Self-Affine Time Series: I. Generation and Analyses

Advances in Geophysics

Volumn 40, Issue C, 1999, Pages 1-90

  Malamud, Bruce D ^a   Turcotte, Donald L ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

STATISTICAL ANALYSIS; TIME SERIES;

EID: 1542285696     PISSN: 00652687     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2687(08)60293-9     Document Type: Article

References (69)

1. Ahnert F. Local relief and the height limits of mountain ranges. Am. J. Sci. 284 (1984) 1035-1055
2. Barabási A.-L., and Stanley H.E. "Fractal Concepts in Surface Growth." (1995), Cambridge University Press, Cambridge
3. Bassingthwaighte J.B., Liebovitch L.S., and West B.J. "Fractal Physiology." (1994), Oxford University Press, Oxford
4. Bassingthwaighte J.B., and Raymond G.M. Evaluating rescaled range analysis for time series. Ann. Biomed. Eng. 22 (1994) 432-444
5. Bassingthwaighte J.B., and Raymond G.M. Evaluation of the dispersional analysis method for fractal time series. Ann. Biomed. Eng. 23 (1995) 491-505
6. Beran J. Statistical methods for data with long-range dependence. Statist. Sci. 7 (1992) 404-427
7. Beran J. "Statistics for Long-Memory Processes." (1994), Chapman & Hall, London Monographs on Statistics and Probability 61.
8. Box G.E.P., Jenkins G.M., and Reinsel G.C. "Time Series Analysis: Forecasting and Control,". 3rd ed. (1994), Prentice-Hall, Englewood Cliffs, NJ
9. Bras R.L., and Rodriguez-Iturbe I. "Random Functions and Hydrology" (1993), Dover, New York
10. Brown S.R. A note on the description of surface roughness using fractal dimension. Geophys. Res. Lett. 14 (1987) 1095-1098
11. Chatfield C. "The Analysis of Time Series,". 5th ed. (1996), Chapman & Hall, London
12. Daubechies I. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41 (1988) 909-996
13. De Santis A. A direct divider method for self-affine fractal profiles andsurfaces. Geophys. Res. Lett. 24 (1997) 2099-2102
14. Feder J. "Fractals." (1988), Plenum Press, New York
15. Flandrin P. Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. Inform. Theory 38 (1992) 910-917
16. Flandrin P. Fractional Brownian motion and wavelets. In: Farge M., Hunt J.C.R., and Vassilicos J.C. (Eds). "Wavelets, Fractals, and Fourier Transforms" (1993), Clarendon Press, Oxford 109-122
17. Gallant J.C., Moore I.D., Hutchinson M.F., and Gessler P. Estimating fractal dimension of profiles: A comparison of methods. Math. Geol. 26 (1994) 455-481
18. Grossmann A., and Morlet J. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 15 (1984) 723-736
19. Hall P. Defining and measuring long-range dependence. Fields Institute Commun. 11 (1997) 153-159
20. Harvard Centroid-Moment Tensor Database. Electronic Data (1997), Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA
21. Hastings H.M., and Sugihara G. "Fractals: A User's Guide for the Natural Sciences." (1993), Oxford University Press, Oxford
22. Hewett T.A. Fractal distribution of reservoir heterogeneity and their influence on fluid transport. Society of Petroleum Engineering Paper 15386 (1986) 1-16
23. Hubbard B.B. "The World According to Wavelets: The Story of a Mathematical Technique in the Making." (1996), A. K. Peters, Wellesley, MA
24. Hurst H.E. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Engineers 116 (1951) 770-808
25. Hurst H.E., Black R.P., and Simaika Y.M. "Long-Term Storage." (1965), Constable, London
26. Jenkins G.M., and Watts D.G. "Spectral Analysis and its Applications." (1968), Holden-Day, San Francisco
27. Journel A.G., and Huijbregts Ch.J. "Mining Geostatistics." (1978), Academic Press, New York
28. Kolmogorov A.N. Wienersche spiralen und einige andere interessante kurven in hlbertschen raum. Comp. rend. (Doklady) Acad. Sci. URSS (N.S.) 26 (1940) 115-118
29. Korvin G. "Fractal Models in the Earth Sciences." (1992), Elsevier, Amsterdam
30. Li W.K., and McLeod A.I. Fractional time series modeling. Biometrika 73 (1986) 217-221
31. Malinverno A. A simple method to estimate the fractal dimension of a self-affine series. Geophys. Res. Lett. 17 (1990) 1953-1956
32. Malinverno A. Fractals and ocean floor topography: A review and a model. In: Barton C.C., and LaPointe P.R. (Eds). "Fractals in the Earth Sciences" (1995), Plenum Press, New York 107-130
33. Mandelbrot B.B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156 (1967) 636-638
34. Mandelbrot B.B. "The Fractal Geometry of Nature." (1982), Freeman, New York
35. Mandelbrot B.B. Self-affine fractals and fractal dimension. Phys. Scripta 32 (1985) 257-260
36. Mandelbrot B.B. Self-affine fractal sets, I: The basic fractal dimensions; II: Length and surface dimensions; III: Hausdorff dimension anomalies and their implications. In: Pietronero L., and Tosatti E. (Eds). "Fractals in Physics" (1986), Elsevier, Amsterdam 21-28
37. Mandelbrot B.B., and Van Ness J.W. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 (1968) 422-437
38. Mandelbrot B.B., and Wallis J.R. Noah, Joseph and operational hydrology. Water Resour. Res. 4 (1968) 909-918
39. Mandelbrot B.B., and Wallis J.R. Computer experiments with fractional Gaussian noises. Parts I, II, and III. Water Resour. Res. 5 (1969) 228-267
40. Mandelbrot B.B., and Wallis J.R. Some long-run properties of geophysical records. Water Resour. Res. 5 (1969) 321-340
41. Mandelbrot B.B., and Wallis J.R. Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence. Water Resour. Res. 5 (1969) 967-988
42. Matheron G. "Traité de Géostatistique Appliquée, Tome I, Théorie Générale." (1962), Editions Technip., Paris
43. Matheron G. "Traité de Géostatistique Appliquée, Tome II, Le Krigéage." (1963), Editions Technip., Paris
44. Matheron G. Principles of geostatistics. Econom. Geol. 58 (1963) 1246-1266
45. McLeod A.I., and Hipel K.W. "The McLeod-Hipel Time-Series Datasets Collection.". Electronic data available from the StatLib electronic database (1995), Carnegie Mellon University Statistics Department
46. The datasets collection accompanies. In: Hipel K.W., and McLeod A.I. (Eds). "Time Series Modeling of Water Resources and Environmental Systems," (1994), Elsevier, Amsterdam
47. Meakin P. The growth of fractal aggregates and their measures. In: Domb C., and Lebowitz J.L. (Eds). "Phase Transitions and Critical Phenomena," 12 (1988), Academic Press, New York 335-489
48. Oliver M., and Webster R. Semi-variograms for modeling the spatial pattern of landform and soil properties. Earth Surf. Proc. Landforms 11 (1986) 491-504
49. Osborne A.R., and Provenzale A. Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35 (1989) 357-381
50. Pelletier J.D., and Turcotte D.L. Self-affine time series: II. Applications and models. In: Dmowska R., and Saltzman B. (Eds). "Advances in Geophysics" 40 (1999), Academic Press, San Diego 91-166
51. Percival D.B., and Walden A.T. "Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques." (1993), Cambridge University Press, Cambridge
52. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. "Numerical Recipes in C: The Art of Scientific Computing,". 2nd ed (1994), Cambridge University Press, Cambridge
53. Priestley M.B. "Spectral Analysis and Time Series." (1981), Academic Press, London
54. Salas J.D. Analysis and modeling of hydrologic time series. In: Maidment D.R. (Ed). "Handbook of Hydrology" (1993), McGraw-Hill, New York 19.1-19.72
55. Schepers H.E., van Beek J.H.G.M., and Bassingthwaighte J.B. Four methods to estimate the fractal dimension from self-affine signals. IEEE Eng. Medicine Biol. 11 (1992) 57-64 71
56. Schmittbuhl J., Vilotte J.-P., and Roux S. Reliability of self-affine measurements. Phys. Rev. E 51 (1995) 131-147
57. Slack J.R., and Landwehr J.M. "Hydro-Climatic Data network (HCDN): A U.S. Geological Survey Streamflow Data Set for the United States for the Study of Climate Variations, 1874-1988." (1992), U.S. Geological Survey, Reston, VA 193 U.S. Geological Survey Open-File Report 92-129. and CD ROM.
58. Smith W.W., and Smith J.M. "Handbook of Real-Time Fast Fourier Transforms." (1995), IEEE Press, New York
59. Stedinger J.R., Vogel R.M., and Foufoula-Georgiou E. Frequency analysis of extreme events. In: Maidment D.R. (Ed). "Handbook of Hydrology" (1993), McGraw-Hill, New York 18.1-18.66
60. Tapiero C.S., and Vallois P. Run length statistics and the Hurst exponent in random and birth-death random motions. Chaos, Solitons & Fractals 7 (1996) 1333-1341
61. Turcotte D.L. "Fractals and Chaos in Geology and Geophysics,". 2nd ed. (1997), Cambridge University Press, Cambridge
62. Voss R.F. Random fractals: Characterization and measurement. In: Pynn R., and Skjeltorp A. (Eds). "Scaling Phenomena in Disordered Systems" (1985), Plenum Press, New York 1-11
63. Voss R.F. Random fractal forgeries: From mountains to music. In: Nash S. (Ed). "Science and Uncertainty" (1985), Science Reviews, London 69-85
64. Voss R.F. Random fractal forgeries. In: Earnshaw R.A. (Ed). "Fundamental Algorithms for Computer Graphics" F17 (1985), Springer-Verlag, New York 805-835 NATO ASI Series
65. Voss R.F. Characterization and measurement of random fractals. Phys. Scripta T13 (1986) 27-32
66. Voss R.F. Fractals in nature: From characterization to simulation. In: Peitgen H.-O., and Saupe D. (Eds). "The Science of Fractal Images" (1988), Springer-Verlag, New York 21-70
67. Voss R.F. Random fractals: Self affinity in noise, music, mountains, and clouds. Physica D 38 (1989) 362-371
68. Wang M.C., and Uhlenbeck G.E. On the theory of the Brownian motion, II. Rev. Mod. Phys. 17 (1945) 323-342
69. Wornell G.W. "Signal Processing with Fractals: A Wavelet-Based Approach." (1996), Prentice-Hall, Englewood Cliffs, NJ