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Spatial variation of coda wave amplitude in media with a localized heterogeneous region


Using an indirect boundary integral method, seismograms are computed for elastic media with localized heterogeneities. Models are two-dimensional homogeneous full spaces (P and SV waves) with many circular cavities as heterogeneities or scatterers. Heterogeneities are localized within a depth range, forming a relatively thin random layer. Seismograms are obtained for receivers at depth 0 km (surface) and for several focal depths, with sources radiating S waves isotropically. Seismograms are composed of the direct S wave and all the possible scattered waves by the heterogeneities, exhibiting late arrivals or coda waves. The coda wave amplitude, or coda energy level, and its duration vary for events with different focal depths. As the focal depth increases and the source gets closer to the layer of localized heterogeneities, the coda level becomes small. When the source is within the heterogeneous layer, however, the coda level becomes larger than for a case of the source either above or below the heterogeneous layer. This local enhancement of coda takes place clearly only in the frequency range for which the scattering is the most effective, that is, when the non-dimensional frequency kd takes values from 2 to 3, where k is the wavenumber and d is the size of each heterogeneity. Such enhancement of coda is not observed when the density of cavities, or strength of the heterogeneities, is reduced. Coda level becomes locally large for a source within the heterogeneous layer only in the case that the heterogeneities are strong enough to excite multiply scattered waves, as compared with the singly scattered ones. Robinson (1987) studied the temporal variation of coda-duration magnitude relative to event magnitude based on P and S wave amplitudes using the seismic network of the Wellington, New Zealand, region. He found that coda-duration magnitude relative to amplitude magnitude decreases with focal depth and becomes large locally for events in the depth range from 65 and 75 km. Our synthetic seismograms explain his results well, implying that there must be a region of localized, strong heterogeneity at depths around 70 km. The effective size of the heterogeneous region may be of about several kilometers because the observation was performed with 1 Hz seismometers. This localized heterogeneous layer is probably associated with the subducting Pacific plate underneath the Wellington region.


  • Aki, K., Analysis of seismic coda of local earthquakes as scattered waves, J. Geophys. Res., 74, 615–631, 1969.

    Article  Google Scholar 

  • Aki, K. and B. Chouet, Origin of coda waves: Source, attenuation, and scattering effects, J. Geophys. Res., 80, 3322–3342, 1975.

    Article  Google Scholar 

  • Benites, R., K. Aki, and K. Yomogida, Multiple scattering of SH waves in 2-D media with many cavities, Pure Appl. Geophys., 138, 353–390, 1992.

    Article  Google Scholar 

  • Benites, R., K. Yomogida, P. M. Roberts, and M. Fehler, Scattering of elastic waves in 2-D composite media I: Theory and test, Phys. Earth Planet. Inter., 104, 161–173, 1997.

    Article  Google Scholar 

  • Chadwick, M. C., The 1991 Hikurangi margin seismic refraction profile, Ph.D. Thesis, Victoria University of Wellington, Wellington, New Zealand, pp. 234, 1997.

    Google Scholar 

  • Gusev, A. A., Vertical profile of turbidity and coda Q, Geophys. J. Int., 123, 665–672, 1995.

    Article  Google Scholar 

  • Herraiz, M. and A. F. Espinosa, Coda waves: A review, Pure Appl. Geophys., 125, 499–577, 1987.

    Article  Google Scholar 

  • Hoshiba, M., Simulation of coda wave envelope in depth dependent scattering, Geophys. Res. Lett., 21, 2853–2856, 1994.

    Article  Google Scholar 

  • Lee, W. H. K., R. E. Bennett, and K. L. Meagher, A method of estimated magnitude of local earthquakes from signal duration, U.S. Geol. Surv. Open File Report, 28, 1972.

  • Li, Y.-G., K. Aki, D. Adams, and A. Hasemi, Seismic guided waves trapped in the fault zone of the Landers, California, earthquake of 1992, J. Geophys. Res., 99, 11705–11722, 1994.

    Article  Google Scholar 

  • Mooney, W. D. and T. M. Brocher, Coincident seismic reflection/refraction studies of the continental lithosphere: A global review, Rev. Geophys., 25, 723–742, 1987.

    Article  Google Scholar 

  • Obara, K. and H. Sato, Existence of an S wave reflector near the upper plane of the double seismic zone beneath the southern Kanto district, Japan, J. Geophys. Res., 93, 15037–15045, 1988.

    Article  Google Scholar 

  • Rautian, T. G. and V. I. Khalturin, The use of the coda for determination of the earthquake source spectrum, Bull. Seismol. Soc. Amer., 68, 923–948, 1978.

    Google Scholar 

  • Robinson, R., Temporal variations in coda duration of local earthquakes in the Wellington region, New Zealand, Pure Appl. Geophys., 125, 579–596, 1987.

    Article  Google Scholar 

  • Sato, H., Attenuation of envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere, J. Geophys. Res., 89, 1221–1241, 1984.

    Article  Google Scholar 

  • Sato, H., H. Nakahara, and M. Ohtake, Synthesis of scattered energy density for non-spherical radiation from a point shear-dislocation source based on the radiative transfer theory, Phys. Earth Planet. Inter., 104, 1–13, 1997.

    Article  Google Scholar 

  • Walcott, R. I., Geodetic strains and large earthquakes in the axial tectonic belt of North Island, New Zealand, J. Geophys. Res., 83, 4419–4429, 1978.

    Article  Google Scholar 

  • Wu, R. S., Attenuation of short period seismic waves due to scattering, Geophys. Res. Lett., 9, 9–12, 1982.

    Article  Google Scholar 

  • Yomogida, K. and R. Benites, Relation between direct wave Q and coda Q: A numerical approach, Geophys. J. Int., 123, 471–483, 1995.

    Article  Google Scholar 

  • Yomogida, K., K. Aki, and R. Benites, Coda Q in two-layer random media, Geophys. J. Int., 128, 425–433, 1997a.

    Article  Google Scholar 

  • Yomogida, K., R. Benites, P. M. Roberts, and M. Fehler, Scattering of elastic waves in 2-D composite media II: Waveforms and spectra, Phys. Earth Planet. Inter., 104, 175–192, 1997b.

    Article  Google Scholar 

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Correspondence to Kiyoshi Yomogida.

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Yomogida, K., Benites, R. & Robinson, R. Spatial variation of coda wave amplitude in media with a localized heterogeneous region. Earth Planet Sp 50, 303–312 (1998).

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  • Depth Range
  • Focal Depth
  • Scattered Wave
  • Event Magnitude
  • Synthetic Seismogram