Log10N = a - bM
where N is the cumulative number of earthquakes with magnitudes equal to or larger than M, and a is the number of events of M = 0. The variable b describes the relationship between the number of large and small events and is the slope of the best-fit line between the number of earthquakes at a given magnitude and the magnitude (Gutenberg and Richter, 1944; Ishimoto and Iida, 1939). A b value close to 1.0 is commonly observed in many parts of the world for tectonic earthquakes. This relationship is often referred to as the Gutenberg-Richter magnitude frequency relationship.
Differences in the slope b reveal information about the potential size and expected number of the events in a population of earthquakes. Analysis of b values around the world has shown that in fluid injection scenarios the b value is often in the range of 2, which reflects a larger number of small events (swarm earthquakes), compared to tectonic earthquakes. In hydraulic fracturing microseismicity, b values in the range of 2 are commonly observed (Maxwell et al., 2008; Urbancic et al., 2010; Wessels et al., 2011). The high b values observed in hydraulic fracturing are thought to represent the opening of numerous small natural fractures during the high-pressure injection (Figure E.2). It is possible for a hydraulic fracture to grow into a nearby fault and reactivate it, if the orientation of the fault is favorable for slip under the current stress conditions in the reservoir. Figure E.3 is an example of a hydraulic fracture reactivating a small fault during injection.
Gutenberg, B., and C.F. Richter. 1944. Frequency of earthquakes in California. Bulletin of the Seismological Society of America 34:185-188.
Hanks, T.C., and H. Kanamori. 1979. A moment magnitude scale. Journal of Geophysical Research 84(B5):2348-2350.
Ishimoto, M., and K. Iida. 1939. Observations of earthquakes registered with the microseismograph constructed recently. Bulletin of the Earthquake Research Institute 17:443-478.
Maxwell, S.C., J. Shemeta, E. Campbell, and D. Quirk. 2008. Microseismic deformation rate monitoring. Society of Petroleum Engineers (SPE) 116596-MS. SPE Annual Technical Conference and Exhibition, Denver, Colorado, September 21-24.
Richter, C.F. 1936. An instrumental earthquake magnitude scale. Bulletin of the Seismological Society of America 25:1-32.
Shemeta, J. 2010. It’s a matter of size: Magnitude and moment estimates for microseismic data. The Leading Edge 29(3):296.
Urbancic, T., A. Baig, and S. Bowman. 2010. Utilizing b-values and Fractal Dimension for Characterizing Hydraulic Fracture Complexity. GeoCanada—Working with the Earth. ESG Solutions. Available at www.geocanada2010.ca/uploads/abstracts_new/view.php?item_id=976 (accessed April 2012).
Wessels, S.A., A. De La Pena, M. Kratz, S. Williams-Stroud, and T. Jbeili. 2011. Identifying faults and fractures in unconventional reservoirs through microseismic monitoring. First Break 29(7):99-104.