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Earth Stress and Seismic Hazard From the Size-Frequency Distribution of Seismic Events


The parameter b in the 1942 Gutenberg-Richter Law (related to the parameter m in the 1939 Ishimodo-Iida relation) is used to describe the power-law relationship between the magnitude and total number of earthquakes in any given region and time period of at least that magnitude. The value of b is generally equal to 1.0 in seismically active regions, and variations in that value have been attributed to various causes including different stress regimes, source mechanism type, depth, and strength and heterogeneity of the rock. Workers applying this analysis to microseismicity have used it to interpret processes related to hydraulic fracturing treatments and have also interpreted b-values as a “stress meter” in the reservoir. If the b-value can indeed provide information about the stress state of the earth without a-priori knowledge of the tectonic setting, it could prove valuable for prediction of earthquake hazards related to induced seismicity by enabling predictions of the potential size and frequency of seismic events. By examining the b-value distribution of earthquake populations within the context of their geological history and present day geological setting, the validity of using stress meter interpretation appears to break down. An analysis of data from 3 case studies, a naturally occuring earthquake, microseismic data from a reservoir stimulation, and induced seismicity data from wastewater injection is presented, showing the relationships of the b-values to the mode of rock failure that generate the seismicity and the utility of an alternative, geologically-based explanation for b-value distributions. This alternative explanation for the b-value distribution can be used to quantify the nature of fault and fracture distributions in the reservoir in addition to providing a possible upper magnitude for potentially damaging earthquakes. 1051