Fractal heterogeneities in sonic logs and low-frequency scattering attenuation
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Browaeys & Fomel: Fractals
Anstey, N. A., and R. F. O'Doherty, 2002a, Cycles, layers, and reflections: part 1: The Leading Edge,
----, 2002b, Cycles, layers, and reflections: part 2: The Leading Edge,
Backus, G. E., 1962, Long-wave elastic anisotropy produced by horizontal layering: Journal of Geophysical Research,
Banik, N. C., I. Lerche, and R. T. Shuey, 1985, Stratigraphic filtering, part I: derivation of the O'Doherty-Anstey formula: Geophysics,
Bleistein, N., J. K. Cohen, and J. W. Stockwell, 2001, Mathematics of multidimensional seismic imaging, migration, and inversion: Springer.
Interdisciplinary applied mathematics.
Born, M., and E. Wolf, 1964, Principles of optics: electromagnetic, theory of propagation, interference and diffraction of light: Pergamon Press.
Chernov, L. A., 1960, Wave propagation in a random medium: McGraw-Hill.
Chesnokov, E. M., Y. A. Kukharenko, and P. Y. Kukharenko, 1998, Frequency dependence of physical parameters of microinhomogeneous media, space statistics: Revue de l'Institut Français du Pétrole,
Dolan, S. S., C. J. Bean, and B. Riollet, 1998, The broad-band fractal nature of heterogeneity in the upper crust from petrophysical logs: Geophysical Journal International,
Frankel, A., and R. W. Clayton, 1986, Finite difference simulations of seismic scattering: implications for the propagation of short period seismic waves in the crust and models of crustal heterogeneity: Journal of Geophysical Research,
Gist, G. A., 1994, Seismic attenuation from 3-D heterogeneities: a possible resolution of the VSP attenuation paradox: 64th Annual International Meeting, SEG, Expanded Abstracts, Society of Exploration Geophysicists, 1042-1045.
Goff, J. A., and K. Holliger, 2003, Heterogeneity in the crust and upper mantle: nature, scaling, and seismic properties: Kluwer Academic/Plenum Publishers.
Goff, J. A., and T. H. Jordan, 1988, Stochastic modeling of seafloor morphology: inversion of sea beam data for second-order statistics: Journal of Geophysical Research,
Golub, G. H., and V. Pereira, 1973, The differentiation of pseudo-inverse and nonlinear least squares problems whose variables separate: SIAM Journal of Numerical Analysis,
Haney, M. M., K. van Wijk, and R. Snieder, 2005, Radiative transfer in layered media and its connection to the O'Doherty-Anstey formula: Geophysics,
, no. 1, T1-T11.
Hewett, T. A., 1986, Fractal distributions of reservoir heterogeneity and their influence on fluid transport: Presented at the 61st Technical Conference, Society of Petroleum Engineering, Society of Petroleum Engineering, SPE 15386.
Holliger, K., and A. R. Levander, 1992, A stochastic view of lower crustal fabric based on evidence from the Ivrea zone: Geophysical Research Letters,
Hurst, H. E., 1951, Long-term storage capacity of reservoirs: Transaction of American Society of Civil Engineering,
Kanaun, S. K., and V. Levin, 2008, Self-consistent methods for composites, vol.2: wave propagation in heterogeneous materials: Springer-Verlag.
Karal, F. C., and J. B. Keller, 1964, Elastic, electromagnetic, and other waves in a random medium: Journal of Mathematical Physics,
Klimes, L., 2002, Correlation functions of random media: Pure and Applied Geophysics,
, 1811 -1831.
Lancaster, S., and D. Whitcombe, 2000, Fast-track `coloured' inversion: 60th Annual International Meeting, SEG, Expanded Abstracts, Society of Exploration Geophysicists, 1572-1575.
Le Gonidec, Y., and D. Gibert, 2007, Multiscale analysis of waves reflected by granular media: acoustic experiments on glass beads and effective medium theories: Journal of Geophysical Research,
Lerche, I., 1986, Stratigraphic filter theory: combined effects of parallel bedding and random inhomogeneities: Geophysics,
Li, C. F., 2003, Rescaled-range and power spectrum analyses on well-logging data: Geophysical Journal International,
Lord, R. D., 1954, The use of the Hankel transform in statistics I. General theory and examples: Biometrika,
Lu, S., F. J. Molz, G. E. Fogg, and J. W. Castle, 2002, Combining stochastic facies and fractal models for representing natural heterogeneity: Hydrogeology Journal,
Mandelbrot, B. B., 1983, The fractal geometry of nature: W. H. Freeman and Co.
Mandelbrot, B. B., and J. R. Wallis, 1969, Some long-run properties of geophysical records: Water Resources Research,
Marsan, D., and C. J. Bean, 2003, Multifractal modeling and analyses of crustal heterogeneity,
Heterogeneity in the crust and upper mantle: nature, scaling, and seismic properties: Kluwer Academic/Plenum Publishers, 207-236.
Morlet, J., G. Arens, E. Fourgeau, and D. Giard, 1982, Wave propagation and sampling theory - part I: complex signal and scattering in multilayered media: Geophysics,
Müller, T. M., and S. A. Shapiro, 2001, Most probable seismic pulses in single realizations of two- and three-dimensional random media: Geophysical Journal International,
O'Doherty, R. F., and N. A. Anstey, 1971, Reflections on amplitudes: Geophysical Prospecting,
Painter, S., and L. Paterson, 1994, Fractional Lévy motion as a model for spatial variability in sedimentary rocks: Geophysical Research Letters,
Resnick, J. R., 1990, Stratigraphic filtering: Pure and Applied Geophysics,
Rivera, N. A., S. Ray, J. L. Jensen, A. K. Chan, and W. B. Ayers, 2004, Detection of cyclic patterns using the wavelets: an example study in the Ormskirk sandstone, Irish sea: Mathematical Geology,
Rytov, S. M., Y. A. Kravtsov, and V. I. Tatarski, 1989, Wave propagation through random media: Springer-Verlag.
Principles of statistical radio physics.
Sato, H., and M. Fehler, 1998, Seismic wave propagation and scattering in the heterogeneous Earth: Springer-Verlag.
Schottky, W., 1926, Small-shot effect and Flicker effect: Physical Reviews,
Shapiro, S. A., and P. Hubral, 1999, Elastic waves in random media: Springer-Verlag.
Shapiro, S. A., and H. Zien, 1993, The O'Doherty-Anstey formula and localization of seismic waves: Geophysics,
Sheng, P., B. White, Z. Q. Zhang, and G. Papanicolaou, 1986, Multiple scattering noise in one dimension: universality through localization length scaling: Physical Review Letters,
Shiomi, K., H. Sato, and M. Ohtake, 1997, Broad-band power-law spectra of well log data in Japan: Geophysical Journal International,
Shtatland, E. S., 1991, Fractal stochastic models for acoustic impedance: an explanation of scaling or 1/f geology and stochastic inversion: 51st Annual International Meeting, SEG, Expanded Abstracts, Society of Exploration Geophysicists, 1598-1601.
Stefani, J., and S. D. Gopa, 2001, On the power-law behavior of subsurface heterogeneity: 61st Annual International Meeting, SEG, Expanded Abstracts, Society of Exploration Geophysicists, 2033-2036.
Stovas, A., and B. Ursin, 2007, Equivalent time-average and effective medium for periodic layers: Geophysical Prospecting,
Tatarski, V. I., 1961, Wave propagation in a turbulent medium: McGraw-Hill.
Todoeschuck, J. P., O. G. Jensen, and S. Labonte, 1990, Gaussian scaling noise model of seismic reflection sequences: evidence from well logs: Geophysics,
Turcotte, D. L., 1997, Fractals and chaos in geology and geophysics: Cambridge University Press.
Uscinski, N. J., 1977, The elements of wave propagation in random media: McGraw-Hill.
van der Baan, M., 2001, Acoustic wave propagation in one-dimensional random media: the wave localization approach: Geophysical Journal International,
van der Baan, M., J. Wookey, and D. Smit, 2007, Stratigraphic filtering and source penetration depth: Geophysical Prospecting,
von Kármán, T., 1948, Progress in the statistical theory of turbulence: Journal of Marine Research,
Walden, A. T., and J. W. J. Hosken, 1985, An investigation of the spectral properties of primary reflection coefficients: Geophysical Prospecting,
Waterman, P. C., and R. Truell, 1961, Multiple scattering of waves: Journal of Mathematical Physics,
White, B., P. Sheng, and B. Nair, 1990, Localization and backscattering spectrum of seismic waves in stratified lithology: Geophysics,
Wu, R. S., 1982, Attenuation of short period seismic waves due to scattering: Geophysical Research Letters,
----, 1988, Discussion on:``Stratigraphic filter theory: combined effects of parallel bedding and random inhomogeneities," I. Lerche, author: Geophysics,
----, 1993, Separation of scattering and absorption in 1-D random media from spatio-temporal distribution of seismic energy: 53rd Annual International Meeting, SEG, Expanded Abstracts, Society of Exploration Geophysicists, 1014-1017.
Wu, R. S., and K. Aki, 1985, Elastic wave scattering by a random medium and the small scale inhomogeneities in the lithosphere: Journal of Geophysical Research,
Ziolkowski, A., P. Hanssen, R. Gatliff, H. Jakubowicz, A. Dobson, G. Hampson, X. Y. Li, and E. Liu, 2003, Use of low frequencies for sub-basalt imaging: Geophysical Prospecting,