Power-law vein-thickness distributions and positive feedback in vein growth

The thicknesses of veins of a single generation from the Kodiak accretionary complex show a power-law distribution with an exponent of D = 1.33. This value (D > 1) indicates that a significant portion of the vein-related extension is accommodated by the thinnest veins. Thick vein segments are typically confined to southeast-dipping brittle-ductile shear zones. Textural observations of veins within these zones indicate a progressive evolution from crack-seal to euhedral growth of quartz with an increase over time in the duration that fractures remained open. Model simulations of vein-thickness distributions show that a constant growth model results in a negative-exponential distribution and that it is necessary to assume size-proportional growth to produce a power-law distribution. Textures and power-law thickness distributions for the Kodiak veins are thus consistent with an increasing time-averaged growth rate as vein thickness increased, comprising a positive feedback. The positive feedback resulted in the progressive evolution from fractures to brittle-ductile shear zones and ultimately to faults.