A. Alvarez, E. Hernandez-garcia, and J. Tintoré, On the effect of small-scale oceanic variability on topography-generated currents, Geophysical Research Letters, vol.100, issue.6, pp.739-742, 2000.
DOI : 10.1029/1999GL011046

B. Audit, E. Bacry, J. F. Muzy, and A. Arnéodo, Wavelet-based estimators of scaling behavior, IEEE Transactions on Information Theory, vol.48, issue.11, pp.48-2938, 2002.
DOI : 10.1109/TIT.2002.802631
URL : https://hal.archives-ouvertes.fr/hal-00344592

C. A. Aviles, C. H. Scholz, and J. Boatwright, Fractal analysis applied to characteristic segments of the San Andreas Fault, Journal of Geophysical Research, vol.XIII, issue.B1, pp.331-344, 1987.
DOI : 10.1029/JB092iB01p00331

G. Balmino, K. Lambeck, and W. Kaula, A spherical harmonic analysis of the Earth's topography, Journal of Geophysical Research, vol.72, issue.2, pp.478-481, 1973.
DOI : 10.1029/JB078i002p00478

G. Balmino, The Spectra of the topography of the Earth, Venus and Mars, Geophysical Research Letters, vol.97, issue.E5, pp.1063-1066, 1993.
DOI : 10.1029/93GL01214

J. R. Banavar, F. Colaiori, A. Flammini, A. Maritan, R. et al., Scaling, optimality, and landscape evolution, Journal of Statistical Physics, vol.104, issue.1/2, pp.1-48, 2001.
DOI : 10.1023/A:1010397325029

G. I. Barenblatt, A. V. Zhivago, Y. P. Neprochnov, and A. A. Ostrovskiy, The fractal dimension: a quantitative characteristic of ocean-bottom relief, Oceanology, pp.24-695, 1984.

T. H. Bell, Statistical features of sea-floor topography, Deep-Sea Res, pp.883-892, 1975.

J. M. Berkson and J. E. Matthews, Statistical properties of seafloor roughness, Acoustics and the Sea-Bed, pp.215-223, 1983.

M. V. Berry and J. H. Hannay, Topography of random surfaces, Nature, vol.273, issue.5663, p.573, 1978.
DOI : 10.1038/271431a0

E. Bouchaud, G. Lapasset, J. Planès, N. , and S. , Statistics of branched fracture surfaces, Physical Review B, vol.48, issue.5, pp.2917-2928, 1993.
DOI : 10.1103/PhysRevB.48.2917

P. A. Burrough, Fractal dimensions of landscapes and other environmental data, Nature, vol.28, issue.5838, pp.240-242, 1981.
DOI : 10.1038/294240a0

C. G. Chase, Fluvial landsculpting and the fractal dimension of topography, Geomorphology Data Announcement 88-MGG-02: Digital relief of the Surface of the Earth, pp.39-57, 1988.

H. J. De-wisj, Statistics of ore distributions Part I: Frequency distributions of assay values, Geol. Mijnb, vol.13, pp.127-144, 1951.

P. S. Dodds and D. H. Rothman, Scaling, Universality, and Geomorphology, Annual Review of Earth and Planetary Sciences, vol.28, issue.1, pp.571-610, 2000.
DOI : 10.1146/annurev.earth.28.1.571

G. Dietler and Y. Zhang, Fractal aspects of the Swiss landscape, Physica A: Statistical Mechanics and its Applications, vol.191, issue.1-4, pp.213-219, 1992.
DOI : 10.1016/0378-4371(92)90530-4

C. G. Fox and D. E. Hayes, Quantitative methods for analyzing the roughness of the seafloor, Reviews of Geophysics, vol.17, issue.B8, pp.1-48, 1985.
DOI : 10.1029/RG023i001p00001

J. Gagnon, Multiscaling and multifractality in the Earth's topography, 2001.

J. Gagnon, S. Lovejoy, and D. Schertzer, Multifractal surfaces and terrestrial topography, Europhysics Letters (EPL), vol.62, issue.6, pp.801-807, 2003.
DOI : 10.1209/epl/i2003-00443-7

J. C. Gallant, I. D. Moore, M. F. Hutchinson, and P. Gessler, Estimating fractal dimension of profiles: A comparison of methods, Mathematical Geology, vol.8, issue.n. 3, pp.455-481, 1994.
DOI : 10.1007/BF02083489

H. Gaonac-'h, S. Lovejoy, and D. Schertzer, Resolution dependence of infrared imagery of active thermal features at Kilauea Volcano, International Journal of Remote Sensing, vol.24, issue.11, pp.2323-2344, 2003.
DOI : 10.1080/01431160210164253

D. Gibert and V. Courtillot, Seasat Altimetry and the South Atlantic Geoid: 1. Spectral analysis, Journal of Geophysical Research, vol.85, issue.1???4, pp.6235-6248, 1987.
DOI : 10.1029/JB092iB07p06235

L. E. Gilbert, Are topographic data sets fractal?, pp.241-254, 1989.

M. F. Goodchild, Fractals and the accuracy of geographical measures, Journal of the International Association for Mathematical Geology, vol.6, issue.2, pp.85-98, 1980.
DOI : 10.1007/BF01035241

A. M. Guarnieri, SAR interferometry and statistical topography, IEEE Transactions on Geoscience and Remote Sensing, vol.40, issue.12, pp.2567-2581, 2002.
DOI : 10.1109/TGRS.2002.807576

D. C. Harvey, H. Gaonac-'h, S. Lovejoy, J. Stix, and D. Schertzer, MULTIFRACTAL CHARACTERIZATION OF REMOTELY SENSED VOLCANIC FEATURES: A CASE STUDY FROM KILAUEA VOLCANO, HAWAII, Fractals, vol.10, issue.03, pp.265-274, 2002.
DOI : 10.1142/S0218348X02001191

U. C. Herzfeld, I. I. Kim, and J. A. Orcutt, Is the ocean floor a fractal?, Mathematical Geology, vol.95, issue.no. 10, pp.421-462, 1995.
DOI : 10.1007/BF02084611

U. C. Herzfeld and C. Overbeck, Analysis and simulation of scale-dependent fractal surfaces with application to seafloor morphology, Computers & Geosciences, vol.25, issue.9, pp.979-1007, 1999.
DOI : 10.1016/S0098-3004(99)00062-X

J. Huang and D. L. Turcotte, Fractal mapping of digitized images: Application to the topography of Arizona and comparisons with synthetic images, Journal of Geophysical Research, vol.20, issue.B6, pp.7491-7495, 1989.
DOI : 10.1029/JB094iB06p07491

J. Huang and D. L. Turcotte, Fractal image analysis: application to the topography of Oregon and synthetic images, Journal of the Optical Society of America A, vol.7, issue.6, pp.1124-1130, 1990.
DOI : 10.1364/JOSAA.7.001124

H. E. Hurst, Long-term storage capacity of reservoirs, Transactions of the, pp.770-808, 1951.

M. Kardar, G. Parisi, and Y. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.56, issue.9, pp.889-892, 1986.
DOI : 10.1103/PhysRevLett.56.889

B. Klinkenberg and M. F. Goodchild, The fractal properties of topography: a comparison of methods, Earth Surface Processes and Landforms, pp.217-234, 1992.

K. Lambeck, Geophysical geodesy: The study of the slow deformations of the Earth, 1988.
DOI : 10.1029/GM060p0007

D. Lavallée, S. Lovejoy, D. Schertzer, P. L. Ladoy, and N. Lam, Nonlinear variability of landscape topography: multifractal analysis and simulation, Fractals in Geography, pp.158-192, 1993.

P. Leary, Rock as a critical-point system and the inherent implausibility of reliable earthquake prediction, Geophysical Journal International, vol.131, issue.3, pp.451-466, 1997.
DOI : 10.1111/j.1365-246X.1997.tb06589.x

G. M. Lewis, S. Pecknold, S. Lovejoy, and D. Schertzer, The scale invariant generator technique for quantifying anisotropic scale invariance, Computers & Geosciences, vol.25, issue.9, pp.963-978, 1999.
DOI : 10.1016/S0098-3004(99)00061-8

S. Lovejoy and D. Schertzer, Our multifractal atmosphere: A unique laboratory for non-linear dynamics, Physics in Canada, vol.46, issue.4, pp.62-71, 1990.

S. Lovejoy and D. Schertzer, Multifractal analysis techniques and the rain and cloud fields from 10 ?3 to 10 6 m, in: Non-linear Variability in Geophysics, pp.111-144, 1991.

S. Lovejoy, D. Lavallée, D. Schertzer, and P. Ladoy, The l 1/2 law and multifractal topography: theory and analysis, Nonlin. Processes Geophys, pp.16-22, 1995.

S. Lovejoy, S. Pecknold, and D. Schertzer, Stratified multifractal magnetization and surface geomagnetic fields-I. Spectral analysis and modelling, Geophysical Journal International, vol.145, issue.1, pp.112-126, 2001.
DOI : 10.1111/j.1365-246X.2001.00344.x

S. Lovejoy, D. Schertzer, Y. Tessier, and H. Gaonac-'h, Multifractals and resolution-independent remote sensing algorithms: The example of ocean colour, International Journal of Remote Sensing, vol.22, issue.7, pp.1191-1234, 2001.
DOI : 10.1080/01431160151144314

S. Lovejoy, D. Schertzer, and J. Gagnon, Multifractal simulations of the Earth's surface and interior: anisotropic singularities and morphology, in: GIS and Spatial Analysis, Proc. of the Inter, pp.37-54, 2005.

B. B. Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Science, vol.156, issue.3775, pp.636-638, 1967.
DOI : 10.1126/science.156.3775.636

B. B. Mandelbrot, Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands, Proc. Nat. Acad. Sci. USA, pp.72-3825, 1975.
DOI : 10.1073/pnas.72.10.3825

B. B. Mandelbrot, The Fractal Geometry of, Nature, 1983.

B. B. Mandelbrot and J. W. Van-ness, Fractional Brownian motions , fractional noises and applications, SIAM review, pp.422-450, 1968.
DOI : 10.1137/1010093

J. Mareschal, Fractal reconstruction of sea-floor topography, PAGEOPH, pp.197-210, 1989.

D. M. Mark and P. B. Aronson, Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping, Journal of the International Association for Mathematical Geology, vol.19, issue.7, pp.671-683, 1984.
DOI : 10.1007/BF01033029

D. Marsan and C. J. Bean, Multiscaling nature of sonic velocities and lithology in the upper crystalline crust: Evidence from the KTB main borehole, Geophysical Research Letters, vol.10, issue.2, pp.275-278, 1999.
DOI : 10.1029/1998GL900295

S. Morel, J. Schmittbuhl, E. Bouchaud, and G. Valentin, Scaling of Crack Surfaces and Implications for Fracture Mechanics, Physical Review Letters, vol.85, issue.8, pp.1678-1681, 2000.
DOI : 10.1103/PhysRevLett.85.1678

J. F. Muzy, E. Bacry, and A. Arnéodo, Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method, Physical Review E, vol.47, issue.2, pp.875-884, 1993.
DOI : 10.1103/PhysRevE.47.875

P. G. Okubo and K. Aki, Fractal geometry in the San Andreas Fault System, Journal of Geophysical Research, vol.81, issue.B1, pp.345-355, 1987.
DOI : 10.1029/JB092iB01p00345

R. Orosei, R. Bianchi, A. Coradini, S. Espinasse, C. Federico et al., Self-affine behavior of Martian topography at kilometer scale from Mars Orbiter Laser Altimeter data, Journal of Geophysical Research, vol.2, issue.B4, pp.8023-8032, 2003.
DOI : 10.1029/2002JE001883

G. Pandey, S. Lovejoy, and D. Schertzer, Multifractal analysis of daily river flows including extremes for basins of five to two million square kilometres, one day to 75 years, Journal of Hydrology, vol.208, issue.1-2, pp.62-81, 1998.
DOI : 10.1016/S0022-1694(98)00148-6

B. Parsons and J. G. Sclater, An analysis of the variation of ocean floor bathymetry and heat flow with age, Journal of Geophysical Research, vol.13, issue.5, pp.803-827, 1977.
DOI : 10.1029/JB082i005p00803

S. Pecknold, S. Lovejoy, and D. Schertzer, Stratified multifractal magnetization and surface geomagnetic fields-II. Multifractal analysis and simulations, Geophysical Journal International, vol.145, issue.1, pp.127-144, 2001.
DOI : 10.1111/j.1365-246X.2001.00345.x

S. Pecknold, S. Lovejoy, D. Schertzer, and C. Hooge, Multifractal and resolution dependence of remotely sensed data: GSI and GIS, Scale in Remote Sensing and GIS, pp.361-394, 1997.

J. Perrin, Les atomes, NRF-Gallimard, 1913.

M. Pilkington and J. Todoeschuck, Scaling nature of crustal susceptibilities, Geophysical Research Letters, vol.123, issue.7, pp.779-782, 1995.
DOI : 10.1029/95GL00486

A. Prey, Darstellung der Höhen-und Tiefenverhältnisse der Erde durch eine Entwicklung nach Kugelfunktionen bis zur 16, Ordnung Abhandl. Ges. Wiss. Göttingen, Math.-physik. Kl, vol.11, issue.1, pp.1-29, 1922.

L. F. Richardson, The problem of contiguity: an appendix to statistics of deadly quarrels, Gen. Syst. Yearb, vol.6, pp.139-187, 1961.

A. Rinaldo, A. Maritan, F. Colaiori, A. Flammini, R. Rigon et al., Thermodynamics of Fractal Networks, Thermodynamics of fractal networks, pp.3364-3368, 1996.
DOI : 10.1103/PhysRevLett.76.3364

A. Rinaldo, I. Rodriguez-iturbe, R. Rigon, R. L. Bras, E. Ijjasz-vasquez et al., Minimum energy and fractal structures of drainage networks, Water Resources Research, vol.9, issue.6, pp.2183-2195, 1992.
DOI : 10.1029/92WR00801

A. Rinaldo, I. Rodriguez-iturbe, R. Rigon, E. Ijjasz-vasquez, and R. L. Bras, Self-organized fractal river networks, Physical Review Letters, vol.70, issue.6, pp.822-825, 1993.
DOI : 10.1103/PhysRevLett.70.822

R. S. Sayles and T. R. Thomas, Surface topography as a nonstationary random process, Nature, vol.87, issue.5644, pp.431-434, 1978.
DOI : 10.1016/0043-1648(77)90057-6

D. Schertzer and S. Lovejoy, Generalized scale invariance in turbulent phenomena, Physico-Chemical Hydrodynamics Journal, vol.6, pp.623-635, 1985.

D. Schertzer and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, Journal of Geophysical Research, vol.2, issue.D8, pp.9693-9714, 1987.
DOI : 10.1029/JD092iD08p09693

D. Schertzer and S. Lovejoy, Nonlinear geodynamical variability: multiple singularities, universality and observables, in: Nonlinear Variability in Geophysics, pp.41-82, 1991.

. Www, nonlin-processes-geophys.net/13, Nonlin. Processes Geophys, vol.541, issue.13, pp.541-570, 2006.

D. Schertzer and S. Lovejoy, Hard and soft multifractal processes, Physica A: Statistical Mechanics and its Applications, vol.185, issue.1-4, pp.187-194, 1992.
DOI : 10.1016/0378-4371(92)90455-Y

D. Schertzer, S. Lovejoy, and R. A. Feddes, From scalar cascades to Lie cascades: Joint multifractal analysis of rain and cloud processes, in: Space/time variability and interdependence for various hydrological processes, pp.153-173, 1995.

D. Schertzer and S. Lovejoy, Universal Multifractals Do Exist!: Comments on ???A Statistical Analysis of Mesoscale Rainfall as a Random Cascade???, Journal of Applied Meteorology, vol.36, issue.9, pp.1296-1303, 1997.
DOI : 10.1175/1520-0450(1997)036<1296:UMDECO>2.0.CO;2

J. Schmittbuhl, F. Schmitt, and C. Scholz, Scaling invariance of crack surfaces, Journal of Geophysical Research: Solid Earth, vol.94, issue.3, pp.5953-5973, 1995.
DOI : 10.1029/94JB02885

J. G. Sclater, R. N. Anderson, L. Bell, and M. , Elevation of ridges and evolution of the central eastern Pacific, Journal of Geophysical Research, vol.231, issue.1, pp.7888-7915, 1971.
DOI : 10.1029/JB076i032p07888

K. Sinclair and R. Ball, Mechanism for Global Optimization of River Networks from Local Erosion Rules, Physical Review Letters, vol.76, issue.18, pp.3360-3363, 1996.
DOI : 10.1103/PhysRevLett.76.3360

D. Sornette and Y. Zhang, Non-linear Langevin model of geomorphic erosion processes, Geophysical Journal International, vol.113, issue.2, pp.382-386, 1993.
DOI : 10.1111/j.1365-246X.1993.tb00894.x

H. Steinhaus, Length, shape and area, pp.1-13, 1954.

I. Tchiguirinskaia, S. Lu, F. J. Molz, T. M. Williams, and D. Lavallée, Multifractal versus monofractal analysis of wetland topography, Stochastic Environmental Research and Risk Assessment (SERRA), vol.14, issue.1, pp.8-32, 2000.
DOI : 10.1007/s004770050002

Y. Tessier, S. Lovejoy, P. Hubert, and D. Schertzer, Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions, Journal of Geophysical Research: Atmospheres, vol.7, issue.2, pp.427-440, 1996.
DOI : 10.1029/96JD01799

D. L. Turcotte, Fractals in geology and geophysics, PAGEOPH, pp.171-196, 1989.

D. L. Turcotte, Fractals and chaos in geology and geophysics, 1992.

D. L. Turcotte and E. R. Oxburgh, Finite amplitude convective cells and continental drift United States Geological Survey: Digital Elevation Models, National Mapping Program Technical Instructions, Data Users Guide, J. Fluid Mech. U.S. Geological Survey, vol.28, issue.1, pp.29-42, 1967.

D. Veneziano and V. Iacobellis, Self-similarity and multifractality of topographic surfaces at basin and subbasin scales, Journal of Geophysical Research: Solid Earth, vol.27, issue.7, pp.797-809, 1999.
DOI : 10.1029/1999JB900083

D. Veneziano and J. D. Niemann, Self-similarity and multifractality of fluvial erosion topography: 1. Mathematical conditions and physical origin, Water Resources Research, vol.3, issue.7, pp.1923-1936, 2000.
DOI : 10.1029/2000WR900053

D. Veneziano and J. D. Niemann, Self-similarity and multifractality of fluvial erosion topography: 2. Scaling properties, Water Resources Research, vol.7, issue.7, pp.1937-1951, 2000.
DOI : 10.1029/2000WR900054

V. Meinesz and F. A. , A remarkable feature of the Earth's topography , origin of continents and oceans, Proc. Koninkl. Ned. Akad. Wetensch. ser. B, vol.55, pp.212-228, 1951.

J. K. Weissel, F. P. Lincoln, and A. Malinverno, The lengthscaling properties of topography, J. Geophys. Res, vol.99, issue.13, pp.997-1011, 1994.

F. Wewel, F. Scholten, and K. Gwinner, High Resolution Stereo Camera (HRSC)-Multispectral 3D-Data Acquisition and Photogrammetric Data Processing, Canadian Journal of Remote Sensing, vol.6, issue.2, pp.466-474, 2000.
DOI : 10.1080/07038992.2000.10855278

T. Xu, I. D. Moore, and J. C. Gallant, Fractals, fractal dimensions and landscapes ??? a review, Geomorphology, vol.8, issue.4, pp.245-262, 1993.
DOI : 10.1016/0169-555X(93)90022-T