equation Seismic Wave Wave Motion Ocean Wave Seismic Trace 
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  1. 1.
    B. Taylor, Methodus Incrementorum Directa et Inversa( London, England, 1715 )Google Scholar
  2. 2.
    D. Bernoulli, Hydrodynamics ( Basel, Switzerland, 1738 )Google Scholar
  3. 3.
    J. Fourier, Théorie Analytique de la Chaleur ( Didot, Paris, 1822 )Google Scholar
  4. 4.
    E.A. Robinson, Seismic Velocity Analysis and the Convolutional Model( Prentice Hall, Englewood Cliffs, N.J., 1983 )Google Scholar
  5. 5.
    E.A. Robinson, Seismic Inversion and Deconvolution( Pergamon Press, New York, 1984 )Google Scholar
  6. 6.
    A.J. Berkhout, Seismic Migration-Imaging of Acoustic Energy by Wave field Extrapolation( Elsevier, Amsterdam, 1980 )Google Scholar
  7. 7.
    J. Claerbout, Fundamentals of Geophysical Data Processing( McGraw-Hill, New York, 1976 )Google Scholar
  8. 8.
    R. Stolt, “Migration by Fourier transform,” Geophys., vol. 43, pp. 23–48, 1978CrossRefGoogle Scholar
  9. 9.
    J. Gazdag, “Wave equation migration with the phase shift method,” Geophys., vol. 43, p. 1342–1351, 1978CrossRefGoogle Scholar
  10. 10.
    E.A. Robinson, Migration of Geophysical Data( Prentice Hall, England Cliffs, N.J., 1983 )Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Enders A. Robinson
    • 1
  1. 1.Department of GeosciencesThe University of TulsaTulsaUSA

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