A big problem for small earthquakes: Benchmarking routine magnitudes and conversion relationships with coda-envelope-derived Mw in southern Kansas and northern Oklahoma

Earthquake magnitudes are widely relied upon measures of earthquake size. Although moment magnitude (⁠Mw">MwMw⁠) has become the established standard for moderate and large earthquakes, difficulty in reliably measuring seismic moments for small (generally Mw<4">Mw<4Mw<4⁠) earthquakes has meant that magnitudes for these events remain plagued by a patchwork of inconsistent measurement scales. Because of this, magnitudes of small earthquakes and statistics derived from them can be biased. Furthermore, because small earthquakes are much more numerous than large ones, many applications, such as seismic hazard modeling, depend critically on analysis of events characterized by magnitudes other than Mw">MwMw⁠. To assess this problem, we apply coda envelope analysis to reliably determine moment magnitudes for a case study of small earthquakes from northern Oklahoma and southern Kansas. Not surprisingly, we find significant differences among ML">MLML⁠, mbLg">mbLgmbLg⁠, and Mw">MwMw for M ∼2–4 earthquakes examined here. More troublingly, we find that relations designed to convert other magnitudes to Mw">MwMw⁠, which are relied upon for important applications such as seismic hazard analysis, often increase rather than decrease this bias for our dataset. In our case study, we find that converted magnitudes can result in a systematic bias sometimes exceeding 0.5 magnitude units, a difference that typically corresponds to a factor of ∼3 in seismicity rate. Moreover, we find a correspondingly large bias in Gutenberg–Richter b‐values, controlled primarily by inaccurate magnitude scaling in the conversion relationships. Although this study focuses on a relatively small geographic area, we can expect that similar issues exist with varying severity in other regions. Therefore, magnitudes of small earthquakes and their associated statistics, including seismicity rates and b‐values, should be treated with caution.