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Fractal velocity models in refraction seismology

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Abstract

The introduction of noise components to a simple crustal velocity model is shown to markedly affect the appearance of synthetic seismograms calculated according to ray theory applied to refraction experiments. Here we simulate noise by a self-similar process with a power spectral density which falls off as inverse wavenumber to a simple power (0–2). The major effect is to destroy the coherency of the arrival branches normally expected from deterministic velocity models; the arrival amplitudes also show large trace-to-trace variations and considerable sensitivity to shot position. Some of these differences can be ascribed to the variety of noise model chosen (i.e., white noise, flicker noise and brown noise). It is argued that there is no clear distinction between coherent noise and geological structure.

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References

  • Berry, M. V. (1979),Diffractals, J. Phys. A: Math. Gen.12, 781–797.

    Google Scholar 

  • Crossley, D. J., Jensen, O. J. andJacobs, J. A. (1986),The Stochastic Excitation of Reversals in Simple Dynamos, Phys. Earth and Planet. Int.42, 143–153.

    Google Scholar 

  • Frankel, A., andClayton, R. W. (1986),Finite Difference Simulations of Seismic Scattering: Implications for the Propagation of Short-period Seismic Waves in the Crust and Models of Crustal Heterogeneity, J. Geophys. Res.91, 6465–6489.

    Google Scholar 

  • Hosken, J. W. J. (1980),A Stochastic Model of Seismic Reflections, Paper G-69 presented at 50th Annual Meeting SEG, Houston, Texas.

  • Hudson, J. A. (1982),Use of Stochastic Models in Seismology, Geophys. J. Roy. Astr. Soc.69, 649–657.

    Google Scholar 

  • Lerche, I. (1985),Multiple Scattering of Seismic Waves in Fractured Media: Cross-correlation as a Probe of Fracture Intensity, Pure Appl. Geophys.123, 503–542.

    Google Scholar 

  • Mandelbrot, B. B.,The Fractal Geometry of Nature (Freeman, San Francisco 1982).

    Google Scholar 

  • Mereu, R. F., andOjo, S. B. (1981),The Scattering of Seismic Waves Through a Crust and Upper Mantle with Random Lateral and Vertical Inhomogeneities, Phys. Earth and Planet. Int.26, 233–240.

    Google Scholar 

  • Mooney, W. D., andBrocher, T. M. (1987),Coincident Seismic Reflection/Refraction Studies of the Continental Lithosphere: A Global Review, Rev. Geophysics25, 723–742.

    Google Scholar 

  • Ojo, S. B., andMereu, R. F. (1986),The Effect of Random Velocity Functions on the Travel Times and Amplitudes of Seismic Waves, Geophys. J. Roy. Astr. Soc.84, 607–618.

    Google Scholar 

  • Sato, H. (1982),Amplitude Attenuation of Impulsive Waves in Random Media Based on Travel Time Corrected Mean Wave Formalism, J. Acoust. Soc. Am.71, 559–564.

    Google Scholar 

  • Spence, G. D., Whittal, K. P., andClowes, R. M. (1984),Practical Synthetic Seismograms for Laterally Varying Media Calculated by Asymptotic Ray Theory, Bull. Seis. Soc. Am.74, 1209–1223.

    Google Scholar 

  • Wenzel, A. R. (1982),Radiation and Attenuation of Waves in a Random Medium, J. Acoust. Soc. Am.71, 26–35.

    Google Scholar 

  • Wu, R-S., andAki, K. (1985),The Fractal Nature of the Inhomogeneities in the Lithosphere Evidenced from Seismic Wave Scattering, Pure Appl. Geophys.123, 805–818

    Google Scholar 

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Crossley, D.J., Jensen, O.G. Fractal velocity models in refraction seismology. PAGEOPH 131, 61–76 (1989). https://doi.org/10.1007/BF00874480

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  • DOI: https://doi.org/10.1007/BF00874480

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