New Estimates of Magnitude‐Frequency Distribution and b‐Value Using Relative Magnitudes for the 2011 Prague, Oklahoma Earthquake Sequence

Abstract

AbstractThe magnitude‐frequency distribution (MFD) describes the relative proportion of earthquake magnitudes and provides vital information for seismic hazard assessment. The b‐value, derived from the MFD, is commonly used to estimate the probability that a future earthquake will exceed a specified magnitude threshold. Improved MFD and b‐value estimates are of great importance in the central and eastern United States where high volumes of fluid injection have contributed to a significant rise in seismicity over the last decade. In this study, we recalculate the magnitudes of 8,775 events for the 2011 Prague, Oklahoma sequence using a relative magnitude approach that depends only on waveform data to calculate magnitudes. We also compare the distribution of successive magnitude differences to the MFD and show that a combination of the magnitude difference distribution (MDFD) and relative magnitudes yields a reliable estimate of b‐value. Using the MDFD and relative magnitudes, we examine the temporal and spatial variations in the b‐value and show that b‐value ranges between ∼0.6 and 0.85 during the aftershock sequence for at least 5 months after the M 5.7 mainshock, though areas surrounding the northeast part of the sequence experience higher b‐values (0.7–0.85) than the southwestern part of the Meeker‐Prague fault where b‐value is the lowest (0.6–0.7). We also identify a cluster of off‐fault events with the highest b‐values in the catalog (0.85). These new estimates of MFD and b‐value will contribute to understanding of the relations between induced and tectonic earthquake sequences and promote discussion regarding the use of b‐value in induced seismic hazard estimation.