Interpreting two-dimensional cuts through broken geologic objects: Fractal and non-fractal size distributions

Geosphere

Volumn 8, Issue 4, 2012, Pages 902-914

  Glazner, Allen F ^a   Mills, Ryan D ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BRECCIA; COMPUTER SIMULATION; DIKE; ELLIPSE; FRACTAL ANALYSIS; GEOSTATISTICS; PARTICLE SIZE; ROCK; SIZE DISTRIBUTION; TWO-DIMENSIONAL MODELING; XENOLITH; BRITTLE DEFORMATION; ENCLAVE; FRAGMENTATION; MAFIC ROCK; NUMERICAL MODEL; STATISTICAL ANALYSIS; THREE-DIMENSIONAL MODELING;

CALIFORNIA; DEATH VALLEY; UNITED STATES;

EID: 84864914890     PISSN: None     EISSN: 1553040X     Source Type: Journal    
DOI: 10.1130/GES00731.1     Document Type: Article

References (65)

1. Allègre, C.J., Le Mouel, J.L., and Provost, A., 1982, Scaling rules in rock fracture and possible implications for earthquake prediction: Nature, v. 297, p. 47-49, doi:10.1038/297047a0.
2. Bagde, M.N., Raina, A.K., Chakraborty, A.K., and Jethwa, J.L., 2002, Rock mass characterization by fractal dimension: Engineering Geology, v. 63, p. 141-155, doi:10.1016/S0013-7952(01)00078-3.
3. Balme, M.R., Rocchi, V., Jones, C., Sammonds, P.R., Meredith, P.G., and Boon, S., 2004, Fracture toughness measurements on igneous rocks using a high-pressure, high-temperature rock fracture mechanics cell: Journal of Volcanology and Geothermal Research, v. 132, p. 159-172, doi:10.1016/S0377-0273(03)00343-3.
4. Barbarin, B., 2005, Mafic magmatic enclaves and mafic rocks associated with some granitoids of the central Sierra Nevada batholith, California: Nature, origin, and relations with the hosts: Lithos, v. 80, p. 155-177, doi: 10.1016/j.lithos.2004.05.010.
5. Bateman, P.C., Kistler, R.W., Peck, D.L., and Busacca, A.J., 1983, Geologic map of the Tuolumne Meadows Quadrangle, Yosemite National Park, California: U.S. Geological Survey Map GQ-1570, scale 1:62,500.
6. Billi, A., 2005, Grain size distribution and thickness of breccia and gouge zones from thin (<1 m) strike-slip fault cores in limestone: Journal of Structural Geology, v. 27, no. 10, p. 1823-1837, doi:10.1016/j.jsg.2005.05.013.
7. Billi, A., and Storti, F., 2004, Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone: Tectonophysics, v. 384, no. 1-4, p. 115-128, doi:10.1016/j.tecto.2004.03.015.
8. Boggs, S., 1992, Petrology of Sedimentary Rocks: New York, Macmillan, 707 p.
9. Broz, M.E., Cook, R.F., and Whitney, D.L., 2006, Microhardness, toughness, and modulus of Mohs scale minerals: The American Mineralogist, v. 91, p. 135-142, doi:10.2138/am.2006.1844.
10. Chanudet, V., and Filella, M., 2008, Size and composition of inorganic colloids in a peri-alpine, glacial flourrich lake: Geochimica et Cosmochimica Acta, v. 72, p. 1466-1479, doi:10.1016/j.gca.2008.01.002.
11. Chayes, F., 1950, On the bias of grain-size measurements made in thin section: The Journal of Geology, v. 58, p. 156-160, doi:10.1086/625716.
12. Crum, S.V., 1990, Fractal concepts applied to bench-blast fragmentation, in Hustrulid, W.A., and Johnson, G.A., eds., Rock Mechanics: Contributions and Challenges: Proceedings of the 31st U.S. Symposium, Colorado School of Mines, Golden, 18-20 June, 1990: Rotterdam, A.A. Balkema, p. 913-919.
13. deMartin, B., Hirth, G., and Evans, B., 2004, Experimental constraints on thermal cracking of peridotite at oceanic spreading centers, in German, C.R., Lin, J., and Parson, L.M., eds., Mid-Ocean Ridges: Hydrothermal Interactions between the Lithosphere and Oceans: Washington, D.C., Geophysical Monograph Series Volume 148, American Geophysical Union, p. 167-185.
14. Devroye, L., 1986, Non-uniform random variate generation: New York, Springer-Verlag, 843 p.
15. Farris, D.W., and Paterson, S.R., 2007, Contamination of silicic magmas and fractal fragmentation of xenoliths in Paleocene plutons on Kodiak Island, Alaska: Canadian Mineralogist, v. 45, no. 1, p. 107-129, doi:10.2113/gscanmin.45.1.107.
16. Folk, R.L., and Ward, W.C., 1957, Brazos River bar [Texas]: A study in the significance of grain size parameters: Journal of Sedimentary Research, v. 27, no. 1, p. 3-26.
17. Ghosh, A., Daemen, J.J.K., and van Zyl, D., 1990, Fractalbased approach to determine the effect of discontinuities on blast fragmentation, in Hustrulid, W.A., and Johnson, G.A., eds., Rock Mechanics: Contributions and Challenges: Proceedings of the 31st U.S. Symposium, Colorado School of Mines, Golden, 18-20 June, 1990: Rotterdam, A.A. Balkema, p. 905-912.
18. Gimenéz, D., Allmaras, R.R., Huggins, D.R., and Nater, E.A., 1998, Mass, surface and fragmentation fractal dimensions of soil fragments produced by tillage: Geoderma, v. 86, p. 261-278, doi:10.1016/S0016-7061 (98)00043-3.
19. Glazner, A.F., and Bartley, J.M., 1990, Early Miocene dome emplacement, diking, and limited tectonism in the northern Marble Mountains, eastern Mojave Desert, California, in Foster, J.F., and Lewis, L.L., eds., Lower Colorado River Extensional Terrane and Whipple Mountains Guidebook, Volume 18: Santa Ana, South Coast Geological Society, p. 89-97.
20. Glazner, A.F., and Bartley, J.M., 2006, Is stoping a volumetrically significant pluton emplacement process?: Geologi cal Society of America Bulletin, v. 118, p. 1185-1195, doi:10.1130/B25738.1.
21. Glazner, A.F., Farmer, G.L., Hughes, W.T., Wooden, J.L., and Pickthorn, W., 1991, Contamination of basaltic magma by mafic crust at Amboy and Pisgah craters, Mojave Desert, California: Journal of Geophysical Research, v. 96, p. 13,673-13,691, doi:10.1029/91JB00175.
22. Glazner, A.F., Bartley, J.M., Coleman, D.S., Gray, W., and Taylor, R.Z., 2004, Are plutons assembled over millions of years by amalgamation from small magma chambers?: GSA Today, v. 14, p. 4-11, doi:10.1130/1052-5173(2004)014<0004:APAOMO>2.0.CO;2.
23. Glazner, A.F., Carl, B.S., Coleman, D.S., Miller, J.S., and Bartley, J.M., 2008, Chemical variability and the composite nature of dikes from the Jurassic independence dike swarm, eastern California, in Wright, J.E., and Shervais, J.W., eds., Ophiolites, Arcs, and Batholiths: A Tribute to Cliff Hopson: Geological Society of America Special Paper 438, p. 455-480.
24. Gray, W., Glazner, A.F., Coleman, D.S., and Bartley, J.M., 2008, Long-term geochemical variability of the Late Cretaceous Tuolumne Intrusive Suite, central Sierra Nevada, California: The Geological Society of London, Special Publications, v. 304, p. 183-201, doi:10.1144/SP304.10.
25. Hagan, J.T., 1981, Impossibility of fragmenting small particles: Brittle-ductile transition: Journal of Materials Science, v. 16, p. 2909-2911, doi:10.1007/BF02402857.
26. Hartmann, W.K., 1969, Terrestrial, lunar, and interplanetary rock fragmentation: Icarus, v. 10, no. 2, p. 201-213, doi:10.1016/0019-1035(69)90022-0.
27. Hatch, T., and Choate, S.P., 1929, Statistical description of the size properties of nonuniform particulate substances: Journal of the Franklin Institute, v. 207, p. 369-387, doi:10.1016/S0016-0032(29)91451-4.
28. Higgins, M.D., 1994, Numerical modeling of crystal shapes in thin section: Estimation of crystal habit and true size: The American Mineralogist, v. 79, p. 113-119.
29. Higgins, M.D., 2000, Measurement of crystal size distributions: The American Mineralogist, v. 85, p. 1105.
30. Holtz, F., Lenné, S., Ventura, G., Vetere, F., and Wolf, P., 2004, Non-linear deformation and breakup of enclaves in a rhyolitic magma: A case study from Lipari Island (southern Italy): Geophysical Research Letters, v. 31, p. L24611, doi:10.1029/2004GL021590.
31. Jolly, R.J.H., and Sanderson, D.J., 1995, Variation in the form and distribution of dykes in the Mull swarm, Scotland: Journal of Structural Geology, v. 17, p. 1543, doi:10.1016/0191-8141(95)00046-G.
32. Kendall, K., 1978, The impossibility of comminuting small particles by compression: Nature, v. 272, p. 710-711, doi:10.1038/272710a0.
33. Krumbein, W.C., and Tisdel, F.W., 1940, Size distribution of source rocks of sediments: American Journal of Science, v. 238, no. 4, p. 296-305, doi:10.2475/ajs.238.4.296.
34. Kueppers, U., Perugini, D., and Dingwell, D.B., 2006, "Explosive energy" during volcanic eruptions from fractal analysis of pyroclasts: Earth and Planetary Science Letters, v. 248, no. 3-4, p. 800-807, doi:10.1016/j.epsl.2006.06.033.
35. Mandelbrot, B.B., 1983, The fractal geometry of nature: San Francisco, W.H. Freeman, 468 p.
36. Marone, C., and Scholz, C.H., 1989, Particle-size distribution and microstructures within simulated fault gouge: Journal of Structural Geology, v. 11, p. 799-814, doi:10.1016/0191-8141(89)90099-0.
37. McCammon, R.B., 1975, Statistics and probability, in McCammon, R.B., ed., Concepts in Geostatistics: New York, Springer-Verlag, p. 1-20.
38. Meibom, A., and Balslev, I., 1996, Composite power laws in shock fragmentation: Physical Review Letters, v. 76, no. 14, p. 2492, doi:10.1103/PhysRevLett.76.2492.
39. Mills, R.D., Glazner, A.F., and Coleman, D.S., 2009, Scale of pluton/wall-rock interaction near May Lake, Yosemite National Park, California, USA: Contributions to Mineralogy and Petrology, v. 158, p. 263-281, doi:10.1007/s00410-009-0381-x.
40. Norris, R.M., 1985, A geologic guide to Titus Canyon, Death Valley National Monument, Inyo County: California Geology, v. 39, p. 195-202.
41. Pabst, A., 1928, Observations on inclusions in the granitic rocks of the Sierra Nevada: Bulletin Department of Geological Science, University of California, v. 17, p. 325-386.
42. Pepe, S., Solaro, G., Ricciardi, G.P., and Tizzani, P., 2008, On the fractal dimension of the fallout deposits: A case study of the 79 A.D. Plinian eruption at Mount Vesuvius: Journal of Volcanology and Geothermal Research, v. 177, no. 1, p. 288-299, doi:10.1016/j.jvolgeores.2008.01.023.
43. Perfect, E., 1997, Fractal models for the fragmentation of rocks and soils: A review: Engineering Geology, v. 48, p. 185-198, doi:10.1016/S0013-7952(97)00040-9.
44. Perugini, D., Valentini, L., and Poli, G., 2007, Insights into magma chamber processes from the analysis of size distribution of enclaves in lava flows: A case study from Vulcano Island (southern Italy): Journal of Volcanology and Geothermal Research, v. 166, p. 193-203, doi:10.1016/j.jvolgeores.2007.07.017.
45. Perugini, D., Speziali, A., Caricchi, L., and Kueppers, U., 2011, 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, v. 202, p. 200-210, doi:10.1016/j.jvolgeores.2011.02.008.
46. Peterson, T.D., 1996, A refined technique for measuring crystal size distributions in thin section: Contributions to Mineralogy and Petrology, v. 124, p. 395-405, doi:10.1007/s004100050199.
47. Pickering, G., Bull, J.M., and Sanderson, D.J., 1995, Sampling power-law distributions: Tectonophysics, v. 248, p. 1-20, doi:10.1016/0040-1951(95)00030-Q.
48. Rogers, J.J.W., 1965, Reproducibility and significance of measurements of sedimentary size distributions: Journal of Sedimentary Petrology, v. 35, no. 3, p. 722-732.
49. Rose, R.L., 1957, Geology of the May Lake area, Yosemite National Park: Berkeley, California, University of California, Berkeley, 224 p.
50. Rosenbaum, J.G., and Reynolds, R.L., 2004, Record of Late Pleistocene glaciation and deglaciation in the southern Cascade Range: II. Flux of glacial flour in a sediment core from Upper Klamath Lake, Oregon: Journal of Paleolimnology, v. 31, p. 235-252, doi:10.1023/B:JOPL.0000019229.75336.7a.
51. Rousell, D.H., Fedorowich, J.S., and Dressler, B.O., 2003, Sudbury Breccia (Canada): A product of the 1850 Ma Sudbury event and host to footwall Cu-Ni-PGE deposits: Earth-Science Reviews, v. 60, p. 147-174, doi:10.1016/S0012-8252(02)00091-0.
52. Russ, J.C., 1994, Fractal Surfaces: New York, Plenum Press, 309 p.
53. Sahagian, D.L., and Proussevitch, A.A., 1998, 3D particle size distributions from 2D observations: Stereology for natural applications: Journal of Volcanology and Geothermal Research, v. 84, no. 3-4, p. 173-196, doi: 10.1016/S0377-0273(98)00043-2.
54. Sammis, C., King, G., and Biegel, R., 1987, The kinematics of gouge deformation: Pure and Applied Geophysics, v. 125, no. 5, p. 777-812, doi:10.1007/BF00878033.
55. Shimamoto, T., and Nagahama, H., 1992, An argument against the crush origin of pseudotachylytes based on the analysis of clast-size distribution: Journal of Structural Geology, v. 14, p. 999-1006, doi:10.1016/0191-8141 (92)90031-Q.
56. Snow, J.K., Wernicke, B.P., Burchfiel, B.C., Hodges, K.V., Axen, G.J., Walker, J.D., and Guth, P.L., 1989, Extensional tectonics in the Basin and Range Province between the southern Sierra Nevada and the Colorado Plateau: Washington, D.C., International Geological Congress Field Trip Guidebook T138, American Geophysical Union, 80 p.
57. Suzuki-Kamata, K., Kusano, T., and Yamasaki, K., 2009, Fractal analysis of the fracture strength of lava dome material based on the grain size distribution of blockand-ash flow deposits at Unzen Volcano, Japan: Sedimentary Geology, v. 220, p. 162-168, doi:10.1016/j.sedgeo.2009.04.026.
58. Tang, D., and Marangoni, A.G., 2006, 3D fractal dimension of fat crystal networks: Chemical Physics Letters, v. 433, p. 248-252, doi:10.1016/j.cplett.2006.11.057.
59. Tavassoli, Z., and Shirvani, A. E., 2000, Models of fragmentation with power law log-normal distributions: Physica A: Statistical Mechanics and Its Applications, v. 286, no. 1-2, p. 29-44.
60. Taylor, R.Z., 2004, Structure and stratigraphy of the May Lake interpluton screen, Yosemite National Park, California [M.S. thesis]: University of North Carolina, 61 p.
61. Tobisch, O.T., McNulty, B.A., and Vernon, R.H., 1997, Microgranitoid enclave swarms in granitic plutons, central Sierra Nevada, California: Lithos, v. 40, p. 321-339, doi:10.1016/S0024-4937(97)00004-2.
62. Turcotte, D.L., 1986, Fractals and fragmentation: Journal of Geophysical Research, v. 91, p. 1921-1926, doi: 10.1029/JB091iB02p01921.
63. Turcotte, D.L., 1989, Fractals in geology and geophysics: Pure and Applied Geophysics, v. 131, p. 171-196, doi: 10.1007/BF00874486.
64. Vernon, R.H., 1984, Microgranitoid enclaves in granites: Globules of hybrid magma quenched in a plutonic environment: Nature, v. 309, p. 438-439, doi:10.1038/309438a0.
65. Yazdi, M., and Esmaeilnia, A., 2009, Natural fragmentation model of Zirab coals, Iran: The Open: Geological Journal, v. 3, p. 1-7.