Fracture network characterization through fractal dimension and Gutenberg–Richter parameter: Decatur open-source dataset as a study case

The fractal formalisms are well known for providing new understandings regarding the geometrical, spatial, and temporal behaviour of seismicity. Particularly, the fractal dimensions give information about the seismic events self-organization and self-similarity. On the other hand, the Gutenberg–Richter value, known as the b-value, has shown through the years to give handy information regarding the statistical distribution of earthquakes, on-site physical parameters, and geomechanical inputs. The Gutenberg–Richter value (b) and the capacity and correlation fractal dimensions, (D₀ and D₂), of the spatial distribution of earthquake hypocentres interact mathematically for micro- and macro-events. From this interaction, it is possible to obtain new insights into the fracture network development and the microseismicity source characterization in terms of single fractures, fault planes, or densely fractured volumetric spaces. Here we show this interaction for the open-source Decatur CO₂ project seismicity catalogue, comparing it with the results obtained for a natural earthquake catalogue of Illinois, in the United States. The fractal dimension D₀ is calculated using two different methodologies: box-counting and correlation integral partitioning. This last method is also used to calculate D₂. The results presented in this study allow us to describe how the fracture network geometry influences the earthquake complexity. Together with the calculation of the b-value, we present clear indications which show that seismicity recorded in the Illinois tectonic environment partially follows the Aki relationship D₀ ∼ 2b, which is not the case for induced events. In addition, the induced earthquake dataset shows that D₂ > D₀, an anomalous behaviour in terms of the fractal formalisms. All these facts might be used to establish spatial fracture network control techniques and seismicity-type distinctions in CO₂ injection sites located in highly active tectonic areas, respectively.