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The propagation of plane waves through statistically layered media is investigated both numerically and with single-scattering theory in the one-dimensional case. Exact apparent or stratigraphic Q, Qs, is determined from synthetic seismograms with the spectral-ratio method. Maximum velocity (impedance) fluctuations up to 30% (~40%) are studied; the fluctuations are uniformly distributed with zero mean. In all cases the trend of Qs as a function of frequency is well described by the analytical Qs, as determined from single-scattering theory under the assumption of an exponential autocorrelation function of the impedance fluctuations. The frequency dependence of the analytical Qs-1 follows a Debye-peak function, its maximum is γ2/2 and corresponds to the wavelength 4πa (γ2 = variance of relative impedance fluctuation, a = correlation distance). In further numerical calculations intrinsic or anelastic Q, Qa, is introduced, and it is shown that total attenuation Q -1 agrees very well with the sum of apparent and anelastic attenuation, Qs-1+Qa-1. Finally, a simple, minimum-phase stratigraphic attenuation operator is derived which describes the amplitude decay and the dispersion in a one-dimensional random medium with good accuracy. Stratigraphic attenuation is similar to the anelastic attenuation of a standard linear solid.
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Banik, N.C., Lerche, I., Resnick, J., Shuey, R.T. (1985b) Stratigraphic filtering, part 2: model spectra. Geophysics 50:2775-2783
DEKORP-Research Group (1985) First results and preliminary interpretation of deep-reflection seismic recordings along profile DEKORP 2-South. J. Geophys. 57:137-163
Frankel, A., Clayton, R.W. (1986) Finite difference simulations of seismic scattering: implication for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity. J. Geophys. Res. 91:6465-6489
Grant, F.W., West, G.F. (1965) Interpretation theory in applied geophysics. McGraw-Hill Book Co., New York
Hudson, J.A., Heritage, J.R. (1981) The use of the Born approximation in seismic scattering problems. Geophys. J. R. Astron. Soc. 66:221-240
Kanamori, H., Anderson, D.L. (1977) Importance of physical dispersion in surface wave and free oscillation problems: review. Rev. Geophys. Space Phys. 15:105-112
Lerche, I., Menke, W. (1986) An inversion method for separating apparent and intrinsic attenuation in layered media. Geophys. J. R. Astron. Soc. 87:333-347
Menke, W. (1983) A formula for the apparent attenuation of acoustic waves in randomly layered media. Geophys. J. R. Astron. Soc. 75:541-544
Menke, W., Dubendorff, B. (1985) Discriminating intrinsic and apparent attenuation in layered rock. Geophys. Res. Lett. 12:721-724
O'Doherty, R.F., Anstey, N.A. (1971) Reflections on amplitudes. Geophys. Prospecting 19:430-458
Richards, P.G., Menke, W. (1983) The apparent attenuation of a scattering medium. Bull. Seism. Soc. Am. 73:1005-1021
Sandmeier, K.-J., Wenzel, F. (1986) Synthetic seismograms for a complex crustal model. Geophys. Res. Lett. 13:22-25
Sato, H. (1979) Wave propagation in one dimensional inhomogeneous elastic media. J. Phys. Earth 27:455-466
Sato, H. (1981) Attenuation of elastic waves in one-dimensional inhomogeneous elastic media. Phys. Earth Planet. Inter. 26:244-245
Sato, H. (1982a) Attenuation of S waves in the lithosphere due to scattering by its random velocity structure. J. Geophys. Res. 87:7779-7785
Sato, H. (1982b) Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism. J. Acoust. Soc. Am. 71:559-564
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
Schoenberger, M., Levin, F.K. (1974) Apparent attenuation due to intrabed multiples. Geophysics 39:278-291
Schoenberger, M., Levin, F.K. (1978) Apparent attenuation due to intrabed multiples II. Geophysics 43:730-737
Sherwood, J.W.C., Trorey, A.W. (1965) Minimum-phase and related properties of the response of a horizontally stratified absorptive earth to plane acoustic waves. Geophysics 30:191-197
Spencer, T.W., Edwards, C.M., Sonnad, J.R. (1977) Seismic wave attenuation in nonresolvable cyclic stratification. Geophysics 42:939-949
Spencer, T.W., Sonnad, J.R., Butler, T.M. (1982) Seismic Q-stratigraphy or dissipation. Geophysics 47:16-24
Temme, P., Muller, G. (1982) Numerical simulation of vertical seismic profiling. J. Geophys. 50:177-189
Wenzel, A.R. (1982) Radiation and attenuation of waves in a random medium. J. Acoust. Soc. Am. 71:26-35
Wu, R.S. (1982) Attenuation of short period seismic waves due to scattering. Geophys. Res. Lett. 9:9-12
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