Analysis of the correlation between fractal attributes of complex seismotectonic variables may offer insights into seismic hazard assessment. The Gutenberg-Richter, moment-magnitude, and moment-source area relations yield a direct fractal relationship among the Gutenberg-Richter b-value, occurrence rate, and the characteristic linear dimension of the fault plane (square root of fault surface area). In contrast, temporal variation in the correlation dimension of epicenters (DC) is found, in several studies, to correlate negatively with the b-value in different regions of the world. Spatial variations between the b-value and DC also tend to oppose each other. In Japan, negative correlations are also observed in the regional scale comparisons of the capacity dimension (Do) of active fault systems and the b-value. However, at local scales, the relationship yields both positive and negative correlation. The occurrence of positive or negative correlation appears to be controlled by different modes of failure within the active fault complex.
Spatial variations between the b-value and DC along the Northern Anatolian Fault Zone (NAFZ) suggest that, on average from 1900 to 1992, earthquake magnitudes were higher and epicenters more scattered within the central NAFZ than in its eastern and western segments. Temporal analysis reveals that the relationship between the b-value and DC are nonstationary. Temporal correlations are generally negative. A period of positive correlation is observed between 1976 and 1988. During the last 3 yr of this period (1985-1988), both the b-value and DC rose significantly, suggesting that stress release occurs through increased levels of low-magnitude and increasingly scattered seismicity. This dispersed pattern of seismicity, in combination with higher slip rates in the central NAFZ, may be one that did not adequately relieve stress along the main fault zone. This change in behavior and the tendency during the last century for the seismicity to migrate westward along the NAFZ may point to an increased risk of larger magnitude events such as the İzmit earthquake.