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Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves

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Abstract

We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by ‘regular’ porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf 3. For a Kolmogorov spectrum of fractures of spectral index ν the attenuation is an order of magnitude or so larger and varies with frequency asf 3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.

For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.

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Authors and Affiliations

  1. Department of Geology, University of South Carolina, 29208, Columbia, South Carolina

    Ian Lerche

  2. Department of Earth and Planetary Sciences, Washington University, 63130, St. Louis, Missouri

    David Petroy

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  1. Ian Lerche
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  2. David Petroy
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Lerche, I., Petroy, D. Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves. PAGEOPH 124, 975–1019 (1986). https://doi.org/10.1007/BF00879928

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  • DOI: https://doi.org/10.1007/BF00879928

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