Size scaling relationships in the active fault networks of Japan and their correlation with Gutenberg-Richter b values

Fractal properties of active fault systems in Japan are evaluated and compared to Gutenberg‐Richter b values. Properties of the active fault network and seismicity were evaluated at 20 km intervals along three lines oriented along the length of Honshu, the main island of Japan. Fractal dimensions for the active fault network are calculated using the box counting method. The box curves often reveal the presence of an abrupt transition in slope at ∼8 km scales. This transition separates linear regions in the box curves that span box sizes of 17.5 to 8.5 km and 7.75 to 2 km. Power law coefficients were computed for the 17.5 to 8.5 km (DL) and 7.75 to 2 km (DS) range of box sizes from overlapping 70×70 km regions of the active fault complex. The maximum likelihood method is used to estimate b value from earthquakes occurring in the seismogenic zone (upper 20 km). The correlation between D and b value are found to vary considerably throughout Japan. In general, D and b are negatively correlated, which suggests that increased complexity in the active fault network accommodates rupture along fault planes of relatively larger surface area. Areas of significant positive correlation are also observed in Japan. The positive correlations arise through joint increases in b and D. In such areas the probability of large magnitude earthquakes decreases in response to increased fragmentation of the active fault network and increased possibility that stress release will take place along faults of smaller surface area. Negative correlations between b and D generally occur when increases in D are paralleled by decreases in b. Negative correlation areas bound the intensely faulted region of central Japan. An area of negative correlation also occurs in the intensely faulted high D area of central Japan where continued increases in D are paralleled by decreases in b. In general, these observations suggest that as fault complexity increases (as measured by D), interconnected planes of larger and larger surface area will accommodate strain release. However, with continued rise in fault complexity, strain release begins to occur on smaller fragments resulting in higher b and lower‐magnitude seismicity. The analysis may provide insights into the relationship between seismicity associated with large‐scale faults populations and earthquake hazard assessment.