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Stratigraphic filtering

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Abstract

A plane-wave signal traveling at normal incidence through the earth's sedimentary layers attenuates, spreads, and changes waveform as it propagates, partly in response to “stratigraphic filtering” resulting from the buildup in the medium of intrabed multiples caused by the layering, and partly in response to absorption. This paper consists of a review of one-dimensional stratigraphic filtering. The action of stratigraphic filtering resembles that of absorption, and the filter's spectrum can be characterized by an effective quality factor. A comparison between the spectra of field data and synthetic data derived from absorption-free one-dimensional models suggests that in some geologic formations, stratigraphic filtering causes a significant fraction of the total attenuation evident on seismic records. In such studies, however, the simplicity of one-dimensional models leaves some uncertainty regarding the generality of the results. Nonetheless, one-dimensional stratigraphic filtering can serve as a useful metaphor that provides insight into the workings of more complex multi-dimensional scattering models.

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References

  • Aki, K., andRichards, P. G.,Quantitative Seismology (W. H. Freeman & Co., San Francisco 1980).

    Google Scholar 

  • Anstey, N. A. (1960),Attacking the Problems of the Synthetic Seismogram, Geophys. Prosp.8, 242–259.

    Google Scholar 

  • Backus, G. E. (1962),Long Wave Elastic Anisotropy Produced by Horizontal Layering, J. Geophys. Res.67, 4427–4440.

    Google Scholar 

  • Balanis, G. N. (1973),Waves in a Periodic Composite, J. Appl. Mech.40, 815–817.

    Google Scholar 

  • Balanis, G. N. (1975),Analysis of the Dispersion of Low Frequency Uniaxial Waves in Heterogeneous Periodic Elastic Media, J. Math. Phys.16, 1383–1387.

    Google Scholar 

  • Bamberger, A., Chavent, G., andLailly, P. (1979),About the Stability of the Inverse Problem in 1-D Wave Equations—Application to the Interpretation of Seismic Profiles, J. Appl. Math. Optim.5, 1–47.

    Google Scholar 

  • Bamberger, A., Chavent, G., Hemon, Ch., andLailly, P. (1982),Inversion of Normal Incidence Seismograms, Geophys.47, 757–770.

    Google Scholar 

  • Banik, N. C., Lerche, I., andShuey, R. T. (1985a),Stratigraphic Filtering, Part I: Derivation of the O'Doherty-Anstey Formula, Geophys.50, 2768–2774.

    Google Scholar 

  • Banik, N. C., Lerche, I., Resnick, J. R., andSheuy, R. T. (1985b),Stratigraphic Filtering, Part II: Model Spectra, Geophys.50, 2775–2783.

    Google Scholar 

  • Behrens, E. (1967),Sound Propagation in Lamellar Composite Materials and Averaged Elastic Constants, J. Acoust. Soc. Am.42, 378–383.

    Google Scholar 

  • Bois, P., Hemon, Ch., andMarescal, N. (1965),Influence de la Largeur du pas d'Echtillonnage du Carottage Continu de Vitesses sur les Sismogrammes Synthetiques a Multiples, Geophys. Prosp.13, 66–104.

    Google Scholar 

  • Brillouin, L.,Wave Propagation and Group Velocity (Academic Press, New York 1960).

    Google Scholar 

  • Bube, K. P., andBurridge, R. (1983),The One-dimensional Inverse Problem of Reflection Seismology, SIAM Review25, 497–559.

    Google Scholar 

  • Burridge, R., Papanicolaou, G. S., andWhite, B. S. (1987),Statistics for Pulse Reflection from a Randomly Layered Medium, SIAM J. Appl. Math.47, 146–168.

    Google Scholar 

  • Burridge, R., Papanicolaou, G. S., andWhite, B. S. (1988),One-Dimensional Wave Propagation in A Highly Discontinuous Medium, Wave Motion10, 19–44.

    Google Scholar 

  • D'erceville, I., andKunetz, G. (1963),Sur l'Influence d'un Empilement de Couches Minces en Sismique, Geophys. Prosp,11, 115–121.

    Google Scholar 

  • Eisner, E. (1967),Complete Solutions of the Webster Horn Equation, J. Acoust. Soc. Am.41, 1126–1146.

    Google Scholar 

  • Futterman, W. I. (1962),Dispersive Body Waves, J. Geophys. Res.67, 5279–5291.

    Google Scholar 

  • Ganley, D. C., andKanasewich, E. R. (1980),Measurement of Absorption and Dispersion from Check Shot Surveys, J. Geophys. Res.85, 5219–5226.

    Google Scholar 

  • Godfrey, R., Muir, F., andRocca, F. (1980),Modeling Seismic Impedance with Markov Chains, Geophys.45, 1331–1372.

    Google Scholar 

  • Goetz, J. F., Dupal, L., andBowles, J. (1979),An Investigation into Discrepancies between Sonic Log and Seismic Check Shot Velocities, Austral. Petr. Explor. Assoc. J.19, 131–141.

    Google Scholar 

  • Gouplllaud, P. L. (1961),An Approach to Inverse Filtering of Near Surface Layer Effects from Seismic Records, Geophys.26, 754–760.

    Google Scholar 

  • Gretener, P. E. F. (1961),An Analysis of Observed Time Discrepancies between Continuous and Conventional Well Velocity Surveys, Geophys.26, 1–11.

    Google Scholar 

  • Gupta, I. N. (1966),Dispersion of Body Waves in Layered Media, Geophys.31, 821–823.

    Google Scholar 

  • Hauge, P. S. (1981),Measurements of Attenuation from Vertical Seismic Profiles, Geophys.46, 1548–1558.

    Google Scholar 

  • Keller, J. B.,Effective behavior of heterogeneous media, InStatisical Mechanics and Statistical Methods in Theory and Application (ed. Landman, U.) (Plenum Press, New York 1977) pp. 631–644.

    Google Scholar 

  • Lee, E. H., andYang, W. H. (1973),On Waves in Composite Materials with Periodic Structure, SIAM J. Appl. Math.25, 492–499.

    Google Scholar 

  • Lerche, I., andMenke, W. (1986),An Inversion Method for Separating Apparent and Intrinsic Attenuation in Layered Media, Geophys. J. R. Astr. Soc.87, 333–347.

    Google Scholar 

  • Mason, W. P. (1927),A Study of the Regular Combination of Acoustic Elements with Applications to Recurrent Acoustic Filters, Tapered Acoustic Filters, and Horns, Bell System Tech. J.6, 258–275.

    Google Scholar 

  • McDonald, F. J., Angona, F. A., Mills, R. L., Sengbush, R. L., Van Nostrand, R. G., andWhite, J. E. (1958),Attenuation of Shear and Compresiional Waves in Pierre Shale, Geophys.23, 421–439.

    Google Scholar 

  • Menke, W. (1983),A Formula for the Apparent Attenuation of Acoustic Waves in Randomly Layered Media, Geophys. J. R. Astr. Soc.75, 541–544.

    Google Scholar 

  • Menke, W., andChen, R. (1984),Numerical Studies of the Coda Falloff Rate of Multiply Scattered Waves in Randomly Layered Media, Bull. Seismol. Soc. Am.74, 1605–1621.

    Google Scholar 

  • Menke, W., andDubendorff, B. (1985),Discriminating Intrinsic and Apparent Attenuation in Layered Rock, Geophys. Res. Lett.12, 721–724.

    Google Scholar 

  • Morlet, J., Arens, G., Fourgeau, E., andGiard, D. (1982),Wave Propagation and Sampling Theory—Part I: Complex Signal and Scattering in Multilayered Media, Geophys.47, 203–221.

    Google Scholar 

  • Morse, P. M.,Vibration and Sound, 2nd ed. (McGraw Hill, New York 1948).

    Google Scholar 

  • O'Brien, P. N. S., andLucas, A. L. (1971),Velocity Dispersion of Seismic Waves, Geophys. Prosp.19, 1–26.

    Google Scholar 

  • O'Doherty, R. F., andAnstey, N. A. (1971),Reflections on Amplitudes, Geophys. Prosp.19, 430–458.

    Google Scholar 

  • Postma, G. W. (1955),Wave Propagation in a Stratified Medium, Geophys.20, 780–806.

    Google Scholar 

  • Rayleigh, J. W. S.,The Theory of Sound, Vol. 1 (Macmillan, London 1894).

    Google Scholar 

  • Rayleigh, J. W. S. (1916),On the Propagation of Sound in Narrow Tubes of Variable Section, Phil Mag.31, 89–96.

    Google Scholar 

  • Resnick, J. R., Lerche, I., andShuey, R. T. (1986),Reflection, Transmission, and the Generalized Primary Wave, Geophys. J. R. Astr. Soc.87, 349–377.

    Google Scholar 

  • Richards, P. G., andMenke, W. (1983),The Apparent Attenuation of a Scattering Medium, Bull. Seismol. Soc. Am.73, 1005–1021.

    Google Scholar 

  • Ricker, N. (1953),The Form and Law of Propagation of Seismic Wavelets, Geophys.18, 10–46.

    Google Scholar 

  • Riznichenko, Y. V. (1949),Seismic Quasi-anisotropy, Bull. Acad. Sci. USSR, Geographical and Geophysical Series13, 518–544.

    Google Scholar 

  • Ruter, H., andSchepers, R. (1978),Investigation of the Seismic Response of Cyclically Layered Carboniferous Rock by Means of Synthetic Seismograms, Geophys. Prosp.26, 29–47.

    Google Scholar 

  • Rytov, S. M. (1956),Acoustical Properties of a Thinly Laminated Medium, Soviet Phys. Acoust.2, 68–80.

    Google Scholar 

  • Sato, H. (1979),Wave Propagation in One-dimensional Inhomogeneous Elastic Media, J. Phys. Earth27, 455–466.

    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 

  • Schoenberger, M., andLevin, F. K. (1974),Apparent Attenuation due to Intrabed Multiples, Geophys.39, 278–291.

    Google Scholar 

  • Schoenberger, M., andLevin, F. K. (1978),Apparent Attenuation due to Intrabed Multiples, II, Geophys.43, 730–737.

    Google Scholar 

  • Schoenberger, M., andLevin, F. K. (1979),The Effect of Subsurface Sampling on One-Dimensional Synthetic Seismograms, Geophys.44, 1813–1829.

    Google Scholar 

  • Sherwood, J. W. C., andTrorey, A. W. (1965),Minimum Phase and Related Properties of the Response of a Horizontally Stratified Absorptive Earth to Plane Acoustic Waves, Geophys.30, 191–197.

    Google Scholar 

  • Sobczyk, K.,Stochastic Wave Propagation (Elsevier, Amsterdam 1985).

    Google Scholar 

  • Spencer, T. W., Edwards, C. M., andSonnad, J. R. (1977),Seismic Wave Attenuation in Nonresolvable Cyclic Stratification, Geophys.42, 939–949.

    Google Scholar 

  • Spencer, T. W., Sonnad, J. R., andButler, T. M. (1982),Seismic Q—Stratigraphy or Dissipation, Geophys.47, 16–24.

    Google Scholar 

  • Stewart, G. W. (1922),Acoustic Wave Filters, Phys. Rev.20, 528–540.

    Google Scholar 

  • Stewart, R. R., Huddleston, P. D., andKan, T. K. (1984),Seismic versus Sonic Velocities: A Vertical Seismic Profiling Study, Geophys.49, 1153–1168.

    Google Scholar 

  • Treitel, S., andRobinson, E. A. (1966),Seismic Wave Propagation in Layered Media in Terms of Communication Theory, Geophys.31, 17–32.

    Google Scholar 

  • Trorey, A. W. (1962),Theoretical Seismograms with Frequency and Depth Dependent Absorption, Geophys.27, 766–785.

    Google Scholar 

  • Tullos, F. K., andReid, A. C. (1969),Seismic Attenuation of Gulf Coast Sediments, Geophys.34, 516–528.

    Google Scholar 

  • Velzeboer, C. J. (1981),The Theoretical Seismic Reflection Response of Sedimentary Sequences, Geophys.46, 843–853.

    Google Scholar 

  • Walden, A. T., andHosken, J. W. J. (1985),An Investigation of the Spectral Properties of Primary Reflection Coefficients, Geophys. Prosp.33, 400–435.

    Google Scholar 

  • Ward, R. W., andHewitt, M. R. (1977),Monofrequency Borehole Traveltime Survey, Geophys.42, 1137–1145.

    Google Scholar 

  • Webster, A. G. (1919),Acoustical Impedance and the Theory of Horns and of the Phonograph, Proc. Nat. Acad. Sci.5, 275–282.

    Google Scholar 

  • White, J. E., andAngona, F. A. (1955),Elastic Wave Velocities in Laminated Media, J. Acoust. Soc. Am.27, 310–317.

    Google Scholar 

  • Wu, R. S. (1982),Attenuation of Short Period Waves Due to Scattering, Geophys. Res. Lett.9, 9–12.

    Google Scholar 

  • Wuenschel, P. C. (1960),Seismogram Synthesis Including Multiples and Transmission Coefficients, Geophys.25, 106–129.

    Google Scholar 

  • Wuenschel, P. C. (1965),Dispersive Body Waves—an Experimental Study, Geophys.30, 539–551.

    Google Scholar 

  • Ziolkowski, A., andFokkema, J. J. (1986),The Progressive Attenuation of High Frequency Energy in Seismic Reflection Data, Geophys. Prosp.34, 981–1001.

    Google Scholar 

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Resnick, J.R. Stratigraphic filtering. PAGEOPH 132, 49–65 (1990). https://doi.org/10.1007/BF00874357

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