A fractal model of granitic intrusion and variability based on cellular automata

Abstract

Among the various mechanisms for magma ascent and emplacement, rock fracturing is a highly significant factor. In this study, a cellular automaton based on the Olami-Feder-Christensen model was used to generate a self-organized network in which magma can ascend and be arrested to form granitic intrusions under the influence of their buoyancy. The model embodies the ascent of discrete magma batches in a stepwise style by opening the fractures and then closing them after passage of the magma. In the model, magma ascends towards the subsurface via self-organized networks of rock fractures as long as the density of the surrounding rocks is greater than that of the magma. If magma rises to a zone with negative buoyancy, it stops and starts to solidify; thus forming granitic intrusions. Two fractal dimensional measures, perimeter-area (P-A) and number-area (N-A), were used to quantify the irregularity and spatial distribution of the modeled intrusions. The fractal dimension DAP of P-A, as well as the fractal dimension DP of the perimeter, show that the irregularity of the intrusions increases as the thickness of the negative buoyancy region increases. The N-A exponent D reflects the irregular size and spatial scale-invariance of the intrusions, and an abrupt inflection point occurs at an area of 100 cells, owing to the coalescence of small batches of intrusions into a larger intrusion. The scale-invariance exhibited by this system indicates that magma ascent and the formation process of granitic intrusions is a self-organized critical process and we demonstrate that a cellular automaton and fractal model is suitable for capturing, quantifying and modeling the spatial and temporal evolution of complex granitic intrusions.