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Wu Y Q，Zhang H M. 2018. Determining the threshold value in upper limit of wavenumber integration by reflection-transmission coefficient in theoretical seismograms calculation. Acta Seismologica Sinica，40（6）：719−727. doi：10.11939/jass.20180013. DOI: 10.11939/jass.20180013
Citation: Wu Y Q，Zhang H M. 2018. Determining the threshold value in upper limit of wavenumber integration by reflection-transmission coefficient in theoretical seismograms calculation. Acta Seismologica Sinica，40（6）：719−727. doi：10.11939/jass.20180013. DOI: 10.11939/jass.20180013
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Determining the threshold value in upper limit of wavenumber integration by reflection-transmission coefficient in theoretical seismograms calculation

  • School of Earth and Space Sciences，Peking University，Beijing 100871，China

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  • Received Date: January 14, 2018
  • Revised Date: July 08, 2018
  • Available Online: November 04, 2018
  • Published Date: October 31, 2018
    Graphical Abstract
    • Abstract
  • In multi-layered half-space, the displacement field is expressed as the integration of wavenumber k using reflection-transmission (R/T) coefficient when the seismogram is calculated in numerical ways in the frequency domain. Therefore, some special methods were introduced to solve those kinds of integration as to accelerate computation. For example, when the depth of source is equal or close to that of receiver, the peak-trough averaging method (PTAM) is applied. To apply PTAM, however, one must determine the threshold value called kc after which the integration oscillates regularly. In previous studies, kc was estimated empirically without theoretical support. In this study, a scheme based on theoretical analysis to determine kc is proposed, and kc is related to the R/T coefficients. According to the generalized R/T coefficient method, violent variation of integrand will occur when the determinant of relevant R/T coefficient vanishes. We show by examples that for a given frequency, root of the determinant of the reflection coefficient on the free surface is a proper value for kc. Compared with the method calculated with empirical formula, the new method to determine kc will be more efficient for a given precision to prove the validity.
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    • References (31)
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