Determination of the fractal dimension of a shore platform profile

Journal of the Geological Society of India

Volumn 81, Issue 1, 2013, Pages 122-128

  Dasgupta, Rajarshi ^a  

^a VIDYASAGAR COLLEGE   (India)

Author keywords

Co seismic uplift; Fractal; New Zealand; Roughness; Shore platforms; Tectonics

Indexed keywords

COASTAL EVOLUTION; COSEISMIC PROCESS; FRACTAL ANALYSIS; GEOMORPHOLOGICAL RESPONSE; MORPHOMETRY; SURFACE ROUGHNESS; TECTONIC EVOLUTION; TECTONIC SETTING; UPLIFT;

HOUGHTON BAY; NEW ZEALAND; NORTH ISLAND; WELLINGTON [NORTH ISLAND];

EID: 84872922454     PISSN: 00167622     EISSN: 09746889     Source Type: Journal    
DOI: 10.1007/s12594-013-0011-0     Document Type: Article

References (58)

1. Ahmadi, A., Neyshabouri, M.R., Rouhipour, H. and Asadi, H. (2011) Fractal dimension of soil aggregates as an index of soil erodibility. Jour. Hydrol., v.400, pp.305-311.
2. Armstrong, A. (1986) On the fractal dimension of some transient soil properties. Jour. Soil Sci., v.37, pp.641-652.
3. Begg, J.G. and Mazengarb, C. (1996) Geology of the Wellington area, scale 1: 50000. Inst. of Geol. Nucl. Sci. Geol. Map, v.22, Lower Hutt, New Zealand.
4. Begg, J.G. and Mcsaveney, M.J. (2005) Wairarapa fault rupturevertical deformation in 1855 and a history of similar events from Turakirae Head. In: J. Townend, R. Langridge, and A. Jones, A. (comp.), Proc. 1855 Wairarapa Earthquake Symp. Greater Wellington Regional Council, Wellington, pp.21-30.
5. Bell, T. (1979) Mesoscale sea floor roughness. Deep Sea Res., v.26, pp.65-76.
6. Berryman, K.R. (1993) Age, height, and deformation of Holocene marine terraces at Mahia Peninsula, Hikurangi subduction margin, New Zealand. Tectonics, v.12, pp.1347-1364.
7. Brown, S. (1987) A note on the description of surface roughness using fractal dimension. Geophy. Res. Lett., v.14, pp.1095-1098.
8. Burg, J.P. (1967) Maximum entropy spectral analysis. In: D.G. Childers (Ed.), Modern Spectrum Analysis. IEEE Press, New York, pp. 34-41.
9. Burrough, P.A. (1981) Fractal dimensions of landscapes and other environmental data. Nature, v.294, pp.240-242.
10. Carr, J.R. (1997) Statistical self-affinity, fractal dimension and geologic interpretation. Engg. Geol., v.48, pp.269-282.
11. Carter, L. and Lewis, K. (1995) Variability of the modern sand cover on a tide and storm driven inner shelf, south Wellington, New Zealand. New Zealand Jour. Geol. Geophys., v.38, pp.451-470.
12. Chakraborty, J., Mahale, V., Shashikumar, K. and Srinivas, K. (2007) Quantitative characteristics of the Indian Ocean seafloor relief using fractal dimension. Indian Jour. Mar. Sci., v.36, pp.152-161.
13. Charola, A.E., Grissom, C.A., Erder, E., Wachowiak, M.J. and Oursler, D. (1996) Measuring surface roughness: three techniques. In: J. Riederer (Ed.), Proc. 8th Internat. Congress on Deterioration and Conservation of Stone. Moller, Berlin, pp.1421-1434.
14. Demets, C., Gordon, R.G., Argus, D.F. and Stein, S. (1990) Current plate motions. Geophys. Jour. Int., v.101, pp.425-478.
15. Dimri, V.P., Srivastava, R.P. and Vedanti, N. (2011) Fractals and chaos. In: H.K. Gupta (Ed.), Encyclopedia of Solid Earth Geophysics. Springer, Dordrecht, pp.297-302.
16. Elliott, J.K. (1989) An investigation of the change in surface roughness through time on the foreland of Austre Okstindbreen, north Norway. Comp. Geosci., v.15, pp.209-217.
17. Gallant, J.C., Moore, I.D., Hutchinson, M.F. and Gessler, P. (1994) Estimating fractal dimension of profiles: a comparison of methods. Math. Geol., v.26, pp.455-481.
18. Gao, J. and Xia, Z. (1996) Fractals in physical geography. Prog. Phys. Geog., v.20, pp.178-191.
19. Goodchild, M.F. (1980) Fractals and the accuracy of geographical measures. Math. Geol., v.12, pp.85-98.
20. Goodchild, M.F. and Mark, D.M. (1987) The fractal nature of geographic phenomena. Ann. Assoc Am. Geog. v.77, pp.265-278.
21. Håkanson, L. (1978) The length of closed geomorphic lines. Math. Geol., v.10, pp.141-167.
22. Hirata, T. (1989) Fractal dimension of fault systems in Japan: fractal structure in the rock fracture geometry of at various scales. Pure Appld. Geophys., v.131, pp.157-170.
23. Kennedy, D.M. and Beban, J.G. (2005) Shore platform morphology on a rapidly uplifting coast, Wellington, New Zealand. Earth Surf. Proc. Landf., v.30, pp.823-832.
24. Klinkenberg, B. (1992) Fractals and morphometric measures: is there a relationship? Geomorphology, v.5, pp.5-20.
25. Klinkenberg, B. and Goodchild, M.F. (1992) The fractal properties of topography: a comparison of methods. Earth Surf. Proc. and Landf., v. 17, pp.217-234.
26. Kulatilake P.H.S.W., Um, J. and Pan, G. (1998) Requirements for accurate quantification of self-affine roughness using the variogram method. Int. Jour. of Solid Struc., v.35, pp.4167-4189.
27. Lam, N.S.N. and Quattrochi, D.A. (1992) On the issues of scale, resolution and fractal analysis in the mapping sciences. The Prof. Geog., v.44, pp.88-98.
28. Malinverno, A. (1990) A simple method to estimate the fractal dimension of a self-affine series. Geophy. Res. Lett., v.17, pp.1953-1956.
29. Mandal, P., Mabawonku, A.O. and Dimri, V.P. (2005) Self organized fractal seismicity of reservoir triggered earthquakes in the Koyna-Warna seismic zone, western India. Pure Appld. Geophy., v.162, pp.73-90.
30. Mandelbrot, B. (1967) How long is the coastline of Britain? Statistical self similarity and fractional dimension. Science, v.156, pp.636-638.
31. Mandelbrot, B.B. (1977) Fractals: Form, Chance and Dimensions. Freeman, San Francisco, 365p.
32. Mandelbrot, B.B. (1983) The Fractal Geometry of Nature. Freeman, New York, 468p.
33. Mareschal, J.C. (1989) Fractal reconstruction of sea-floor topography. Pure Appld. Geophys., v.131, pp.197-210.
34. Mark, D. and Aronson, P. (1984) Scale-dependent fractal dimensions of topographic surfaces: an empirical investigation, with applications in geomorphology and computer mapping. Math. Geol., v.16, pp.67-683.
35. Mccarroll, D. (1992) A new instrument and techniques for the field measurement of rock surface roughness. Zeit. für Geomorph. N.F., v.36, pp.69-79.
36. Mccarroll, D. (1997) A template for calculating rock surface roughness. Earth Surf. Proc. Landf., v.22, pp.1229-1230.
37. Mcconchie, J., (2000) From shaky beginnings: a geomorphic analysis of Wellington. In: J. McConchie, D. Winchester and R. Willis (Eds.), Dynamic Wellington. Institute of Geography, Victoria University of Wellington, Wellington, pp.9-33.
38. Mcsaveney, M.J., Graham, I.J., Begg, J.G., Beu, A.G., Hull, A.G., Kim, K. and Zondervan, A. (2006) Late Holocene uplift of beach ridges at Turakirae Head, south Wellington coast, New Zealand. New Zeal. Jour. Geol. Geophy., v.49, pp.337-358.
39. Morton, J.E. (2004) Seashore ecology of New Zealand and the Pacific. Bateman, Auckland, 504p.
40. Naylor, L.A., Stephenson, W.J. and Trenhaile, A.S. (2010) Rock coast geomorphology: recent advances and future research directions. Geomorphology, v.114, pp.3-11.
41. Oleschko, K., Parrot, J.F., Ronquillo, G., Shoba, S., Stoops, G. and Marcelino, V. (2004) Weathering: towards a fractal quantifying. Math. Geol., v.36, pp.607-626.
42. Oliver, M. and Webster, R. (1986). Semi-variograms for modeling the spatial pattern of landforms and soil properties. Earth Surf. Proc. Landf., v.11, pp.491-504.
43. Pillans, B. (1986) A late Quaternary uplift map for North Island, New Zealand. Bull. Roy. Soc. New Zeal., v.24, pp.409-417.
44. Pillans, B. and Huber, P. (1995) Interpreting coseismic deformation using Holocene coastal deposits, Wellington, New Zealand. Quat. Int., v.26, pp.87-95.
45. Quale, A.M. (1984) Weather and sea condition of Wellington Harbour and South Coast. New Zeal. Met. Serv. Tech. Info. Circ., v.196.
46. Roberts, S., Sanderson, D.J. and Gurniel, P. (1998) Fractal analysis of Sn-W mineralization from central Iberia, insights into the role of fracture connectivity in the formation of an ore deposit. Econ. Geol., v.93, pp.360-365.
47. Rouai, M. and Jaaidi, E.B. (2003) Scaling properties of landslides in the Rif Mountains of Morocco. Engg. Geol., v.68, pp.353-359.
48. Sulebak, J.R. (1999) Fractal analysis of surface topography. Nor. Geogr. Tidsskr., v.57, pp.213-225.
49. Sunamura, T. (1992) Geomorphology of rocky coasts. John Wiley and Sons, Chichester, 314p.
50. Suneson, N.H. (1992) Geology of Torlesse rocks around the Wellington coast between Paekakariki and Pencarrow Head. Inst. Geol. Nucl. Sci. Rep., v.92/8, pp.1-52.
51. Sunmonu, L.A. and Dimri, V.P. (1999) Fractal analysis and seismicity of Bengal basin and Tripura fold belt, northeast India. Jour. Geol. Soc. India, v.53, pp.587-592.
52. Tanner, B.R., Perfect, E. and Kelley, J.T. (2006) Fractal analysis of Maine's glaciated shoreline tests established coastal classification scheme. Jour. Coast. Res, v.22, pp.1300-1304.
53. Trenhaile, A.S. (1987) The geomorphology of rock coasts. Clarendon Press, Oxford, 384p.
54. Trenhaile, A.S. (2002a) Rock coasts, with particular emphasis on shore platforms. Geomorphology, v.48, pp.7-22.
55. Trenhaile, A.S. (2002b) Modelling the development of marine terraces on tectonically mobile rock coasts. Mar. Geol., v.185, pp.34-361.
56. Wang, Q., Deng, J., Liu, H., Yang, L., Wan, L. and Zhang, R. (2010) Fractal models for ore reserve estimation. Ore Geol. Rev., v.37, pp.2-14.
57. Whalley, W.B. and Rea, B.R. (1994) A digital surface roughness meter. Earth Surf. Proc. Landf., v.19, pp.809-814.
58. Xu, T., Moore, I.D. and Gallant, J.C. (1993) Fractals, fractal dimensions and landscapes - a review. Geomorphology, v.8, pp.245-262.