Fractal Dimension of Microseismic Events via the Two-Point Correlation Dimension, and its Correlation with b Values

The magnitude distribution of a microseismic dataset can be described by the b value. Similarly, the spatial distribution of events can be described by the two-point correlation dimension (Dc), which provides an objective and quantifiable assessment of the dimensionality of a datasets (i.e., do the events fall along a linear or planar feature, or fill up a 3D volume?). Typically, spatial distributions are identified by eye (the interpreter will indentify linear or planar features on a hypocentral map). We begin this paper by describing the calculation of Dc, before going on to evaluate the correlation between Dc and the seismic b value. We perform our analysis on a range of microseismic datasets, including hydraulic fracture stimulation, enhanced oil recovery and a mining dataset. It has been suggested that elevated b values indicate a more distributed deformation. We find strong, statistically significant correlation between b and Dc, implying that the inferences made regarding b values during reservoir stimulation stimulation - that elevated b values correspond to areas with greater stimulation complexity, while lower b values imply activity on simpler, planar features - are appropriate.