EVOLUTION OF GUTENBERG-RICHTER A- AND B-VALUES FOR OKLAHOMA EARTHQUAKES

The rate of M >= 3 earthquakes in Oklahoma as reported by the Oklahoma Geological Survey Leonard Geophysical Observatory (LGO) has increased from an average of about 1.6/year for the period 1990 – 2009 (maximum 3 in 1990, 1995, 1998, 2002, and 2006) to an average of over 145/year for the period 2009-2014 with a maximum of over 550 in 2014. While the Gutenberg-Richter magnitude-scaling relationship (GR law) has proven robust for local, regional, and global catalogs across various time scales. the dramatic increase in the annual seismicity rate implicitly raises questions of whether the GR law applies to a geographical region and a period where the seismicity rate changes so rapidly.

Application of the GR law to the LGO catalog for the period 1990 – 2003 for ML >= 1.9 indicates that the model matches the catalog very well (least-squares r^2 = 0.99) with a b-value = 1.07, statistically indistinguishable from the presumed b-value of 1. Application to the period 1990 – 2014 also indicates a very good fit (r^2 = 0.99), but with a b-value = 1.19. Application to shorter periods 2012-2014, 2013-2014, and 2014 (through 8 August) have equally good fits with b-values in the range of 1.2. An analysis of a more complete 2014 catalog (1 January - 2 December) fits slightly less well (r^2 = 0.97) with a very steep b-value of 1.36. The quality of the fit for the several periods is likely an artifact of the catalog being dominated by later events. The high b-value suggests that the seismicity in Oklahoma is not similar to the seismicity in areas where it is caused by long-term tectonic processes, presuming that the least-squares estimate is appropriate.

In contrast, the MLE b-value for the 2014 catalog through 2 December is 0.88 (evaluation of r^2 for the MLE ongoing). This model better predicts the number of small-magnitude earthquakes, up to ML about 3.0, but significantly over predicts the number of larger earthquakes: catalog N(4.0) = 21 and MLE N(4.0) = 30.

Although the number of events since 2009 is large enough to support statistical analysis, the rapidly-changing rate should caution against inferring strong conclusions from these analyses. Not simply more data but also continual analyses over time are required to characterize and understand the evolving seismicity in Oklahoma.