Abstract
This paper presents the theory which describes how the lateral correlation of vertical displacement is influenced by multiple scattering of seismic waves caused by the presence of fluid-filled fractures, along with an observational methodology to show how to extract fracture-related quantities (e.g. fracture porosity, degree of anisotropy of the fractures, change in orientation of the fractures, density of fluid filling the fractures) from seismic data using the theoretical development as an underpinning framework. A simple physical picture is given of the basic process, as well as some rough order of magnitude estimates to show that the parameters quantifying the size of the multiple scattering fall squarely in the seismic regime.
These calculations serve to create a basis to determine, by seismic means ahead of the drill, (1) the degree of fracturing of reservoir rocks (such as the Monterey shale), and (2) the type of fluid filling the fractures.
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References
Aki, K. (1973),Scattering of P-waves under Montana LASA. J. Geophys. Res.78, 1334–1346.
Aki, K., Christofferson, A. andHysebye, E.S. (1976),Three-dimensional Seismic Structure of the Lithosphere Under Montana LASA. Bull. Seis. Soc. Am.66:2, 501–524.
Aki, K. (1981),Scattering and Attenuation of High-Frequency Body Waves (1–25 Hz) in the Lithosphere, Phys. Earth and Planet. Int.26, 241–243.
Aki, K. (1982),Scattering and Attenuation. Bull. Seism. Soc. Am.78, B6, S319–330.
Banik, N. C., Lerche, I. andShuey, R. T. (1985),Stratigraphic Filtering, Part I: Derivation of the O'Doherty-Anstey Formula. Geophysics50, 2764–2774.
Banik, N. C., Lerche, I., Resnick, J. andShuey, R. T. (1985),Stratigraphic Filtering, Part II: Model Spectra. Geophysics50, 2775–2783.
Berteussen, K. A., Christofferson, A., Husebye, E. S. andDahle, A. (1975),Wave scattering theory in analysis of P-wave anomalies at NORSAR and LASA. Geophys. J. Roy. astr. Soc.42, 403–417.
Berteussen, K. A. (1975a),Crustal Structure and P-wave Travel Time Anomalies at NORSAR. J. Geophys.41, 71–84.
Berteussen, K. A. (1975b),P-wave amplitude variability at NORSAR. J. Geophys.41, 595–613.
Born, M. andWolf, E. (1964),Principles of Optics (The MacMillan Co., New York).
Capon, J. (1974),Characterization of crust and upper mantle structure under LASA as a random medium. Bull. Seis. Soc. Am.64, 235–266.
Chang, A. andvon Seggern, D. H. (1980),A study of amplitude anomaly and m bias at LASA subarrays. J. Geophys. Res.85, 4811–4828.
Chernov, L. A. (1960),Wave propagation in a Random Medium. McGraw-Hill.
Clayton, R. andEngquist B. (1977),Absorbing boundary conditions for acoustic and elastic waves equations, Bull. Soc. Seis. A.67, 1529–1540.
Dainty, A. M. (1981),A scattering model to explain seismic Q observations in the lithosphere between 1 and 30 Hz. Geophys. Res. Lett.8, 1126–1128.
Dainty, A. M. (1984),High Frequency Acoustic Backscattering and Seismic attenuation. J. Geophys. Res.89, 3172–3176.
Dashen, R. (1979),Path integrals for waves in random media. J. Math. Phys.20, 894–920.
Der, Z. A., McElfresh, T. W. andO'Donnell, A. (1982),An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the United States in the 0.54 Hz band. Geophys. J.R.A.S.69, 67–100.
Frankel, A. andClayton R. W. (1984),A finite difference Simulation of Wave Propagation Two-Dimensional Random Media. Submitted to Bull. Seism. Soc. Am.
Hudson, J. A. andHeritage, J. R. (1981),The use of the Born approximation in seismic scattering problems. Geophys. J. Roy. astr. Soc.66, 221–240.
Hudson, J. A. (1982),Use of stochastic models in seismology. Geophys. J. Roy. astr. Soc.69, 649–657.
Ishimaru, A. (1976)Wave Propagation and Scattering in Random Media, VI and II. Academic Press.
Kelly, K. R., Ward, R. W., Treitel, S. andAlford, R. M. (1976),Synthetic seismograms, a finite difference approach. Geophysics41, 2–27.
Kikuchi, M. (1981a),Dispersion and attenuation of elastic waves due to multiple scattering from inclusions. PEPI25, 159–162.
Kikuchi, M. (1981b),Dispersion and attenuation of elastic waves due to multiple scattering from cracks. PEPI27, 100–105.
Lee, L. C. (1974),J. Math. Phys. 15, 1431.
Lerche, I. andPetroy, D. E. (1985),‘Multiple scattering of Seismic Waves in Fractured Media: Velocity and Effective Attenuation of the Coherent Components of P-waves and S-waves.’ (In preparation.)
Lerche, I. (1979),Scintillations in Astrophysics I. An Analytic Solution of the Second Order Moment Equation. Astrophys. J.234, 262–272.
McCoy, J. J. (1980),Parabolic wave theories and some recent applications. Phys. Earth and Planet. Inter.21, 126–133.
McLaughlin, K. L. (1983),Coherency of Seismic Waveforms. Ph.d. Thesis, Univ. Calif., Berkeley.
Menke, W. (1983a),On the effect of P-S coupling on the apparent attenuation of elastic waves in randomly layered media. Geophys. Res. Lett.10, 1145–1147.
Menke, W. (1983b),A formula for the apparent attenuation of acoustic waves in randomly layered media. Geophys. J. Roy. astr. Soc.75, 541–544.
Powell, C. A. andMeltzer, A. S. (1984)Scattering of P-waves Beneath SCARLET in Southern California. Geophys. Res. Lett.11, 481–484.
Richards, P. G. andMenke, W. (1983)The apparent attenuation of a scattering medium. Bull. Seis. Soc. Am.73, 1005–1021.
Sato, H. (1982a)Attenuation of S-waves in the lithosphere due to scattering by its random velocity structure. J. Geophys. Res.87, 7779–7786.
Sato, H. (1982b),Amplitude attenuation of impulsive waves in random media on the travel time corrected wave formalism. J. Acoust. Soc. Am.71, 559–564.
Tatarskii, V. I. (1961),Wave Propagation in a Turbulent Medium. Dover, 285pages.
Tatarskii, V. I. (1971),The Effects of the Turbulent Atmosphere on Wave Propagation. (Israel Program for Scientific Translation.)
Thompson, C. (1983),Ray-theoretical amplitude inversion for laterally varying velocity structure below NORSAR. Geophys. J. Roy. astr. Soc.74, 525–558.
Uscinski, B. J. (1977),The Elements of Wave Propagation in a Random Medium. McGraw-Hill.
Wu, Ru-Shan, (1982a),Attenuation of Short Period Seismic Waves due to Scattering. Geophys. Res. Lett.9, 9–12.
Wu, Ru-Shan (1982b),Mean Field Attenuation and Amplitude Attenuation Due to Wave Scattering. Wave Motion4, 305–316.
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Lerche, I. Multiple scattering of seismic waves in fractured media: Crosscorrelation as a probe of fracture intensity. PAGEOPH 123, 503–542 (1985). https://doi.org/10.1007/BF00877451
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DOI: https://doi.org/10.1007/BF00877451