Development of an Empirical Local Magnitude Formula for Northern Oklahoma

Abstract:

In this paper we focus on determining a local magnitude formula for northern Oklahoma that is unbiased with distance by empirically constraining the attenuation properties within the region of interest based on the amplitude of observed seismograms. For regional networks detecting events over several hundred kilometres, distance correction terms play an important role in determining the magnitude of an event. Standard distance correction terms such as Hutton and Boore (1987) may have a significant bias with distance if applied in a region with different attenuation properties, resulting in an incorrect magnitude. We have presented data from a regional network of broadband seismometers installed in bedrock in northern Oklahoma. The events with magnitude in the range of 2.0 and 4.5, distributed evenly across this network are considered. We find that existing models show a bias with respect to hypocentral distance. Observed amplitude measurements demonstrate that there is a significant Moho bounce effect that mandates the use of a trilinear attenuation model in order to avoid bias in the distance correction terms. We present two different approaches of local magnitude calibration. The first maintains the classic definition of local magnitude as proposed by Richter. The second method calibrates local magnitude so that it agrees with moment magnitude where a regional moment tensor can be computed. To this end, regional moment tensor solutions and moment magnitudes are computed for events with magnitude larger than 3.5 to allow calibration of local magnitude to moment magnitude. For both methods the new formula results in magnitudes systematically lower than previous values computed with Eaton’s (1992) model. We compare the resulting magnitudes and discuss the benefits and drawbacks of each method. Our results highlight the importance of correct calibration of the distance correction terms for accurate local magnitude assessment in regional networks.