TSK 11 Göttingen 2006 Peternell & Kruhl Crystal distribution pat- terns and their anisotropy behaviour in igneous rocks: towards an automated quan- tification, first resultsVortrag Mark Peternell1 Jörn H. Kruhl1 Introduction Since approximately two decades frac- tal geometry offers tools for the quan- tification of rock fabrics, and new methods are currently under develop- ment to investigate the inhomogene- ity of crystal distributions, grain- and phase-boundary patterns as well as their anisotropy behaviour (Kruhl et al. 2004). These methods are now adapted for automated processing and suit- able to quantify the inhomogeneity and anisotropy of rock fabrics from macro to microscale. Applications for quantifying inhomogeneity are mainly based on the box-counting and map-counting (Pe- ternell 2002) methods, for anisotropy behaviour mainly based on modified Cantor-dust methods and provide frac- tal dimensions, fractal-dimension iso- lines and azimuthal anisotropies of frac- tal dimension (AAD, Volland & Kruhl, 2004). For instance, the results provide information about the local variations of fabric patterns and their prefer orienta- tion behaviour at macro and microscale. Measurements Inhomogeneity Different types of granites from the Tuolumne Batholith (Sierra Nevada, USA), the Piquiri Syenite Massif (Neoproterozoic basement of southern Brazil) and a fine-grained granite 1 Tectonics and Material Fabrics Section, Technische Universität München, D-80290 München, Germany from central China (plates sold by a do-it-yourself store, Munich) have been investigated. Based on digital pho- tographs of flat non-polished, polished and stained surfaces of fine-grained granites, the distributions of phase- boundary patterns for biotite, quartz, plagioclase and K-feldspar have been quantified by the box-counting method (Fig. 1). All distributions and patterns Figure 1: [A] Image of quartz (qtz), pla- gioclase (plg), K-feldspar (fsp) and bt (black) phases based on data from a stained plate of a fine-grained granite from Central China (plates sold by a do-it-yourself store, Munich). [B] Results of box counting on [A] - the linear relation between the number of occupied boxes and the box-side length plotted in a double-logarithm diagram for all phases shows that the pattern for each face is self similar. The box dimension (DB — defined as the slope of the line) for all different patterns is app. the same, except for biotite (marked by the dashed lines). 1 Peternell & Kruhl TSK 11 Göttingen 2006 are self-similar, and their fractal box- dimensions range from 1.71 to 1.80 for all phases and for all different surfaces of the samples, but they are signif- icantly different within the box-size interval of approx. 0.2mm to 2mm for biotite. This indicates the influence of at least two pattern-forming processes during crystallization: 1. equilibrium crystallization condi- tions for all minerals, and 2. biotite distribution controlled by feldspar, as biotite crystals may have either grown in the remaining spaces or rotated during feldspar growth. A comparison of manually (highest precision) and automatically digitized crystal distribution and grain-boundary patterns shows no significant differ- ences in fractal-dimension values, and indicates the possibility of fully auto- mated data processing. Box-counting measurements of crystal distribution for hornblende/pyroxene- and feldspar- phases on differently-oriented cuts of a foliated syenite show significantly differ- ent box-dimensions for mafic and felsic minerals. This may result either from feldspar having controlled the crystal- lization and/or orientation of the mafic minerals, or from the influence of early- formed pyroxene cumulates now dis- rupted and found as schlieren. Other- wise the cut orientation has no influence on the results of the measurements, indi- cating that the box-counting method is not useful for analyzing anisotropic be- haviour of rock patterns. Anisotropy Because of the impracticalness of the box-counting method for analyzing the anisotropic rock pattern behaviour of the syenite, the hornblende/pyroxene and feldspar phases on the differently- oriented cuts are analyzed with a new automated process based on the work of Volland & Kruhl (2004). First re- sults should show different orientation behaviour of; 1. the mineral phases in relation to the differently-oriented cuts and 2. different anisotropic behaviour between the hornblende/pyroxene and the feldspar phases. The results from the differently-oriented cuts could be potentially useful as a step towards the analyses of 3D anisotropic material as well as the interpretation of the 2D cut effect of such material. Different anisotropic behaviour of differ- ent mineral phases in the syenite possi- bly indicate complex geometrical as well as chemical phase-to-phase interactions caused by either different pattern form- ing processes, for each phase, during the crystallization of the rock or by differ- ent crystallization time during the same process. Results The application of box-counting, a clas- sical fractal geometry method for ana- lyzing inhomogeneity distributions indi- cates: 1. Stained, polished and even non- polished granite surfaces yield the same information about the rock pattern distribution and, there- fore, about the pattern-forming processes of different phases like quartz, feldspars, and opaque phases even if the precision for dig- itizing the outlines of the different 2 TSK 11 Göttingen 2006 Peternell & Kruhl phases is not the same in different surfaces. Such record forms the ba- sis of automated fractal geometry procedures and, consequently, of detailed pattern analysis of larger areas. 2. Pattern differences between differ- ent minerals may be detected, even if they are not apparent, and quan- tified, as a necessary basis for the further investigation of pattern- forming processes. 3. Box-counting seems not to be ade- quate for analyzing the anisotropic behaviour of rock patterns. Thus an automated process based on the Cantor dust method was applied on anistropic mineral-phases patterns. The results show different orienta- tion behaviour of this pattern due to differently oriented rock cuts and mineral phases, potentially indicat- ing 4. complex mineral-phases growth in- teractions, influenced by one or sev- eral pattern forming processes at the same time or at different times, during the crystallisation of the syenite. 5. Combining fractal and non-fractal data, i.e., chemical and/or miner- alogical properties of rocks, may provide even more useful data sets. References Kruhl, JH, Andries, F, Peternell, M & Volland, S (2004) Fractal geometry analyses of rock fabric anisotropies and inhomogeneities. In: Kolymbas, D (ed) Fractals in Geotechnical Engineering. Advances in Geotechnical En- gineering and Tunnelling 9. Logos, Berlin, 115–135 Peternell, M (2002) Geology of syntectonic granites in the Itapema Regiona (SE Brazil) — Magmatic structures of the Rio Pequeno Granite (SE Brazil) and analyses with meth- ods of fractal geometry. Unpubl. Diploma Thesis, TU München, pp 90 Volland, S & Kruhl, JH (2004) Anisotropy quantification: the application of fractal ge- ometry methods on tectonic fracture pat- terns of a Hercynian fault zone in NW- Sardinia. Journal of Structural Geology 26, 1489–1500 3