Extended power-law scaling of self-affine signals exhibiting apparent multifractality

Geophysical Research Letters

Volumn 38, Issue 13, 2011, Pages

  Guadagnini, Alberto ^a   Neuman, Shlomo P ^b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; AGGREGATES; ATMOSPHERIC PRESSURE; COSMOLOGY; FRACTALS; FUSION REACTORS; MAGNETOSPHERE; METAL INSULATOR BOUNDARIES; METAL INSULATOR TRANSITION; SEMICONDUCTOR INSULATOR BOUNDARIES; SURFACE TOPOGRAPHY; TIME SERIES; TURBULENCE; TURBULENT FLOW;

BAROMETRIC PRESSURE; COSMIC MICROWAVE BACKGROUND RADIATION; DIFFUSION-LIMITED AGGREGATES; EARTH'S MAGNETOSPHERE; ENVIRONMENTAL VARIABLES; EXTENDED SELF SIMILARITY; FUSION DEVICES; GAUSSIANS; HEAVY-TAILED DISTRIBUTION; HUMAN HEARTBEAT; KINETIC SURFACE ROUGHENING; LOW ENERGIES; MAGNETIZED PLASMAS; MORPHOMETRY; MULTI FRACTALS; MULTIFRACTAL SCALING; MULTIFRACTALITY; NATURAL IMAGES; POWER LAW SCALINGS; SAND WAVES; SELF-AFFINE; TEMPORAL INCREMENT; TURBULENT BOUNDARY LAYERS;

ENVIRONMENTAL REGULATIONS;

BAROMETRY; COSMIC RAY; EMPIRICAL ANALYSIS; GAUSSIAN METHOD; GRAVEL BED STREAM; MAGNETOSPHERE; MARS; MORPHOMETRY; PLASMA; POWER LAW; SAND WAVE; SIGNAL; SPATIOTEMPORAL ANALYSIS; SURFACE ROUGHNESS; TOPOGRAPHIC MAPPING; TURBULENCE;

EID: 79959962203     PISSN: 00948276     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011GL047727     Document Type: Article

References (32)

1. Atyabi, F., M. A. Livari, K. Kaviani, and M. R. R. Tabar (2006), Two sta-tistical methods for resolving healthy individuals and those with conges-tive heart failure based on extended self-similarity and a recursive method, J. Biol. Phys., 32, 489-495, doi:10.1007/s10867-006-9031-y. (Pubitemid 46872925)
2. Benzi, R., S. Ciliberto, C. Baudet, G. R. Chavarria, and R. Tripiccione (1993a), Extended self-similarity in the dissipation range offully devel-oped turbulence, Europhys. Lett., 24(4), 275-279, doi:10.1209/0295-5075/24/4/007.
3. Benzi, R., S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi (1993b), Extended self-similarity in turbulent flows, Phys. Rev. E, 48, R29-R32, doi:10.1103/PhysRevE.48.R29.
4. Benzi, R., L. Biferale, S. Ciliberto, M. V. Struglia, and R. Tripiccione (1996), Generalised scaling in fully developed turbulence, Physica D, 96, 162-181, doi:10.1016/0167-2789(96)00018-8. (Pubitemid 126687387)
5. Bershadskii, A. (2002), Extended self-similarity of low-energy cosmic rays, Europhys. Lett., 59(3), 472-476, doi:10.1209/epl/i2002-00219-7.
6. Bershadskii, A., and K. R. Sreenivasan (2003), Extended self-similarity of the small-scale cosmic microwave background anisotropy, Phys. Lett. A, 319, 21-23, doi:10.1016/j.physleta.2003.09.079.
7. Budaev, V. P., N. Ohno, S. Masuzaki, T. Morisaki, A. Komori, and S. Takamura (2008a), Extended self-similarity ofintermittent turbulence in edge magnetized plasmas, Nucl. Fusion, 48, 024014, doi:10.1088/0029-5515/48/2/024014. (Pubitemid 351496087)
8. Budaev, V. P., N. Ohno, S. Takamura, S. Masuzaki, A. Komori, and T. Morisaki (2008b), Extended self-similarity in edge plasma turbulence of fusion devices, Contrib. PlasmaPhys., 48(1-3), 42-47, doi:10.1002/ctpp.200810007.
9. Budaev, V. P., S. Savin, L. Zelenyi, N. Ohno, S. Takamura, and E. Amata (2008c), Intermittency and extended self-similarity in space and fusion plasma: boundary effects, Plasma Phys. Control. Fusion, 50, 074014, doi:10.1088/0741- 3335/50/7/074014.
10. Chakraborty, S., U. Frisch, and S. S. Ray (2010), Extended self-similarity works for the Burgers equation and why, J. FluidMech., 649, 275-285, doi:10.1017/S0022112010000595.
11. Deutsch, C. V., and A. G. Journel (1998), GSLIB: Geostatistical Software Library and User's Guide, 2nd ed., Oxford Univ. Press, New York.
12. Di Federico, V., and S. P. Neuman (1997), Scaling ofrandom fields by means of truncated power variograms and associated spectra, Water Resour. Res., 33(5), 1075-1085, doi:10.1029/97WR00299.
13. Fraysse, A. (2007), Generic validity of the multifractal formalism, SIAM J. Math. Anal., 39(2), 593-607, doi:10.1137/060669760. (Pubitemid 351456396)
14. Kundagrami, A., C. Dasgupta, P. Punyindu, and S. Das Sarma (1998), Extended self-similarity in kinetic surface roughening, Phys. Rev. E, 57, R3703-R3706, doi:10.1103/PhysRevE.57.R3703. (Pubitemid 128595804)
15. Lovejoy, S., and D. Schertzer (1995), Multifractals and rain, in New Uncer-tainty Concepts in Hydrology and Hydrological Modelling, edited by A. W. Kundzewicz, pp. 61\103, Cambridge Univ. Press, New York, doi:10.1017/ CBO9780511564482.009.
16. Mandelbrot, B. B., and J. W. Van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAMRev., 10, 422-437, doi:10.1137/1010093.
17. Molz, F. J., H. Rajaram, and S. Lu (2004), Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions, Rev. Geophys., 42, RG1002, doi:10.1029/2003RG000126.
18. Monin, A. S., and A. M. Yaglom (1975), Statistical Fluid Mechanics: Mechanics ofTurbulence, 874 pp., MIT Press, Cambridge, Mass.
19. Moriconi, L. (2003), Extended self-similarity in the two-dimensional metal-insulator transition, Phys. Rev. E, 68, 036135, doi:10.1103/PhysRevE.68. 036135.
20. Neuman, S. P. (2010a), Apparent/spurious multifractality of data sampled from fractional Brownian/Lévy motions, Hydrol. Processes, 24, 2056-2067, doi:10.1002/hyp.7611.
21. Neuman, S. P. (2010b), Apparent/spurious multifractality ofabsolute increments sampled from truncated fractional Gaussian/Lévy noise, Geophys. Res. Lett., 37, L09403, doi:10.1029/2010GL043314.
22. Neuman, S. P. (2011), Apparent multifractality and scale-dependent distribution of data sampled from self-affine processes, Hydrol. Processes, 25, 1837-1840, doi:10.1002/hyp.7967.
23. Neuman, S. P., and V. Di Federico (2003), Multifaceted nature of hydrogeologic scaling and its interpretation, Rev. Geophys., 41(3), 1014, doi:10.1029/2003RG000130.
24. Nikora, V. (2005), High-order structure functions for planet surfaces: A turbulence metaphor, IEEE Geosci. Remote Sens. Lett., 2(3), 362-365, doi:10.1109/LGRS.2005.851553. (Pubitemid 41633150)
25. Nikora, V. I., and D. G. Goring (2001), Extended self-similarity in geophysical and geological applications, Math. Geol., 33(3), 251-271, doi:10.1023/A:1007630021716. (Pubitemid 33745544)
26. Qian, J. (2000), Closure approach to high-order structure functions of turbulence, Phys. Rev. Lett., 84(4), 646-649, doi:10.1103/PhysRevLett. 84.646.
27. Queiros-Conde, D. (1997), Geometrical extended self-similarity and intermittency in diffusion-limited aggregates, Phys. Rev. Lett., 78(23), 4426-4429, doi:10.1103/PhysRevLett.78.4426. (Pubitemid 127655515)
28. Rodriguez-Iturbe, I., and A. Rinaldo (1997), Fractal River Basins, Cambridge Univ. Press, Cambridge, U. K.
29. Samorodnitsky, G., and M. S. Taqqu (1994), Stable Non-Gaussian Random Processes, Chapman and Hall, New York.
30. Tessier, Y., S. Lovejoy, and D. Schertzer (1993), Universal multifractals: Theory and observations for rain and clouds, J. Appl. Meteorol., 32, 223-250, doi:10.1175/1520-0450(1993)0322.0. CO;2. (Pubitemid 23381912)
31. Turiel, A., G. Mato, and N. Parga (1998), Self-similarity properties of natural images resemble those of turbulent flows, Phys. Rev. Lett., 80(5), 1098-1101, doi:10.1103/PhysRevLett.80.1098. (Pubitemid 128622283)
32. Veneziano, D., A. Langousis, and P. Furcolo (2006), Multifractality and rainfall extremes: A review, Water Resour. Res., 42, W06D15, doi:10.1029/2005WR004716. (Pubitemid 44156596)