Is the outcrop topology of dolerite dikes of the Precambrian Singhbhum Craton fractal?

Abstract

In the Precambrian Singhbhum Craton of eastern India, newer dolerite dikes occur profusely with varying outcrop lengths. We have analysed the nature of their length-size and orientation distributions in relation to the theory of fractals. Two orientational sets of dikes (NW-SE and NE-SW) are present. Both the sets show strongly non-power-law size distributions, as reflected in non-linear variations in logarithmic space. We analyzed thousands of data, revealing that polynomial functions with a degree of 3 to 4 are the best representatives of the non-linear variations. Orientation analysis shows that the degree of dispersions from the mean trend tends to decrease with increasing dike length. The length-size distributions were studied by simulating fractures in physical models. Experimental fractures also show a non-power-law distribution, which grossly conforms to those of the dolerite dikes. This type of complex size distributions results from the combined effects of nucleation, propagation and coalescence of fractures.