Session 51: Generation of granitic rocks and deep crustal processes

Jan H. Behrmann1

(behrmann@perm.geologie.uni-freiburg.de)

David C. Tanner1

(tanner@perm.geologie.uni-freiburg.de)1

Geologisches Institut, Universität Freiburg, Albertstr. 23B, D-79104 Freiburg, Germany

The fractal geometry of leucosome networks in migmatitic gneisses from the western Bohemian Massif has been analysed in a well-exposed area near Waldmünchen (Bavaria, Germany). Migmatisation is Carboniferous in age, and was followed by the intrusion of large volumes of late-orogenic granitoids. The aim of our investigation was to determine the fractal dimension, if any, of the leucosome networks, and to constrain physical models for gravity-driven extraction of melts from a system with self-similar geometry. Migmatite structure was determined in a series of samples using the box-counting method. For all line spacings (r) between 0.5 mm and 10 cm the number of boxes (N) containing leucosome material and r are proportional. Within this range of scales, therefore, the structure is scale invariant. According to all our data the migmatite structure has a constant fractal dimension (D) of 1.81 + 0.1, independent of the orientations of the sections analysed. The structure can therefore be modelled as that of a Sierpinski carpet, a two-dimensional theoretical fractal object with D = 1.89 and multiple symmetry. Its 3D counterpart is Menger´s sponge, which is taken as geometrical object for the physical modelling of magma extraction. Our modelling results show that Menger´s sponge is an excellent transport system for granitic partial melts with viscosities between 106 and 109 Pa s, moving under the influence of gravity. This is because melt located in a leucosome of size "a" only has to move a distance 2a to reach a leucosome of size 3a. Massive leucosome channels of 5-10 m diameter, also present in the area, can serve as conduits for granitic melts of 108 - 1010 Pa s viscosity over a vertical distance of 30 km. Under the most restrictive assumptions (5 m conduit width, 1010 Pa s viscosity) rates of melt ascent are 9.1 x 106 mMa-1, allowing fast release of large melt quantities of appropriate viscosity from migmatite terrains.