Fractal distributions of stress and strength and variations of b-value

A two-dimensional planar fault zone on which the difference between stress and strength follows a fractal distribution is simulated to study the variation of the frequency-magnitude b-value under different distributions of heterogeneities and ambient stress levels. It is suggested that earthquakes occur in regions where this difference exceeds a specified value and that the size of these regions is a measure of the magnitude of the associated earthquake. A systematic variation in b-value is observed. It is found that the b-value has a positive correlation with the fractal dimension of the distribution and is inversely related to the ambient stress level. Observational data are compared with the simulation, showing that the observed b-value variation before and during earthquake sequences is a result of changes in both the ambient stress level and in the fractal dimension of the stress-strength distribution.