pure and applied geophysics

, Volume 123, Issue 6, pp 805–818 | Cite as

The fractal nature of the inhomogeneities in the lithosphere evidenced from seismic wave scattering

  • Ru-Shan Wu
  • Keiiti Aki


In this paper we show evidences of the fractal nature of the 3-D inhomogeneities in the lithosphere from the study of seismic wave scattering and discuss the relation between the fractal dimension of the 3-D inhomogeneities and that of the fault surfaces. Two methods are introduced to measure the inhomogeneity spectrum of a random medium: 1. the coda excitation spectrum method, and 2. the method of measuring the frequency dependence of scattering attenuation. The fractal dimension can be obtained from the inhomogeneity spectrum of the medium. The coda excitation method is applied to the Hindu-Kush data. Based on the observed coda excitation spectra (for frequencies 1–25 Hz) and the past observations on the frequency dependence of scattering attenuation, we infer that the lithospheric inhomogeneities are multiple scaled and can be modeled as a bandlimited fractal random medium (BLFRM) with an outer scale of about 1 km. The fractal dimension of the 3-D inhomogeneities isD3=31/2–32/3, which corresponds to a scaling exponent (Hurst number)H=1/2–1/3. The corresponding 1-D inhomogeneity spectra obey the power law with a powerp=2H+1=2–5/3. The intersection between the earth surface and the isostrength surface of the 3-D inhomogeneities will have fractal dimensionD1=1.5–1.67. If we consider the earthquake fault surface as developed from the isosurface of the 3-D inhomogeneities and smoothed by the rupture dynamics, the fractal dimension of the fault trace on the surface must be smaller thanD1, in agreement with recent measurements of fractal dimension along the San Andreas fault.

Key words

Fractal wave scattering seismic coda wave lithospheric inhomogeneities earthquake faults 


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Copyright information

© Birkhäuser Verlag 1985

Authors and Affiliations

  • Ru-Shan Wu
    • 1
  • Keiiti Aki
    • 2
  1. 1.Earth Resource Laboratory, Department of Earth, Atmospheric and Planetary SciencesMassachusetts Institute of TechnologyMassachusettsUSA
  2. 2.Department of Geological SciencesUniversity of Southern CaliforniaLos Angeles

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