Skip to main content
Log in

Calcite formation in microbial mats: modeling and quantification of inhomogeneous distribution patterns by a cellular automaton model and multifractal measures

  • Original paper
  • Published:
Geologische Rundschau Aims and scope Submit manuscript

Abstract

The evolution of early diagenetic calcite cements in microbial mats of recent supratidal sediments of the southern North Sea is modeled in a two-dimensional microscale approach by a cellular automaton model (CAM). Calcite is traced out in the model by virtual calcium distribution patterns obtained from runs under different assumptions concerning sediment-intrinsic conditions. For justification of the CAM, real calcium distribution patterns, documented by scanning electron microscopy coupled with energy-dispersive X-ray spectrometry (SEM/EDX), are quantitatively compared with the virtual patterns on the basis of multifractal analyses. The formation of high magnesian calcite as a consequence of biogenic anaerobic decomposition of organic matter starts at certain initial calcite domains. In this stage an inhomogeneous and multifractal calcium distribution is characteristic. Nearly complete remineralization of organic matter leads to monofractal behavior of generalized fractal dimensions (DB(q) ±1.84). The CAM results confirm that calcite formation is a self-determining morphogenetical process and diffusive transport processes of reactants within the mat affect the biogenic calcite formation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Avnir D, Farm D (1989) The fractal nature of molecule-surface interactions on reactions. In: Avnir D (ed) The fractal approach to heterogeneous chemistry. Wiley, Chichester

    Google Scholar 

  • Berner RA (1971) Principles of chemical sedimentology. McGraw-Hill, New York, pp 1–240

    Google Scholar 

  • Bölviken B, Stokke PR, Feder J, Jössang T (1992) The fractal nature of geochemical landscapes. J Geochem Explor 43:91–109

    Article  Google Scholar 

  • Block A, Blob W von, Schellnhuber HJ (1990) Efficient box-counting determination of generalized fractal dimensions. Phys Rev A 42:1869–1874

    Article  Google Scholar 

  • Block A, Blob W von, Klenke T, Schellnhuber HJ (1991) Multifractal analysis of the microdistribution of elements in sedimentary structures using images from scanning electron microscopy and energy dispersive X-ray spectrometry. J Geophys Res 96:16223–16230

    Article  Google Scholar 

  • Havlin S (1989) Molecular diffusion and reactions. In: Avnir D (ed) The fractal approach to heterogeneous chemistry. Wiley, Chichester

    Google Scholar 

  • Halsey TC, Jensen MH (1986) Spectra of scaling indices for fractal measures: theory and experiment. Physica D 23:112–117

    Article  Google Scholar 

  • Hayakawa H, Sato S, Matsushita M (1987) Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes. Phys Rev A 36:1963–1966

    Article  Google Scholar 

  • Hentschel HGE, Procaccia I (1983) The infinite number of fractal dimensions of fractals and strange attractors. Physica D 8:4435–4444

    Article  Google Scholar 

  • Feder J (1992) Fractals. Plenum Press, New York, pp 1–283

    Google Scholar 

  • Gerdes G, Krumbein WE, Reineck HE (1985) The depositional record of sandy versicolored tidal flats (Mellum Island, southern North Sea). J Sediment Petrol 55:265–278

    Google Scholar 

  • Klenke T, Block A, Blob W von, Kappertz P, Schellnhuber HJ (1992) Fraktale Strukturen: Dokumente genetischer Prozesse and intrinsischer Eigenschaften von Sedimenten. Zentralbl. Geol Paläontol II 12: 2785–2795

    Google Scholar 

  • Korvin G (1992) Fractal models in the earth science. Elsevier, Amsterdam, pp 1–396

    Google Scholar 

  • Krohn CE (1988a) Sandstone fractal and Euclidean pore volume distributions. J Geophys Res 93:3286–3296

    Google Scholar 

  • Krohn CE (1988b) Fractal measurements of sandstones, shales and carbonates. J Geophys Res 93:3297–3305

    Google Scholar 

  • Kropp J, Block A, Bloh W von, Klenke T, Schellnhuber HJ (1994) Characteristic multifractal element distributions in recent bioactive marine sediments. In: Kruhl JH (ed) Fractals and dynamic systems in geosciences. pp 369–375

  • Riege H, Villbrandt M (1994) Microbially meditated processes in tide influenced deposits and their importance in stabilization and diagenesis of sediments: seasonal field studies, Norderney survey. In: Krumbein WE, Stal LJ, Paterson DM (eds) Biostabilization of sediments. pp 339–360

  • Tél T (1988) Fractals, multifractals and thermodynamics. An introductory review. Z Naturforsch 43a: 1154–1174

    Google Scholar 

  • Toffoli T, Margolus N (1987) Cellular automata machines: a new environment for modeling. MIT Press, Cambridge, pp 1–259

    Google Scholar 

  • Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kropp, J., von Blob, W. & Klenke, T. Calcite formation in microbial mats: modeling and quantification of inhomogeneous distribution patterns by a cellular automaton model and multifractal measures. Geol Rundsch 85, 857–863 (1996). https://doi.org/10.1007/BF02440116

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02440116

Key words

Navigation