Some distinctions between self-similar and self-affine estimates of fractal dimension with case history

Mathematical Geology

Volumn 32, Issue 3, 2000, Pages 319-335

  Wilson, Thomas H ^a  

^a WEST VIRGINIA UNIVERSITY   (United States)

Author keywords

Fractal dimension; Self affine; Self similar; Shortening; Strain estimation

Indexed keywords

FRACTAL ANALYSIS; STRAIN;

EID: 0034088619     PISSN: 08828121     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007585811281     Document Type: Article

References (25)

1. Brigham, E. O., 1974, The fast Fourier transform: Prentice-Hall, Englewood Cliffs, New Jersey.
2. Brown, S., 1987, A note on the description of surface roughness using fractal dimension: Geophys. Res. Lett., v. 14, no. 11, p. 1085-1098.
3. Douds, A. S. B., 1998, Fractal analysis of topography and structure across the Appalachian foreland of West Virginia: unpubl. Masters thesis, West Virginia University, 119 p.
4. Fox, C., 1985, Description, analysis, and prediction of sea-floor roughness using spectral models: Naval Oceanographic Office Technical Report 279, Bay St. Louis, MO, 218 p.
5. Fox, C., 1989, Empirically derived relationships between fractal dimension and power law form frequency spectra: Pure and Applied Geophysics, v. 131, p. 211-239.
6. Gilbert, L., 1989, Are topographic data sets fractal? Pure and Applied Geophysics, v. 131, p. 241-254.
7. Klinkenberg, B., 1994, A review of methods used to determine the fractal dimension of linear features: Math. Geology, v. 26, no. 1, p. 23-46.
8. Malenverno, A., 1989, Testing linear models of sea-floor topography: Pure and Applied Geophysics, v. 131, p. 139-155.
9. Mandelbrot, B. B., 1967, How long is the coast of Britain? Statistical similarity and fractional dimension: Science, v. 156, p. 636-638.
10. Mandelbrot, B. B., 1985, Self-affine fractals and fractal dimension: Physica Scripta, v. 32, p. 257-260.
11. Mandelbrot, B. B., and van Ness, J., 1968, Fractional Brownian motions, fractional noises and Applications: SIAM Review, v. 10, no. 7, p. 422-437.
12. Mareschal, J., 1989, Fractal reconstruction of sea-floor topography: Pure and Applied Geophysics, v. 131, p. 197-210.
13. Oppenheim, A., and Schafer, R., 1975, Digital signal processing: Prentice-Hall, Englewood Cliffs, New Jersey, 585 p.
14. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1988, Numerical recipes: The art of scientific computing: Cambridge University Press, Cambridge, 818 p.
15. Termonia, Y., and P. Meakin, 1986, Formation of fractal cracks in a kinetic fracture model: Nature, v. 320, p. 429-431.
16. Turcotte, D. L., 1989, Fractals in geology and geophysics: Pure and Applied Geophysics, v. 131, p. 171-196.
17. Turcotte, D. L., 1992, Fractals and chaos in geology and geophysics: Cambridge University Press, Cambridge, 221 p.
18. Turcotte, D. L., 1997, Fractals and chaos in geology and geophysics, 2nd ed.: Cambridge University Press, Cambridge, 398 p.
19. Voss, R. F., 1985a, Random fractals: Characterization and measurement: Scaling phenomena in disordered systems, R. Pynn and A Skejeltorp, eds.; Plenum Press, New York, pp. 1-11.
20. Voss, R. F., 1985b, Random fractal forgeries: Fundamental algorithms for computer graphics, NATO ASI Series, vol. F17, R. A. Earnshaw, ed., Springer-Verlag, Berlin, pp. 805-835.
21. Voss, R. F., 1988, Fractals in nature: From characterization to simulation: The Science of Fractal Images, H. O. Peitgen and D. Saupe, eds., Springer-Verlag, New York, pp. 21-70.
22. Wilson, T. H., 1997, Fractal strain distribution and its implications for cross-section balancing further discussion: Jour. of Structural Geology, v. 19, no. 1, p. 129-132.
23. Wilson, T. H., and Dominic, J., 1998, Fractal interrelationships between topography and structure: Earth Surf. Processes Landforms, v. 23, p. 509-525.
24. Wong, P., 1987, Fractal Surfaces in porous media: Amer. Inst. Phys. v. 154, p. 304-318.
25. Wu, S., 1993, Fractal strain distribution and its implications on cross-section balancing: Jour. of Structural Geology, v. 15, p. 1497-1507.