Empirical and Synthetic Approaches to the Calibration of the Local Magnitude Scale, ML, in Southern Kansas

We calibrate the local magnitude (M-L) scale in southern Kansas, a region of increased seis- micity due to oil and gas activities, using both an empirical and a synthetic approach to derive the attenuation curve. In the empirical approach, we use the classic Richter (1935) log A(0) attenuation model to calculate M-L using amplitude data from the southern Kansas Network catalog and calibrate it using moment magnitudes (M-w) from St. Louis University moment tensor solutions and Trugmant et al.(2017). In the synthetic approach, we utilize a crustal velocity model to generate synthetic seismograms from which we measure amplitudes to estimate the attenuation curve. This second approach presents a novel way to calibrate M-L , in any region of interest, when earthquake data are scarce or unavailable. Both approaches show lower attenuation in southern Kansas than in the relations being used by the U.S. Geological Survey and Oklahoma Geological Survey to compute M-L values in this area. This difference results in a systematic decrease of similar to 0.1 magnitude unit between our results and those reported in the southern Kansas Network catalog. We also find a dependence of M L on stress drop for earthquakes with corner frequencies near and below the Wood-Anderson instrumental corner of 1.25 Hz. The derived attenuation curve is consistent with a mean stress drop of 3-4 MPa for these earthquakes.