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Jiang Yan, Chen Xiaofei. 2014: Born approximation paradox of linear finite-frequency theory. Acta Seismologica Sinica, 36(3): 372-389. DOI: 10.3969/j.issn.0253-3782.2014.03.004
Citation: Jiang Yan, Chen Xiaofei. 2014: Born approximation paradox of linear finite-frequency theory. Acta Seismologica Sinica, 36(3): 372-389. DOI: 10.3969/j.issn.0253-3782.2014.03.004
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Born approximation paradox of linear finite-frequency theory

  • 1.

    Institute of Geophysics, China Earthquake Administration, Beijing 100081, China

  • 2.

    School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China

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  • Received Date: May 26, 2013
  • Revised Date: December 14, 2013
  • Published Date: April 30, 2014
    Graphical Abstract
    • Abstract
  • After reviewing the Born approximation problem of linear finite-frequency tomography theory, its scope of application is statistically analyzed by numerical method. The result indicates that the maximum velocity perturbation should not exceed 1% for Born approximation. Then the statistical analyses on the first-order approximation of cross-correlation travel-time also show that it only meets the case of the maximum velocity perturbation less than 1%. However, the maximum velocity perturbation can be 10% for linear finite-frequency theory, which combines Born approximation with the first-order approximation of cross-correlation travel-time. This apparent logic paradox is called “Born approximation paradox”, which is caused by misusage of Born approximation. Thus, Born approximation is discarded in this study; Fréchet derivative and implicit functional theorem are used to deduce linear finite-frequency theory. As a result, Born approximation paradox is explained thoroughly. Since Born approximation has been discarded early in nonlinear finite-frequency theory, this concept is unnecessary in finite-frequency tomography theory.
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