Fractal-geometry techniques in the quantification of complex rock structures: A special view on scaling regimes, inhomogeneity and anisotropy

Journal of Structural Geology

Volumn 46, Issue , 2013, Pages 2-21

  Kruhl, Jörn H ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Anisotropy; Complex rock structures; Fractal geometry; Inhomogeneity; Scaling regimes

Indexed keywords

DIFFERENT SCALE; FRACTAL GEOMETRY; INHOMOGENEITIES; ROCK PROPERTIES; ROCK STRUCTURES; SCALING REGIMES;

ANISOTROPY; FRACTALS; GEOMECHANICS;

ROCKS;

ANISOTROPY; FRACTAL ANALYSIS; GEOMETRY; INHOMOGENEITY; ROCK MECHANICS;

EID: 84870899107     PISSN: 01918141     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsg.2012.10.002     Document Type: Review

References (315)

1. Ackermann R.V., Schlische R.W., Withjack M.O. The geometric and statistical evolution of normal fault systems: an experimental study of the effects of mechanical layer thickness on scaling laws. Journal of Structural Geology 2001, 23:1803-1819.
2. Adams B.L., Wright S.I., Kunze K. Orientation imaging: the emergence of a new microscopy. Metallurgical Transactions 1993, 24A:819-831.
3. Agterberg F.P. Multifractal modelling of the sizes and grades of giant and supergiant deposits. Global Tectonics and Metallogeny 1997, 6:131-136.
4. Agterberg F.P., Cheng Q., Brown A., Good D. Multifractal modeling of fractures in the Lac Du Bonnet Batholith, Manitoba. Computers & Geosciences 1996, 22:497-507.
5. Allègre C.J., Le Mouel J.L., Provost A. Scaling rules in rock fracture and possible implications for earthquake prediction. Nature 1982, 297:47-49.
6. Amidzic O., Riehle H.J., Fehr T., Wienbruch C., Elbert T. Pattern of focal γ-bursts in chess players. Nature 2001, 412:603.
7. An L.-J., Sammis C. Particle size distribution of cataclastic fault materials from southern California: a 3-D study. Pure and Applied Geophysics 1994, 143:203-227.
8. André-Mayer A.-S., Sausse J. Thickness and spatial distribution of veins in a porphyry copper deposit, Rosia Poieni, Romania. Journal of Structural Geology 2007, 29:1695-1708.
9. Andriani G.F., Walsh N. Physical properties and textural parameters of calcarenitic rocks: qualitative and quantitative evaluations. Engineering Geology 2002, 67:5-15.
10. Armienti P., Tarquini S. Power law olivine crystal size distributions in lithospheric mantle xenoliths. Lithos 2002, 65:273-285.
11. Ashby R.W. An Introduction to Cybernetics 1956, Chapman & Hall, London.
12. Aviles S.R., Scholz C.H., Boatwright J. Fractal analysis applied to characteristic segments of the San Andreas fault. Journal of Geophysical Research 1987, 92:331-334.
13. Avnir D., Biham O., Lidar D., Malcai O. Is the geometry of nature fractal?. Science 1998, 279(5347):39-40.
14. Ayunova O.D., Kalush Yu.A., Loginov V.M. Relationship of the seismic activity of the Tuvinian and adjacent Mongolian areas with the fractal dimensionality of a fault system. Russian Geology and Geophysics 2007, 48:593-597.
15. Babadagli T. Scanline method to determine the fractal nature of 2-D fracture networks. Mathematical Geology 2002, 34:647-670.
16. Baccar M., Gee L.A., Gonzalez R.C., Abidi M.A. Segmentation of range images via data fusion and morphological watersheds. Pattern Recognition 1996, 29:1673-1687.
17. Bahat D. Tectonofractography 1991, Springer, Berlin/Heidelberg/New York.
18. Baker B.R., Gessner K., Holden E.J., Squelch A.P. Automatic detection of anisotropic features on rock surfaces. Geosphere 2008, 4:418-428.
19. Barenblatt G.I., Zhivago A.V., Neprochnov Yu.P., Ostrovskyi A.A. The fractal dimension: a quantitative characteristic of ocean bottom relief. Oceanology 1984, 24:695-697.
20. Barnsley M. Fractals Everywhere 1988, Academic Press.
21. Barraud J. The use of watershed segmentation and GIS software for textural analysis of thin sections. Journal of Volcanology and Geothermal Research 2006, 154:17-33.
22. Barthélémy P., Jacquin C., Yao J., Thovert J.F., Adler P.M. Hierarchical structures and hydraulic properties of a fractures network in the Causse of Larzac. Journal of Hydrology 1996, 187:237-258.
23. Barton C.C. Fractal analysis of scaling and spatial clustering of fractures. Fractals in the Earth Sciences 1995, 141-178. Plenum Press, New York. C.C. Barton, P.R. La Pointe (Eds.).
24. Baykan N.A., Yilmaz N. Mineral identification using color spaces and artificial neural networks. Computers & Geosciences 2010, 36:91-97.
25. Bérubé D., Jébrak M. High precision boundary fractal analysis for shape characterization. Computers & Geosciences 1999, 25:1059-1071.
26. Biegel R.L., Sammis C.G., Dieterich J. The frictional properties of a simulated gouge having a fractal particle distribution. Journal of Structural Geology 1989, 11:827-846.
27. Billi A. Grain size distribution and thickness of breccia and gouge zones from thin (<1 m) strike-slip fault cores in limestone. Journal of Structural Geology 2005, 27:1823-1837.
28. Billi A. On the extent of size range and power law scaling for particles of natural carbonate fault cores. Journal of Structural Geology 2007, 29:1512-1521.
29. Billi A., Storti F. Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone. Tectonophysics 2004, 384:115-128.
30. Bistacchi A., Griffith W.A., Smith S.A.F., Di Toro G., Jones R., Nielsen S. Fault roughness at seismogenic depth from LIDAR and photogrammetric analysis. Pure and Applied Geophysics 2011, 168:2345-2363.
31. Blenkinsop T.G. Thickness-displacement relationships for deformation zones: discussion. Journal of Structural Geology 1989, 11:1053-1054.
32. Blenkinsop T.G. Cataclasis and processes of particle size reduction. Pure and Applied Geophysics 1991, 136:59-86.
33. Blenkinsop T.G. The fractal distribution of gold mineralisation: two examples from the Zimbabwe Archaean craton. Fractal and Dynamic Systems in Geoscience 1994, 247-258. Springer, Berlin/Heidelberg. J.H. Kruhl (Ed.).
34. Blenkinsop T.G. Fractal measures for size and spatial distributions of gold mines: economic applications. Geological Society of Zimbabwe, Special Publication 3 1995, 177-186. T.G. Blenkinsop, P.L. Tromp (Eds.).
35. Blenkinsop T.G., Fernandes T.R.C. Fractal characterization of particle distributions in chromites from the Great Dyke, Zimbabwe. Fractals and Dynamic Systems in Geoscience. Pure and Applied Geophysics 2000, vol. 157:505-521. Birkhäuser, Basel, (Topical Issue).
36. Blenkinsop T.G., Sanderson D.J. Are gold deposits in the crust fractals? A study of gold mines in the Zimbabwe craton. Geological Society London Special Publications 155 1999, 141-151. K.J.W. McCaffrey (Ed.).
37. Bonnet E., Bour O., Odling N.E., Davy P., Main I.G., Cowie P.A., Berkowitz B. Scaling of fracture systems in geological media. Reviews of Geophysics 2001, 39:347-383.
38. Bornyakov S.A., Truskov V.A., Cheremnykh A.V. Dissipative structures in fault zones and their diagnostic criteria (from physical modeling data). Russian Geology and Geophysics 2006, 49:138-143.
39. Bour O., Davy P. Connectivity of random fault networks following a power law fault length distribution. Water Resources Research 1997, 33:1567-1583.
40. Bour O., Davy P. On the connectivity of three-dimensional fault networks. Water Resources Research 1998, 34:2611-2622.
41. Bour O., Davy P., Darcel C., Odling N. A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway). Journal of Geophysical Research 2002, 107(B6):2113.
42. Brooks B.A., Manning C.E. Fractal clustering of metamorphic veins: comment and reply. Geology 1994, 22:1147-1149.
43. Brosch F.J., Pölsler P., Riedmüller G. The use of fractal dimension in engineering geology. Bulletin of Engineering Geology and the Environment 1992, 45:83-88.
44. Brown S.R. A note on the description of surface roughness using fractal dimension. Geophysical Research Letters 1987, 14:1095-1098.
45. Bunde A., Havlin S. Fractals in Science 1994, Springer, Berlin/Heidelberg/New York.
46. Carlson C.A. Spatial distribution of ore deposits. Geology 1991, 19:111-114.
47. Carpinteri A., Chiaia B. Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy. Materials and Structures 1995, 28:435-443.
48. Carpinteri A., Chiaia B. Multifractal scaling laws in the breaking behaviour of disordered materials. Chaos, Solitons & Fractals 1997, 8:135-150.
49. Carpinteri A., Pugno N. A multifractal comminution approach for drilling scaling laws. Powder Technology 2003, 131:93-98.
50. Carpinteri A., Puzzi S. The crack surface anomalous scaling and its connection with the size-scale effects. International Journal of Fracture 2005, 133:43-60.
51. Carpinteri A., Spagnoli A., Vantadori S. A multifractal analysis of fatigue crack growth and its application to concrete. Engineering Fracture Mechanics 2010, 77:974-984.
52. Castaing C., Halawani M.A., Gervais F., Chilès J.P., Genter A., Bourgine B., Ouillon G., Brosse J.M., Martin P., Genna A., Janjou D. Scaling relationships in intraplate fracture systems related to Red Sea rifting. Tectonophysics 1996, 261:291-314.
53. Cello G. Fractal analysis of a Quaternary fault array in the central Apennines, Italy. Journal of Structural Geology 1997, 19:945-953.
54. Cello G., Gambini R., Mazzoli S., Read A., Tondi E., Zucconi V. Fault zone characteristics and scaling properties of the Val d'Agri Fault System (Southern Apennines, Italy). Journal of Geodynamics 2000, 29:293-307.
55. Chase W.G., Simon H.A. Perception in chess. Cognitive Psychology 1973, 4:55-81.
56. 4 wear and fracture surfaces. Journal of Materials Science 1997, 32:6317-6323.
57. Cheng Q. Discrete multifractals. Mathematical Geology 1997, 29:245-266.
58. Cheng Q., Agterberg F.P. Multifractal modeling and spatial statistics. Mathematical Geology 1996, 28:1-16.
59. Chilès J.P. Fractal and geostatistical methods for modeling of a fracture network. Mathematical Geology 1988, 20:631-654.
60. Choudhury R.K., Meere P.A., Mulchrone K.F. Automated grain boundary detection by CASRG. Journal of Structural Geology 2006, 28:363-375.
61. Clark N.N. Three techniques for implementing digital fractal analysis of particle shape. Powder Technology 1986, 46:45-52.
62. Clark M.B., Brantley S.L., Fisher D.M. Power-low vein thickness distributions and positive feedback in vein growth. Geology 1995, 23:975-978.
63. Coster M., Chermant J.-L. Image analysis and mathematical morphology for civil engineering materials. Cement and Concrete Composites 2001, 23:133-151.
64. Da Rocha B.R.P., Habashy T.M. Fractal geometry, porosity and complex resistivity: from rough pore interfaces to hand specimens. Geological Society London Special Publications 122 1997, 277-286.
65. Davy P. On the frequency-length distribution of the San Andreas Fault system. Journal of Geophysical Research 1993, 98:12.141-12.151.
66. Davy P., Sornette A., Sornette D. Some consequences of a proposed fractal nature of continental faulting. Nature 1990, 348:56-58.
67. Davy P., Sornette A., Sornette D. Experimental discovery of scaling laws relating fractal dimensions and the length distribution exponent of fault systems. Geophysical Research Letters 1992, 19:361-363.
68. Dawers N.H., Anders M.H., Scholz C.H. Growth of normal faults: displacement-length scaling. Geology 1993, 21:1107-1110.
69. Denison C., Carlson W.D., Ketcham R.A. Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography: part I: methods and techniques. Journal of Metamorphic Geology 1997, 15:29-44.
70. Dougan L.T., Addison P.S., McKenzie W.M.C. Fractal analysis of fracture: a comparison of dimension estimates. Mechanics Research Communications 2000, 27:383-392.
71. Drolon H., Hoyez B., Druaux F., Faure A. Multiscale roughness analysis of particles. Application to the classification of detrital sediments. Mathematical Geology 2003, 35:805-817.
72. Evertsz C.J.G., Mandelbrot B.B. Multifractal measures. Chaos and Fractals 1992, 922-953. Springer, Berlin/Heidelberg/New York. H.-O. Peitgen, H. Jürgens, D. Saupe (Eds.).
73. Fagereng Å. Fractal vein distributions within a fault-fracture mesh in an exhumed accretionary mélange, Chrystalls Beach Complex, New Zealand. Journal of Structural Geology 2011, 33:918-927.
74. Falconer K. Fractal Geometry 1990, Wiley, Chichester, 288 pp.
75. Falconer K. Techniques in Fractal Geometry 1997, Wiley, Chichester, 256 pp.
76. Feder J. Fractals 1988, Plenum Press, New York, 283 pp.
77. Feng Z.C., Zhao Y.S., Zhao D. Investigating the scale effects in strength of fractured rock mass. Chaos, Solitons & Fractals 2009, 41:2377-2386.
78. Feranie S., Fauzi U., Bijaksana S. 3D fractal dimension and flow properties in the pore structure of geological rocks. Fractals 2011, 19:291-297.
79. Flook, A.G., 1979. The Characterization of Textural and Structural Profiles by the Automated Measurement of Their Fractal Dimensions. In: 2nd European Symposium on Particle Characterization, pp. 591-599.
80. Fomin S., Hashida T., Shimizu A., Matsuki K., Sakaguchi K. Fractal concept in numerical simulation of hydraulic fracturing of the hot dry rock geothermal reservoir. Hydrological Processes 2003, 17:2975-2989.
81. Ford A., Blenkinsop T.G. Combining fractal analysis of mineral deposit clustering with weights of evidence to evaluate patterns of mineralization: application to copper deposits of the Mount Isa Inlier, NW Queensland, Australia. Ore Geology Reviews 2008, 33:435-450.
82. Ford A., Blenkinsop T.G. Evaluating geological complexity and complexity gradients as controls on copper mineralisation, Mt. Isa Inlier. Australian Journal of Earth Sciences 2008, 55:13-23.
83. Ford A., Blenkinsop T.G. An expanded de Wijs model for multifractal analysis of mineral production data. Mineralium Deposita 2009, 44:233-240.
84. Fossen H., Hesthammer J. Geometric analysis and scaling relations of deformation bands in porous sandstone. Journal of Structural Geology 1997, 17:1479-1493.
85. Fowler A.D. Self-organized mineral texture of igneous rocks: the fractal approach. Earth-Science Reviews 1990, 29:47-55.
86. Fowler A.D., Stanley H.E., Daccord G. Disequilibrium silicate mineral textures: fractal and non-fractal features. Nature 1989, 341:134-136.
87. Foxford K.A., Nicholson R., Polya D.A., Hebblethwaite R.P.B. Extensional failure and hydraulic valving at Minas da Panasqueira, Portugal: evidence from vein spatial distributions, displacements and geometries. Journal of Structural Geology 2000, 22:1065-1086.
88. Fueten F. A computer controlled rotating polarizer stage for the petrographic microscope. Computers & Geosciences 1997, 23:203-208.
89. Fueten F., Mason J. An artificial neural net assisted approach to editing edges in petrographic images collected with the rotating polarizer stage. Computers & Geosciences 2007, 33:1176-1188.
90. Gerik A., Kruhl J.H. Towards automated pattern quantification: time-efficient assessment of anisotropy of 2D pattern with AMOCADO. Computers & Geosciences 2009, 35(6):1087-1097.
91. Gerik A., Kruhl J.H., Caggianelli A. Quantification of flow patterns in sheared tonalite crystal-melt mush: application of fractal-geometry methods. Journal Geological Society of India 2010, 75:210-224.
92. Gillespie P.A., Howard C.B., Walsh J.J., Watterson J. Measurement and characterization of spatial distributions of fractures. Tectonophysics 1993, 226:131-141.
93. Gillespie P.A., Johnston J.D., Loriga M.A., McCaffrey K.J.W., Walsh J.J., Watterson J. Influence of layering on vein systematics in line samples. Geological Society London Special Publications 155 1999, 35-56. K.J.W. McCaffrey, L. Lonergan, J.J. Wilkinson (Eds.).
94. Gillespie P.A., Walsh J.J., Watterson J., Bonson C.G., Manzocchi T. Scaling relationships of joint and vein arrays from The Burren, Co. Clare, Ireland. Journal of Structural Geology 2001, 23:183-201.
95. Gonzato G. A practical implementation of the box counting algorithm. Computers & Geosciences 1998, 24:95-100.
96. Gonzato G., Mulargia F., Marzocchi W. Practical application of fractal analysis: problems and solutions. Geophysical Journal International 1998, 132:275-282.
97. Gonzato G., Mulargia F., Ciccotti M. Measuring the fractal dimensions of ideal and actual objects: implications for application in geology and geophysics. Geophysical Journal International 2000, 142:108-116.
98. Goodchild M.F. Fractal and the accuracy of geographical measures. Journal of Mathematical Geology 1980, 12:85-98.
99. Goodchild J.S., Fueten F. Edge detection in petrographic images using the rotating polarizer stage. Computers & Geosciences 1998, 24:745-751.
100. Grassberger P., Procaccia I. Characterization of strange attractor. Physical Review Letters 1983, 50:346-349.
101. Hadizadeh J., Johnson W. Estimating local strain due to comminution in experimental cataclastic textures. Journal of Structural Geology 2003, 25:1973-1979.
102. Hamdi E. A fractal description of simulated 3d discontinuity networks. Rock Mechanics and Rock Engineering 2008, 41:587-599.
103. Harris C., Franssen R., Loosveld R. Fractal analysis of fractures in rocks: the Cantor's Dust method - comment. Tectonophysics 1991, 198:107-111.
104. Hasting H.M., Sugihara H. Fractals: A User's Guide for the Natural Sciences 1993, Oxford Science Publications, Oxford, 235 pp.
105. Hatton C.G., Main I.G., Meredith P.G. A comparison of seismic and structural measurements of fractal dimension during tensile subcritical crack growth. Journal of Structural Geology 1993, 15:1485-1494.
106. Hecht C.A. Appolonian packing and fractal shape of grains improving geomechanical properties in engineering geology. Fractals and Dynamic Systems in Geoscience. Pure and Applied Geophysics 2000, vol. 157:539-557. Birkhäuser, Basel, (Topical Volume).
107. Heilbronner R., Keulen N. Grain size and grain shape analysis of fault rocks. Tectonophysics 2006, 427:199-216.
108. Hentschel H.G.E., Procaccia I. The infinite number of generalized dimensions of fractals and strange attractors. Physica D 1983, 8:435-444.
109. Herzfeld U.C., Overbeck C. Analysis and simulation of scale-dependent fractal surfaces with application to searfloor morphology. Computers & Geosciences 1999, 25:979-1007.
110. Higgins M.D. Quantitative Textural Measurements in Igneous and Metamorphic Petrology 2006, Cambridge University Press, Cambridge, 276 pp.
111. Hirata T. Fractal dimension of fault systems in Japan: fractal structure in rock fracture geometry at various scales. Pure and Applied Geophysics 1989, 131:157-169.
112. Hirata T., Imoto M. Multifractal analysis of spatial distribution of microearthquakes in the Kanto region. Geophysical Journal International 1991, 107:155-162.
113. Hirata T., Satoh T., Ito K. Fractal structure of spatial distribution of microfracturing in rock. Royal Astronomical Society Geophysical Journal 1987, 90:369-374.
114. Hirose T., Shimamoto T. Fractal dimension of molten surfaces as a possible parameter to infer the slip-weakening distance of faults from natural pseudotachylytes. Journal of Structural Geology 2003, 25:1569-1574.
115. Hisada E. Clast-size analysis of impact-generated pseudotachylite from Vredefort Dome, South Africa. Journal of Structural Geology 2004, 26:1419-1424.
116. Hooker J.N., Laubach S.E., Gomez L., Marrett R., Eichhubl P., Diaz-Tushman K., Pinzon E. Fracture size, frequency, and strain in the Cambrian Eriboll Formation sandstones, NW Scotland. Scottish Journal of Geology 2011, 47:45-56.
117. Horovistiz A.L., de Campos K.A., Shibata S., Prado C.C.S., de Oliveira Hein L.R. Fractal characterization of brittle fracture in ceramics under mode I stress loading. Material Science and Engineering A 2010, 527:4847-4850.
118. Hull J. Thickness-displacement relationships for deformation zones. Journal of Structural Geology 1988, 10:431-435.
119. Hyslip J.P., Vallejo J.P. Fractal analysis of the roughness and size distribution of granular materials. Engineering Geology 1997, 48:231-244.
120. Imre B., Laue J., Springman S.M. Fractal fragmentation of rocks within sturzstroms: insight derived from physical experiments within the ETH geotechnical drum centrifuge. Granular Matter 2010, 12:267-285.
121. Jackson P., Sanderson D.J. Scaling of fault displacements from the Badajoz-Córdoba shear zone, SW Spain. Tectonophysics 1992, 210:179-190.
122. Jensen E., Cembrano J., Faulkner D., Veloso E., Arancibia G. Development of a self-similar strike-slip duplex system in the Atacama Fault system, Chile. Journal of Structural Geology 2011, 33:1611-1626.
123. Johnston J.D., McCaffrey K.J.W. Fractal geometries of vein systems and the variation of scaling relationships with mechanism. Journal of Structural Geology 1996, 18:349-358.
124. Kagan Y.Y. Fractal dimension of brittle fracture. Journal of Nonlinear Science 1991, 1:1-16.
125. Kagan Y.Y. Earthquake size distribution: power-law with exponent β ≡?. Tectonophysics 2010, 490:103-114.
126. Kaye B.H. Specification of the ruggedness and/or texture of a fine particle profile by its fractal dimension. Powder Technology 1978, 21:207-213.
127. Kaye B.H. Fractal description of fineparticle systems. Particle Characterization in Technology 1984, vol. 1. CRC Press, Boca Raton, Chapt. 5.
128. Kaye B.H. A Random Walk through Fractal Dimensions 1989, VCH Publishers, Weinheim.
129. Kaye B.H. Chaos and Complexity 1993, VCH Publishers, Weinheim.
130. Kaye B.H. Fractal Geometry and the Mining Industry, a Review. Fractals and Dynamic Systems in Geoscience 1994, 233-245. Springer, Berlin/Heidelberg/New York. J.H. Kruhl (Ed.).
131. Kaye B.H., Clark G.G. Fractal Dimension of Extraterrestrial Fineparticles 1985, Dept. Physics Laurentian University, Sudbury, Ontario, Canada, 16 p.
132. Ketcham R.A., Iturrino G.J. Nondestructive high-resolution visualization and measurement of anisotropic effective porosity in complex lithologies using high-resolution X-ray computed tomography. Journal of Hydrogeology 2005, 302:92-106.
133. Keulen N., Heilbronner R., Stünitz H., Boullier A.-M., Ito H. Grain size distributions of fault rocks: a comparison between experimentally and naturally deformed granitoids. Journal of Structural Geology 2007, 29:1282-1300.
134. Kindratenko V.V., Van Espen P.J.M., Treiger B.A., Van Grieken R.E. Fractal dimensional classification of aerosol particles by computer-controlled scanning electron microscopy. Environmental Science & Technology 1994, 28:2197-2202.
135. King G. The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault systems: the geometrical origin of b-value. Pure and Applied Geophysics 1983, 121:761-815.
136. Korvin G. Fractured but not fractal: fragmentation of the Gulf of Suez basement. Pure and Applied Geophysics 1989, 131:289-305.
137. Korvin G. Fractal Models in the Earth Sciences 1992, Elsevier, p. 396.
138. Kranz R.L., Velde B. Fractal and length analysis of fractures during brittle to ductile changes. Comment and reply. Journal of Geophysical Research 1994, 99(B8):15645-15650.
139. Kreuzer O.P., Blenkinsop T.G., Morrison R.J., Peters S.G. Ore controls in the Charters Towers goldfield, NE Australia: constraints from geological, geophysical and numerical analyses. Ore Geology Reviews 2007, 32:37-80.
140. Krištáková Z., Kupková M. Correlation of fractal surface description parameters with fracture toughness. Fractals and Dynamic Systems in Geoscience 1994, 77-94. Springer, Berlin/Heidelberg/New York. J.H. Kruhl (Ed.).
141. Krohn C.E. Sandstone fractal and Euclidean pore volume distribution. Journal of Geophysical Research 1988, 93(B4):3286-3296.
142. Krohn E.E., Thompson A.H. Fractal sandstone pores: automated measurements using scanning-electron-microscope images. Physical Review B 1986, 33:6366-6374.
143. Kruhl J.H. The formation of extensional veins: an application of the Cantor-dust model. Fractals and Dynamics Systems in Geoscience 1994, 95-104. Springer, Berlin/Heidelberg/New York. J.H. Kruhl (Ed.).
144. Kruhl J.H., Nega M. The fractal shape of sutured quartz grain boundaries: application as a geothermometer. Geologische Rundschau 1996, 38-43.
145. Kruhl J.H., Andries F., Peternell M., Volland S. Fractal geometry analyses of rock fabric anisotropies and inhomogeneities. Fractals in Geotechnical Engineering. Advances in Geotechnical Engineering and Tunnelling 2004, vol. 9:115-135. Logos, Berlin.
146. Kueppers U., Perugini D., Dingwell D.B. "Explosive energy" during volcanic eruptions from fractal analysis of pyroclasts. Earth and Planetary Science Letters 2006, 248:800-807.
147. Kulatilake P.H.S.W., Fiedler R., Panda B.B. Box fractal dimension as a measure of statistical homogeneity of jointed rock masses. Engineering Geology 1997, 48:217-229.
148. Kusunose K., Lei X., Nishizawa O., Satoh T. Effect of grain size on fractal structure of acoustic emission hypocenter distribution in granitic rocks. Physics of Earth and Planetary Interior 1991, 67:194-199.
149. La Pointe P.R. A method to characterize fracture density and connectivity through fractal geometry. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 1988, 25:421-429.
150. Launeau P., Robin P.Y.F. Fabric analysis using the intercept method. Tectonophysics 1996, 267:91-119.
151. Launeau P., Bouchez J.-L., Benn K. Shape preferred orientation of object population: automatic analysis of digitized images. Tectonophysics 1990, 180:201-211.
152. Ledésert B., Dubois J., Velde B., Meunier A., Genter A., Badri A. Geometrical and fractal analysis of a three-dimensional vein network in a fractured granite. Journal of Volcanology and Geothermal Research 1993, 56:267-280.
153. Ledésert B., Dubois J., Genter A., Meunier A. Fractal analysis of fractures applied to Soultz-sous-Forêts hot dry rock geothermal program. Journal of Volcanology and Geothermal Research 1993, 57:1-7.
154. Ledésert B., Hebert R., Genter A., Bartier D., Clauer N., Grall C. Fractures, hydrothermal alterations and permeability in the Soultz Enhanced Geothermal System. Comptes Rendus Geoscience 2010, 342:607-615.
155. Li J., Du Q., Sun C. An improved box-counting method for image fractal dimension estimation. Pattern Recognition 2009, 42:2460-2469.
156. Long J.J., Imber J. Geological controls on fault relay zone scaling. Journal of Structural Geology 2011, 33:1790-1800.
157. Loriga M.A. Scaling systematics of vein size: an example from the Guanajuato mining district (Central Mexico). Geological Society of London Special Publications 155 1999, 57-67. K.J.W. McCaffrey, L. Lonergan, J.J. Wilkinson (Eds.).
158. Lorilleux G., Jébrak M., Cuney M., Baudemont D. Polyphase hydrothermal breccias associated with unconformity-related uranium mineralization (Canada): from fractal analysis to structural significance. Journal of Structural Geology 2002, 24:323-338.
159. Lovejoy S. Area-perimeter relation for rain and cloud areas. Science 1982, 216:185-187.
160. Lunina O.V., Mart Y., Gladkov A.S. Fracturing patterns, stress fields and earthquakes in the Southern Dead Sea rift. Journal of Geodynamics 2005, 40:216-234.
161. Main I.G., Peacock S., Meredith P.G. Scattering attenuation and fractal geometry of fracture systems. Pure and Applied Geophysics 1990, 133:283-304.
162. Main I.G., Kwon O., Ngwenya B.T., Elphick S.C. Fault sealing during deformation band growth in sandstone. Geology 2000, 28:1131-1134.
163. Mair K., Abe S. Breaking up: comminution mechanisms in sheared simulated fault gouge. Pure and Applied Geophysics 2011, 168:2277-2288.
164. Mair K., Frye K.M., Marone C. Influence of grain characteristics on the friction of granular shear zones. Journal of Geophysical Research 2002, 107(B10):ECV1-ECV4.
165. Majumder S., Mamtani M.A. Fractal analysis of quartz grain boundary sutures in a granite (Malanjkhand, Central India) - implications to infer regional tectonics. Journal Geological Society of India 2009, 73:309-319.
166. Malik F. Komplexität, Management und patterns of control. Die andere Intelligenz 2004, 174-187. Klett-Cotta, Stuttgart. B.V. Mutius (Ed.).
167. Mamtani M.A. Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks. Journal Geological Society of India 2010, 75:202-209.
168. Mandelbrot B.B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 1967, 156:636-638.
169. Mandelbrot B.B. Fractals - Form, Chance and Dimension 1977, Freeman, San Francisco.
170. Mandelbrot B.B. The Fractal Geometry of Nature 1982, Freeman & Co., New York, 468 pp.
171. Mandelbrot B.B. Self-affine fractals and fractal dimension. Physica Scripta 1985, 32:257-260.
172. Mandelbrot B.B. Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics 1989, 131:6-42.
173. Mandelbrot B.B., Passoja D.E., Paullay A.J. Fractal character of fracture surfaces of metals. Nature 1984, 308:721-722.
174. Manning C.E. Fractal clustering of metamorphic veins. Geology 1994, 22:335-338.
175. Mareschal J.-C. Fractal reconstruction of sea-floor topography. Pure and Applied Geophysics 1989, 131:197-210.
176. Marone C., Scholz C.H. Particle-size distribution and microstructures within simulated fault gouge. Journal of Structural Geology 1989, 11:799-814.
177. Marrett R., Allmendinger R.W. Estimates of strain due to brittle faulting: sampling of fault populations. Journal of Structural Geology 1991, 13:735-738.
178. Marrett R., Ortega O.J., Kelsey C.M. Extent of power-law scaling for natural fractures in rock. Geology 1999, 27:799-802.
179. Marschallinger R. Automatic mineral classification in the macroscopic scale. Computers & Geosciences 1997, 23:119-126.
180. Marschallinger R. A method for three-dimensional reconstruction of macroscopic features in geological materials. Computers & Geosciences 1998, 24:875-883.
181. Marschallinger R. Three-dimensional reconstruction and visualization of geological materials with IDL - examples and source code. Computers & Geosciences 2001, 27:419-426.
182. Marschallinger R., Johnson S.E. Presenting 3-D models of geological materials on the World Wide Web. Computers & Geosciences 2001, 27:467-476.
183. Marsh B.D. Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization I. Theory. Contributions to Mineralogy and Petrology 1988, 99:277-291.
184. Mazzarini F., Armienti P. Flank cones at Mount Etna volcano: do they have a power-law distribution?. Bulletin of Volcanology 2001, 62:420-430.
185. McCaffrey K.J.W., Johnston J.D. Fractal analysis of a mineralised vein deposit: Curraghinalt gold deposit, County Tyrone. Mineralium Deposita 1996, 31:52-58.
186. McCaffrey K.J.W., Johnston J.D., Feely M. Use of fractal statistics in the analysis of Mo-Cu mineralization at Mace Head, County Galway. Irish Journal of Earth Sciences 1993, 12:139-148.
187. Mecholsky J., Mackin T.J. Fractal analysis of fracture in Ocala chert. Journal of Materials Science Letters 1988, 7:1145-1147.
188. Mechtcherine V. Fracture mechanical behavior of concrete and the condition of its fracture surface. Cement and Concrete Research 2009, 39:620-628.
189. Merceron T., Velde B. Application of Cantor's Method for fractal analysis of fractures in the Toyoha Mine, Hokkaido, Japan. Journal of Geophysical Research 1991, 96(B10):16641-16650.
190. Micarelli L., Benedicto A., Wibberley C.A.J. Structural evolution and permeability of normal fault zones in highly porous carbonate rocks. Journal of Structural Geology 2006, 28:1214-1227.
191. Milman V.Y., Stelmashenko N.A., Blumenfeld R. Fracture surfaces: a critical review of fractal studies and a novel morphological analysis of scanning tunneling microscopy measurements. Progress in Material Science 1994, 38:425-474.
192. Mohsen A.I., Mahmoud A.I., Islam Md.S., Chudnovsky A. Fractal dimension - a measure of fracture roughness and toughness of concrete. Engineering Fracture Mechanics 2003, 70:125-137.
193. Monzawa N., Otsuki K. Comminution and fluidization of granular fault materials: implications for fault slip behavior. Tectonophysics 2003, 367:127-143.
194. Morgan J.K., Boettcher M.S. Numerical simulations of granular shear zones using the distinct element method. 1. Shear zone kinematic and the micromechanics of localization. Journal of Geophysical Research 1999, 104:2703-2719.
195. Morse D.R., Lawton J.H., Dodson M.M., Williamson M.H. Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature 1985, 314:731-733.
196. Nagahama H. Fracturing in the solid earth. The Science Reports of the Tohoku University. Second Series, Geology 1991, 61:103-126.
197. Nagahama H. Fractal fragment size distribution for brittle rocks. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 1993, 30:469-471.
198. Nagahama H., Yoshii K. Fractal dimension and fracture of brittle rocks. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 1993, 30:173-175.
199. Nakaya S., Nakamura K. Percolation conditions in fractured hard rocks: a numerical approach using the three-dimensional binary fractal fracture network (3D-BFFN) model. Journal of Geophysical Research - Solid Earth 2007, 112:B12203.
200. Nanjo K., Nagahama H. Spatial distribution of aftershocks and the fractal structure of active fault systems. Pure and Applied Geophysics 2000, 157:575-588.
201. Nanjo K., Nagahama H., Satomura M. Rates of aftershock decay and the fractal structure of active fault systems. Tectonophysics 1998, 287:173-186.
202. Narr W., Suppe J. Joint spacing in sedimentary rocks. Journal of Structural Geology 1991, 13:1037-1048.
203. Nicol A., Walsh J.J., Watterson J., Gillespie P.A. Fault size distributions - are they really power-law?. Journal of Structural Geology 1996, 18:191-199.
204. Nolte D.D., Pyrak-Nolte L.J., Cook N.G.W. The fractal geometry of flow paths in natural fractures in rock and the approach to percolation. Pure and Applied Geophysics 1989, 131:111-138.
205. Odling N.E., Gillespie P., Bourgine B., Castaing C., Chilés J.P., Christensen N.P., Fillion E., Genter A., Olsen C., Thrane L., Trice R., Aarseth E., Walsh J.J., Watterson J. Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs. Petroleum Geoscience 1999, 5:373-384.
206. Okubo P.G., Aki K. Fractal geometry in the San Andreas fault system. Journal of Geophysical Research 1987, 92:345-355.
207. Orford J.D., Whalley W.B. The use of the fractal dimension to quantify the morphology of irregular-shaped particles. Sedimentology 1983, 30:655-668.
208. Orford J.D., Whalley W.B. The quantitative description of highly irregular sedimentary particles: the use of fractal dimension. Clastic Particles 1987, 267-280. Van Nostrand Reinhold Company, New York. J.R. Marshall (Ed.).
209. Paggi M., Carpinteri A. Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue. Chaos, Solitons & Fractals 2007, 40:1136-1145.
210. Panozzo R. Two-dimensional strain from the orientation of lines in a plane. Journal of Structural Geology 1984, 6:215-221.
211. Panozzo Heilbronner R.P., Pauli C. Integrated spatial and orientation analysis of quartz c-axes by computer-aided microscopy. Journal of Structural Geology 1993, 15:369-382.
212. Park S.-I., Kim Y.-S., Ryoo C.-R., Sanderson D.J. Fractal analysis of the evolution of a fracture network in a granite outcrop, SE Korea. Geoscience Journal 2010, 14:99-234.
213. The Beauty of Fractals 1986, Springer, Berlin/Heidelberg/New York. H.-O. Peitgen, H.P. Richter (Eds.).
214. The Science of Fractal Images 1988, Springer, Berlin/Heidelberg/New York, 312 pp. H.-O. Peitgen, D. Saupe (Eds.).
215. Peitgen H.-O., Jürgens H., Saupe D. Fractals for the Classroom, Part 1 1992, Springer, Berlin/Heidelberg/New York.
216. Peitgen H.-O., Jürgens H., Saupe D. Chaos and Fractals: New Frontiers of Science 1992, Springer, Berlin/Heidelberg/New York.
217. Pérez-López R., Paredes C. On measuring the fractal anisotropy of 2-D geometrical sets: application to the spatial distribution of fractures. Geoderma 2006, 134:402-414.
218. Pérez-López R., Paredes C., Muñoz-Martín A. Relationship between the fractal dimension anisotropy of the spatial faults distribution and the paleostress fields on a Variscan granitic massif (Central Spain): the F-parameter. Journal of Structural Geology 2005, 27:663-677.
219. Perugini D., Kueppers U. Fractal analysis of experimentally generated pyroclasts: a tool for volcanic hazard assessment. Acta Geophysica 2012, 60:682-698.
220. Perugini D., Poli G. Chaotic dynamics and fractals in magmatic interaction processes: a different approach to the interpretation of mafic microgranular enclaves. Earth and Planetary Science Letters 2000, 175:93-103.
221. Perugini D., Speziali A., Caricchi L., Kueppers U. Application of fractal fragmentation theory to natural pyroclastic deposits: insights into volcanic explosivity of the Valentano scoria cone (Italy). Journal of Volcanology and Geothermal Research 2011, 2002:200-210.
222. Peternell, M., 2007. Fabric Patterns in Magmatic Rocks: Method Development, Automation and Geological Significance. PhD thesis., Technical University Munich, Faculty of Civil and Geodetic Engineering, p. 124.
223. Peternell M., Kruhl J.H. Automation of pattern recognition and fractal-geometry-based pattern quantification, exemplified by mineral-phase distribution patterns in igneous rocks. Computers & Geosciences 2009, 35:1415-1426.
224. Peternell M., Andries F., Kruhl J.H. Magmatic flow-pattern anisotropies - analyzed on the basis of a new 'map-counting' fractal geometry method. Journal of the Czech Geological Society 2003, 48:104.
225. Peternell M., Bitencourt M.F., Kruhl J.H., Stäb C. Macro and microstructures as indicators of the development of syntectonic granitoids and host rocks in the Camboriú region, Santa Catarina, Brazil. Journal of South American Earth Sciences 2010, 29:738-750.
226. Peternell M., Bitencourt M.F., Kruhl J.H. Combined quantification of anisotropy and inhomogeneity of magmatic rock fabrics - an outcrop scale analysis recorded in high resolution. Journal of Structural Geology 2011, 33:609-623.
227. Petford N., Bryon D., Atherton M.P., Hunter R.H. Fractal analysis in granitoid petrology: a means of quantifying irregular grain morphologies. European Journal of Mineralogy 1993, 5:593-598.
228. Pettijohn E.J. Sedimentary Rocks 1975, Harper & Row, New York, 628 pp. third ed.
229. Pickering G., Bull J.M., Sanderson D.J., Harrison P. Fractal fault displacements: a case study from the Moray Firth, Scotland. Fractal and Dynamic Systems in Geoscience 1994, 105-119. Springer, Berlin/Heidelberg/New York. J.H. Kruhl (Ed.).
230. Pickering G., Bull J.M., Sanderson D.J. Sampling power-law distributions. Tectonophysics 1995, 248:1-20.
231. Piggott A.R. Fractal relations for the diameter and trace length of disc-shaped fractures. Journal of Geophysical Research 1997, 102(B8):18,121-18,125.
232. Power W.L., Tullis T.E. Euclidian and fractal models for the description of rock surface roughness. Journal of Geophysical Research 1991, 96(B1):415-424.
233. Qin J., Zhong D., Ng S.L., Wang G. Scaling behavior of gravel surfaces. Mathematical Geosciences 2012, 44:583-594.
234. Rantzsch U., Franz A., Kloess G. Fractal dimension and maximum roughness applied as sculpture descriptor for tektites. Mathematical Geosciences 2012, 44:711-720.
235. Rawls W.J., Brakensiek D.L. Utilizing fractal principles for predicting soil hydraulic properties. Journal of Soil and Water Conservation 1995, 50:463-465.
236. Rawls W.J., Brakensiek D.L., Logsdon S.D. Predicting saturated hydraulic conductivity utilizing fractal principles. Soil Science Society of America Journal 1993, 57:1193-1197.
237. Reither F. Komplexität als Herausforderung und Chance - Befunde aus Forschung, Praxis und Simulation. Die andere Intelligenz 2004, 160-173. Klett-Cotta, Stuttgart. B.V. Mutius (Ed.).
238. Renshaw C.E. Connectivity of joints networks with power-law length distributions. Water Resources Research 1999, 35:2661-2670.
239. Renshaw C.E., Park J.C. Effect of mechanical interactions on the scaling of fracture length and aperture. Nature 1997, 386:482-484.
240. Richardson R.L. The problem of contiguity: an appendix to statistics of deadly quarrels. General Systems Yearbook 1961, 6:139-187.
241. Roach D.E., Fowler A.D. Dimensionality analysis of patterns: fractal measurements. Computers & Geosciences 1993, 19:849-869.
242. Roberts S., Sanderson D.J., Gumiel P. Fractal analysis and percolation properties of veins. Geological Society London Special Publication 155 1999, 7-16. K.J.W. McCaffrey, L. Lonergan, J.J. Wilkinson (Eds.).
243. Rundle J.B. Derivation of the complete Gutenberg-Richter magnitude-frequency relation using the principle of scale invariance. Journal of Geophysical Research 1989, 94:12337-12342.
244. Russ J.C., Russ J.C. Uses of the Euclidean distance map for the measurement of features in images. Journal of Computer Assisted Microscopy 1989, 1:343.
245. Sadovskii M.A. Some results in seismology obtained on the basis of the new media model. Bulgarian Geophysical Journal 1986, 3:3-7.
246. Sadovskii M.A., Golubeva T.V., Pisarenko V.F., Shnirman M.G. Characteristic dimensions of rock and hierarchical properties of seismicity. Izvestiya, Academy of Sciences, USSR, Physics of the Solid Earth 1984, 20:87-96. (English translation).
247. Sahimi M., Robertson M.C., Sammis C.G. Fractal distribution of earthquake hypocenters and its relation to fault patterns and percolation. Physical Review Letters 1993, 70:2186-2189.
248. Sammis C.G., Biegel R.L. Fractals, fault-gouge, and friction. Pure and Applied Geophysics 1989, 131:255-271.
249. Sammis C.G., Osborne R.H., Anderson J.L., Banerdt M., White P. Self-similar cataclasis in the formation of fault gouge. Pure and Applied Geophysics 1986, 124:53-78.
250. Sammis C.G., King G., Biegel R. The kinematics of gouge deformation. Pure and Applied Geophysics 1987, 125:777-812.
251. Sanderson D.J., Zhang X. Critical stress localization of flow associated with deformation of well-fractured rock masses, with implications mineral deposits. Geological Society London Special Publications 155 1999, 69-81. K.J.W. McCaffrey (Ed.).
252. Sanderson D.J., Roberts S., Gumiel P., Greenfield C. Quantitative analysis of tin and tungsten bearing sheeted vein systems. Economic Geology 2008, 103:1043-1056.
253. Schmittbuhl J., Gentier S., Roux S. Field measurement of the roughness of fault surfaces. Geophysical Research Letters 1993, 20:639-641.
254. Schmittbuhl J., Schmitt F., Scholz C. Scaling invariance of crack surfaces. Journal of Geophysical Research 1995, 100:5953-5973.
255. Sharon E., Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 1999, 397:332-335.
256. Shepherd R.G. Correlations of permeability and grain-size. Ground Water 1989, 27:633-638.
257. Shimamoto T., Nagahama H. An argument against the crush origin of pseudotachylytes based on the analysis of clast-size distribution. Journal of Structural Geology 1992, 14:999-1006.
258. Shorrocks B., Marsters J., Ward I., Evennett P.J. The fractal dimension of lichens and the distribution of arthropod body length. Functional Ecology 1991, 5:457-460.
259. Singer H.M., Bilgram J.H. Integral scaling behaviour of different morphologies of 3D xenon crystals. Physica D 2006, 219:101-110.
260. Smalley R.F., Chatellain L.L., Turcotte D.L., Prevot R.A. Fractal approach to the clustering of earthquakes: applications to the seismicity of the New-Hebrides. Bulletin of the Seismological Society of America 1987, 77:1368-1381.
261. Sornette D., Davy P., Sornette A. Structuration of the lithosphere in plate tectonics as a self-organized critical phenomenon. Journal of Geophysical Research 1990, 95:17353-17361.
262. Sornette A., Davy P., Sornette D. Growth of fractal fault patterns. Physical Review Letters 1990, 65:2266-2269.
263. Sornette A., Davy P., Sornette D. Fault growth in brittle-ductile experiments and the mechanics of continental collisions. Journal of Geophysical Research 1993, 98:111-139.
264. Stakhovsky I.R. A multifractal model of crack coalescence in rocks. Physics of the Solid Earth 2011, 47:371-378.
265. Stanley H.E., Meakin P. Multifractal phenomena in physics and chemistry. Nature 1988, 335(6189):405-409.
266. Random Fluctuations and Pattern Growth: Experiments and Models 1988, Kluwer, Dordrecht, NATO ASI Series E 157. H.E. Stanley, N. Ostrowsky (Eds.).
267. Steacy S.J., Sammis C.G. An automaton for fractal patterns of fragmentation. Nature 1991, 353:250-252.
268. Şuţeanu C. Characterization of anisotropy-scale relations for complex irregular structures. Fractals in Geotechnical Engineering. Advances in Geotechnical Engineering and Tunnelling 2004, vol. 9:103-114. Logos, Berlin.
269. Şuţeanu C., Ioana C. Pattern identification in the dynamic fingerprint of seismically active zones. Quaternary International 2007, 171-172:45-51.
270. Şuţeanu C., Kruhl J.H. Investigation of heterogeneous scaling intervals exemplified by sutured quartz grain boundaries. Fractals 2002, 10(4):435-449.
271. Şuţeanu C., Munteanu F., Zugrǎvescu D. Hierarchies, scaling and anisotropy in dehydration cracking. Revue Roumaine de Géophysique 1995, 39:21-39.
272. Şuţeanu C., Munteanu F., Zugrǎvescu D. Scaling regimes and anisotropy: towards an effective approach to complex geologic structures. Revue Roumaine de Géophysique 1997, 41:25-43.
273. Şuţeanu C., Zugrǎvescu D., Munteanu F. Fractal approach of structuring by fragmentation. Fractals and Dynamic Systems in Geoscience. Pure and Applied Geophysics 2000, vol. 157:539-557. Birkhäuser, Basel, (Topical Volume).
274. Takahashi M., Nagahama T., Masuda T., Fujimura A. Fractal analysis of experimentally, dynamically recrystallized quartz grains and its possible application as a strain rate meter. Journal of Structural Geology 1998, 20:269-275.
275. L = 6.4), Taiwan. Tectonophysics 2012, 546-547:1-9.
276. Taylor R.P., Micolich A.P., Jonas D. Fractal analysis of Pollock's drip paintings. Nature 1999, 399:422.
277. Tejedor A., Gómez J.B., Pacheco A.F. Hierarchical model for distributed seismicity. Physical Review E 2010, 82:016118.
278. Thompson S., Fueten F., Bockus D. Mineral identification using artificial neural networks and the rotating polarizer stage. Computers & Geosciences 2001, 27:1081-1089.
279. Laser and Photogrammetric Methods for Rock Face Characterization 2006, American Rock Mechanics Association, Alexandria, Virginia. F. Tonon, J.T. Kottenstette (Eds.).
280. Tricot C. Curves and Fractal Dimension 1995, Springer, New York, 323 pp.
281. Tullis J., Yund R.A. Dynamic recrystallization of feldspar: a mechanism for ductile shear zone formation. Geology 1985, 13:238-241.
282. Turcotte D.L. Fractals and fragmentation. Journal of Geophysical Research 1986, 91:1921-1926.
283. Turcotte D.L. A fractal model for crustal deformation. Tectonophysics 1986, 132:261-269.
284. Turcotte D.L. Fractals and Chaos in Geology and Geophysics 1997, Cambridge University Press, Cambridge. second ed.
285. Velde B., Dubois J., Touchard G., Badri A. Fractal analysis of fractures in rocks: the Cantor's Dust method. Tectonophysics 1990, 179:345-352.
286. Velde B., Dubois J., Moore D., Touchard G. Fractal patterns of fractures in granites. Earth and Planetary Science Letters 1991, 104:25-35.
287. Velde B., Moore D., Badri A., Ledesert B. Fractal and length analysis of fractures during brittle to ductile changes. Journal of Geophysical Research 1993, 98(B7):11935-11940.
288. Vignes-Adler M., Le Page A., Adler P.M. Fractal analysis of fracturing in two African regions from satellite imagery to ground scale. Tectonophysics 1991, 196:69-86.
289. Villemin T., Angelier J., Sunwoo C. Fractal distribution of fault length and offsets: implications of brittle deformation evaluation - Lorraine Coal Basin. Fractals in the Earth Sciences 1995, 205-226. Plenum Press, New York. C.C. Barton, P.R. La Pointe (Eds.).
290. Vincent L., Soille P. Watersheds in digital space: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 1991, 13:583-598.
291. Volland S., Kruhl J.H. Anisotropy quantification: the application of fractal geometry methods on tectonic fracture patterns of a Hercynian fault zone in NW-Sardinia. Journal of Structural Geology 2004, 26:1489-1500.
292. Vontobel P., Lehmann E., Carlson W.D. Comparison of X-ray and neutron tomography investigations of geological materials. IEEE Transactions on Nuclear Science 2005, 52:338-341.
293. Voss R.R., Clarke J. 1/f noise in music and speech. Nature 1975, 258:317-318.
294. Walsh J.J., Watterson J. Analysis of the relationship between displacements and dimensions of faults. Journal of Structural Geology 1988, 10:239-247.
295. Walsh J.J., Watterson J. Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies. Journal of Structural Geology 1993, 15:1509-1512.
296. Walsh J.J., Watterson J., Yielding G. The importance of small-scale faulting in regional extension. Nature 1991, 351:391-393.
297. Wang Z., Cheng Q., Cao L., Xia Q., Chen Z. Fractal modelling of the microstructure property of quartz mylonite during deformation process. Mathematical Geology 2007, 39:53-68.
298. Watanabe K., Takahashi H. Fractal geometry characterization of geothermal reservoir fracture networks. Journal of Geophysical Research 1995, 100(B1):521-528.
299. Watterson J. Fault dimensions, displacements and growth. Pure and Applied Geophysics 1986, 124:365-373.
300. Watterson J., Walsh J.J., Gillespie P.A., Easton S. Scaling systematic of fault sizes on a large-scale range fault map. Journal of Structural Geology 1996, 18:199-214.
301. Weinberg R.F., Hodkiewicz P.F., Groves D.I. What controls gold distribution in Archean terranes?. Geology 2004, 32:545-548.
302. Wibberley C.A.J., Shimamoto T. Internal structure and permeability of major strike-slip fault zones: the Median Tectonic Line in Mie Prefecture, Southwest Japan. Journal of Structural Geology 2003, 25:59-78.
303. Wiener N. Cybernetics or Control and Communication in the Animal and the Machine 1948, The Massachusetts Institute of Technology.
304. Wilson B., Dewers T., Reches Z., Brune J. Particle size and energetics of gouge from earthquake rupture zones. Nature 2005, 434:749-752.
305. Winkler B., Knorr K., Kahle A., Vontobel P., Lehman E., Hennion B., Bayon G. Neutron imaging and neutron tomography as non-destructive tools to study bulk-rock samples. European Journal of Mineralogy 2002, 14:349-454.
306. Wong P.-Z., Lin J.-S. Studying fractal geometry on submicron length scales by small-angle scattering. Mathematical Geology 1988, 20:655-665.
307. Xie H., Pariseau W.G. Fractal character and mechanisms of rock bursts. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 1993, 30:343-350.
308. Yfantis E.A., Flatman G.T., Englund E.J. Simulation of geological surfaces using fractals. Mathematical Geology 1988, 20:667-672.
309. Yuan R.F., Li Y.H. Fractal analysis on the spatial distribution of acoustic emission in the failure process of rock specimens. International Journal of Minerals, Metallurgy and Materials 2009, 16:19-24.
310. Zazoun R.S. The Fadnoun area, Tassili-n-Azdjer, Algeria: fracture network geometry analysis. Journal of African Earth Sciences 2008, 50:273-285.
311. Zhang X., Sanderson D. Fractal structure and deformation of fractured rock masses. Fractals and Dynamic Systems in Geoscience 1994, 37-52. Springer, Berlin/Heidelberg/New York. J.H. Kruhl (Ed.).
312. Zhao Y.H. Crack pattern evolution and a fractal damage constitutive model for rock. International Journal of Rock Mechanics and Mining Sciences 1998, 35:349-366.
313. Zhao Z.Y., Wang Y., Liu X.H. Fractal analysis applied to cataclastic rocks. Tectonophysics 1990, 178:373-377.
314. Zhao Y.S., Feng Z.C., Liang W.G., Yang D., Hu Y.Q., Kang T.H. Investigation of fractal distribution law for the trace number of random and grouped fractures in a geological mass. Engineering Geology 2009, 109:224-229.
315. Zygouri V., Verroios S., Kokkalas S., Xypolias P., Koukouvelas I.K. Scaling properties within the Gulf of Corinth, Greece; comparison between offshore and onshore active faults. Tectonophysics 2008, 453:193-210.