Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 14 6 2007 10.5194/npg-14-811-2007 http://www.nonlin-processes-geophys.net/14/811/2007/ http://www.nonlin-processes-geophys.net/14/811/2007/npg-14-811-2007.html http://www.nonlin-processes-geophys.net/14/811/2007/npg-14-811-2007.pdf 811 821 2007-12-10 Statistical measures of distribution patterns of silicon and calcium in marine sedimentary layers K. Bube T. Klenke J. A. Freund U. Feudel feudel@icbm.de Institut für Chemie und Biologie des Meeres, Carl von Ossietzky Universität Oldenburg, Germany We analyze electron microscope X-ray spectroscopy data of recent supratidal marine sediments. Statistical measures are used to characterize the distribution of silicon and calcium in different layers of the sediments. We also use cluster analysis and symbolic dynamics to filter measurement noise and to classify different density regions. This allows to calculate characteristic patch sizes which reflect the sizes of individual clastic grains and the corresponding pore sizes. Silicon indicates the independent processes in the sedimentation history of certain grains. Calcium is capable to monitor intrinsic early diagenetic processes of biogeochemical calcium mineralization of primary organic matter as documented in more organized distributions with higher clustering. Allain, C. and Cloitre, M.: Characterizing the lacunarity of random and deterministic fractal sets, Phys. Rev. A, 44, 3552–3558, 1991. Anguy, Y., Ehrlich, R., Ahmadi, A., and Quintard, M.: On the ability of a class of random models to portray the structural features of real, observed, porous media in relation to fluid flow, Cement and Concrete Composites, 23, 313–330, 2001. Block, A., von Bloh, W., Klenke, T., and Schellnhuber, H J.: Multifractal Analysis of the Microdistribution of Elements in Sedimentary Structures Using Images From Scanning Electron Microscopy and Energy Dispersive X Ray Spectroscopy, J. Geophys. Res., 96, 223–230, 1991. Bube, K., Klenke, T., and Feudel, U.: An algorithm for detecting layer boundaries in sediments, Nonlin. Processes Geophys., 13, 661–669, 2006. Gerdes, G., Krumbein, W E., and Reineck, H.-E.: The depositional record of sandy, versicolored tidal flats (Mellum island, southern North Sea), J. Sediment. Petrol., 55, 265–278, 1985. Green, D. and Swets, J.: Signal detection theory and psychophysics, Wiley, New York, 1966. Hao, B.-L.: Symbolic dynamics and characterization of complexity, Physica D, 51, 161–176, 1991. Hartigan, J.: Clustering Algorithms, Wiley, New York, 1975. Hartigan, J. and Wong, M.: A $K$-Means Clustering Algorithm, Appl. Statist., 28, 100–108, 1979. Haussels, R., Klenke, T., Kropp, J., and Ebenhöh, W.: Observations on the influence of pore space geometry on concentration patterns and transportation properties of dissolved oxygen in a bioactive sandy sediment by a lattice Boltzmann automaton model, Hydrol. Proc., 15, 81–96, 2001. Kropp, J., Block, A., von Bloh, W., Klenke, T., and Schellnhuber, H.: Multifractal characterization of microbially induced calcite formation in recent tidal flat sediments, Sediment. Geol., 109, 37–52, 1997. Kullback, S. and Leibler, R.: On Information and Sufficiency, Annals of Math.\ Stat., 22, 79–86, 1951. Kurths, J., Schwarz, U., Witt, A., Krampe, R., and Abel, M.: Measures of Complexity in Signal Analysis, in: Chaotic, Fractal and Nonlinear Signal Processing, edited by: Katz, R., American Institute of Physics Conference Proceedings, vol. 375, pp. 33–54, New York, 1996. Laplace, P.: A Philosophical Essay on Probabilities, Dover, New York, 1819. Mandelbrot, B.: The Fractal Geometry of Nature, Freeman, New York, 1983. Morford, J., Kalnejais, L., Martin, W., Francois, R., and Karle, I.: Sampling marine pore waters for Mn, Fe, U, Re and Mo: Modifications on diffusional equilibration thin film gel probes, J. Exper. Mar. Biol. and Ecol., 285/286, 85–103, 2003. Ott, E.: Chaos in dynamical systems, Cambridge University Press, Cambridge, 1993. Papoulis, A.: Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, 1984. Pettijohn, F. and Potter, P.: Atlas and glossary of primary sedimentary structures, Springer, Berlin, 1964. Plotnick, R., Gardner, R., Hargrove, W., Prestegaard, K., and Perlmutter, M.: Lacunarity analysis: A general technique for the analysis of spatial patterns, Phys. Rev. E, 53, 5461–5468, 1996. Tucker, M.: Sedimentary Petrology, Blackwell, 2001. Visscher, P., Reid, R., and Bebout, B.: Microscale observation of sulfate reduction: Correlation of microbial activity and lithified micritic laminae in modern marine stromatolithes, Geology, 28, 919–922, 2000.