Enhancement of direct waves based on the probability density function of seismic wave amplitudes

Mitsutaka Oshima, Hiroshi Takenaka

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The enhancement of direct waves in seismic records is desirable in various seismological situations, where the accurate picking of seismic phases is necessary for hypocentre location, spectral inversion, waveform inversion and seismic tomography. In this study, we developed a new method to enhance direct waves in seismic waveforms based on the statistical distribution (probability density function, PDF) of the amplitudes of waveforms. The seismic waveform changes from a direct wave to a coda wave as time proceeds, which also causes the PDF of its amplitude to vary with time. The PDF becomes similar to a Gaussian or Rayleigh distribution with time, and hence, direct waves can be enhanced using the dissimilarity between the PDF of the amplitude of the seismic waveform and the Gaussian or Rayleigh distribution. In the proposed method, the Kullback-Leibler divergence is used to measure dissimilarity and it is applied as a weight. We confirmed that the method can effectively enhance direct P and S waves by applying it to seismic records of the 2016 Kumamoto earthquake, synthetic waveforms with noise and volcanic events. The method was also applied to waveforms of the 2008 Iwate-Miyagi Nairiku earthquake, which revealed that direct waves were enhanced, and an overview of the wave field and rupture process was obtained. The proposed method can detect direct waves even from subevents, thereby producing detailed information on the earthquake rupture process. We detected two significant pulses and determined their source location and rupture times. The estimated pulse sources were consistent with parts of the rupture scenario proposed by the previous studies. In addition, for local and teleseismic event records, the proposed method was compared with other methods to study its merits and demerits. The present method can enhance seismic phases on records of local and teleseismic events. Our method detects or enhances direct waves based neither on their amplitudes nor on their temporal variations but on the statistical distribution of their amplitudes, which has both advantages and disadvantages. Although polarization filtering is a powerful method that can enhance seismic phases, it requires three-component waveforms. The proposed method can be applied even to a single component record, which is a significant advantage.

Original languageEnglish
Pages (from-to)327-354
Number of pages28
JournalGeophysical Journal International
Issue number1
Publication statusPublished - Oct 1 2022


  • Body waves
  • Coda waves
  • Statistical methods
  • Time-series analysis
  • Wave scattering and diffraction

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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