New Estimates of Magnitude-Frequency Distribution and b-Value Using
Relative Magnitudes for the 2011 Prague, Oklahoma Earthquake Sequence
Abstract
The 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
provide new MFD and b-value estimates for the 2011 Prague, Oklahoma
sequence using a relative magnitude approach that depends only on
waveform data to recalculate magnitudes. We recalculate the magnitudes
of 8775 events that occurred between March 2010 and March 2012 and find
that the distribution of relative magnitudes exhibits less curvature
than the MFD of cataloged magnitudes. We also compare the distribution
of successive magnitudes differences to the traditional MFD and show
that a combination of the magnitude difference distribution (MDFD) and
relative magnitudes yields the most stable estimate of b-value. Using
the MDFD and relative magnitudes, we examine the temporal and spatial
variations in the b-value and observe low b-values during the aftershock
sequence for at least 5 months after the M5.7 mainshock, though areas
surrounding the northeast part of the sequence experience elevated
b-values. These new estimates of MFD and b-value will contribute to
further hazard assessment for induced earthquake sequences and promote
discussion regarding the use of b-value to understand the evolution of
induced seismic sequences.