Advertisement

pure and applied geophysics

, Volume 132, Issue 1–2, pp 363–400 | Cite as

Physical modeling observations of wave velocity and apparent attenuation in isotropic and anisotropic two-phase media

  • Bruce Dubendorff
  • William Menke
Article

Abstract

We study wave propagation through isotropic and anisotropic scatterer distributions in order to observe azimuthal variations in velocity and apparent attenuation. Using thin aluminum plates as physical models, we obtained seismograms for compressional and shear wave propagation through heterogeneous media. Three random distributions of scatterers are studied: circular scatterers in isotropic distributions (modeling circular scatterers), elongated scatterers in isotropic distributions (modeling randomly oriented elliptical scatterers), and elongated scatterers in anisotropic distributions (modeling aligned elliptical scatterers). All scatterers had approximately the same cross-sectional area and were filled with epoxy in order to reduce the impedance contrast. In addition to seismograms recorded for no scatterers, seismograms were recorded for several scatterer volume fractions. Azimuths were measured relative to the long axis of the aligned elongated scatterers. Velocities were calculated using travel times and phase shifts at low frequencies. The velocities measured from the data were compared to simple low-frequency average-velocity theories based on thin lamellae or on distributions of penny-shaped cracks. The apparent attenuation for different scatterer distributions was computed using spectral ratios.

Comparisons of the results for circular and randomly oriented elongated scatterers were made to determine the effects of scatterer shape. As expected, the circular and randomly oriented elongated scatterers showed no systematic azimuthal variation in velocity. The velocity anomalies were systematically larger for the randomly oriented elongated scatterers than for the circular scatterers. Both methods of theoretical estimation for the isotropic velocities produced velocities significantly larger than those measured. The spectral ratios showed more apparent attenuation for the randomly oriented elongated scatterers than for the circular scatterers.

Comparisons of the results for the randomly oriented and aligned elongated scatterers were made to determine the effects of anisotropy in the scatterer distribution. Compressional waves for the aligned elongated scatterers with wave propagation parallel to the scatterers had larger velocities than for the aligned elongated scatterers with wave propagation perpendicular to the scatterers for all velocity calculations. Shear wave velocities were complicated by an anomalous phase change in the shear wave seismograms for azimuths less than 40° and were not as conclusive. The general trend of the theoretical velocities is similar to the velocities calculated from the data. There are, however, what appear to be significant differences. The spectral ratios showed more apparent attenuation for the randomly oriented elongated scatterers than for the aligned elongated scatterers with wave propagation parallel to the scatterers, and less attenuation than for the aligned elongated scatterers with wave propagation perpendicular to the scatterers.

Key words

Crustal scattering apparent attenuation anisotropy physical models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Backus, G. E. (1962),Long-wave Elastic Anisotropy Produced by Horizontal Layering, J. Geophys. Res.67, 4427–4440.Google Scholar
  2. Backus, G. E. (1965),Possible Forms of Seismic Anisotropy of the Uppermost Mantle under Oceans, J. Geophys. Res.70, 3429–3439.Google Scholar
  3. Bullitt, J. T., andToksöz, M. N. (1985),Three-dimensional Ultrasonic Modeling of Rayleigh Wave Propagation, Bull. Seismol. Soc. Am.75, 1087–1104.Google Scholar
  4. Crampin, S. (1977),A Review of the Effects of Anisotropic Layering on the Propagation of Seismic Waves, Geophys. J. R. Astron. Soc.49, 9–27.Google Scholar
  5. Crampin, S. (1978),Seismic-wave Propagation Through a Cracked Solid: Polarization as a Possible Dilatancy Diagnostic, Geophys. J. R. Astr. Soc.53, 467–496.Google Scholar
  6. Dubendorff, B., andMenke, W. (1986),Time-domain Apparent-attenuation Operators for Compressional and Shear Waves: Experiment versus Single-scattering Theory, J. Geophys. Res.91, 14023–14032.Google Scholar
  7. Hudson, J. A. (1981),Wave Speeds and Attenuation of Elastic Waves in Material Containing Cracks, Geophys. J. R. Astr. Soc.64, 133–150.Google Scholar
  8. Lerche, I., andMenke, W. (1986),An Inversion Method for Separating Apparent and Intrinsic Attenuation in Layered Media, Geophys, J. R. Astron. Soc.87, 333–347.Google Scholar
  9. Lerche, I., andPetroy, D. W. (1986),Multiple Scattering of Seismic Waves in Fractured Media: Velocity and Effective Attenuation of the Coherent Components of P Waves and S Waves, Pure Appl. Geophys.124, 975–1019.Google Scholar
  10. Little, S. A., andStephen, R. A. (1985),Costa Rica Rift Borehole Seismic Experiment, Deep Sea Drilling Project, Hole 504B, 92, Init. Repts. DSDP, 83 (U. S. Govt. Printing Office, Washington) pp. 517–527.Google Scholar
  11. Malin, P. E., andPhinney, R. A. (1985),On the Relative Scattering of P-and S-waves, Geophys. J. R. Astron. Soc.80, 603–618.Google Scholar
  12. McDonald, J. A., Gardner, G. H. F., andHilterman, F. J., editors (1983),Seismic Studies in Physical Modeling (International Human Resources Development Corp., Boston).Google Scholar
  13. Menke, W. (1986),Few 2–50 km Corrugations on the Core-mantle Boundary, Geophys. Res. Lett.13, 1501–1504.Google Scholar
  14. Menke, W., andDubendorff, B. (1985),Discriminating Intrinsic and Apparent Attenuation in Layered Rock, Geophys. Res. Lett.12, 721–724.Google Scholar
  15. Menke, W., andDubendorff, B.,Physical modeling, InEncyclopedia of Geophysics (ed. James, D. E.) (Van Nostrand Reinhold, 1989).Google Scholar
  16. Menke, W., Witte, D., andChen, R. (1985),Laboratory Tests of Apparent Attenuation Formulas, Bull. Seismol. Soc. Am.75, 1383–1393.Google Scholar
  17. Mow, C.-C., andPao, Y.-H.,The Diffraction of Elastic Waves and Dynamic Stress Concentrations, Rep. R-482-PR (Rand Corp., Santa Monica, Calif. 1971).Google Scholar
  18. O'Connell, R. J., andBudiansky, B. (1974),Seismic Velocities in Dry and Saturated Cracked Solids, J. Geophys. Res.79, 5412–5426.Google Scholar
  19. Oliver, J. A., Press, F., andEwing, M. (1954),Two-dimensional Model Seismology, Geophysics14, 202–219.Google Scholar
  20. Purnell, G. W. (1986),Observations of Wave Velocity and Attenuation in Two-phase Media, Geophysics51, 2193–2199.Google Scholar
  21. Sato, H. (1982),Attenuation of S Waves in the Lithosphere due to Scattering by its Random Velocity Structure, J. Geophys. Res.87, 7779–7785.Google Scholar
  22. Sato, H. (1984),Attenuation and Envelope Formation of Three-component Seismograms of Small Local Earthquakes in Randomly Inhomogeneous Lithosphere, J. Geophys. Res.89, 1221–1241.Google Scholar
  23. Shearer, P., andOrcutt, J. (1985),Anisotropy in the Oceanic Lithosphere—Theory and Observations from the Ngendei Seismic Refraction Experiment in the South-west Pacific, Geophys. J. R. Astron. Soc.80, 493–526.Google Scholar
  24. Stephen, R. A. (1981),Seismic Anisotropy Observed in the Upper Oceanic Crust, Geophys. Res. Lett.8, 865–868.Google Scholar
  25. Stephen, R. A. (1985),Seismic Anisotropy in the Upper Oceanic Crust, J. Geophys. Res.90, 11383–11396.Google Scholar
  26. Varadan, V. K., Bringi, V. N., Varadan, V. V., andMa, Y. (1983),Coherent Attenuation of Acoustic Waves by Pair-correlated Random Distribution of Scatterers with Uniform and Gaussian Size Distributions, J. Acoust. Soc. Am.73, 1941–1947.Google Scholar
  27. Wu, R.-S. (1982),Attenuation of Short Period Seismic Waves due to Scattering, Geophys. Res. Lett.9, 9–12.Google Scholar
  28. Wu, R.-S. (1986),Heterogeneity Spectrum, Wave Scattering Response of a Fractal Random Medium and the Rupture Processes in the Medium, J. Wave-Material Interaction1, 79–96.Google Scholar
  29. Wu, R.-S., andAki, K. (1985),Scattering Characteristics of Elastic Waves by an Elastic Heterogeneity, Geophysics50, 582–595.Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Bruce Dubendorff
    • 1
  • William Menke
    • 2
  1. 1.College of OceanographyOregon State UniversityCorvallisUSA
  2. 2.Lamont-Doherty Geological Observatory and Department of Geological SciencesColumbia UniversityPalisadesUSA

Personalised recommendations