pure and applied geophysics

, Volume 132, Issue 1–2, pp 123–150 | Cite as

Time domain solution for multiple scattering and the coda envelopes

  • Long-Sheng Gao
  • Song Lin Li


This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathLs and time in terms of the mean-free timesLs/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQi. Of course, this conclusion is coincident with the presumption of the diffusion theory,Qs>Qi. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQi, then as the distance increases, effects of scatteringQs, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQi should not be smaller than one tenth ofQs.

Key words

Coda wave attenuation scattering multiple scattering absorption Q factor intrinsicQ discriminating betweenQs andQi 


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Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Long-Sheng Gao
    • 1
  • Song Lin Li
    • 2
  1. 1.Institute of GeophysicsState Seismological BureauBeijingChina
  2. 2.Geophysical Prospecting BrigadeState Seismological BureauBeijingChina

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