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ABSTRACT Precise knowledge of earthquake magnitudes is vital for accurate characterization of seismic hazards. However, the estimation of earthquake magnitude, particularly for small events, is complicated by differences in network procedures and completeness. This produces disparate magnitude estimates for the same event and emphasizes the need for a consistent and transportable magnitude estimation procedure. Here, we investigate the use of the relative magnitude method, which measures earthquake magnitude from a least-squares inversion of interlinked waveform amplitude ratios. Our results show that that the relative magnitude method can establish both local and moment magnitudes for many events in the 2019 Ridgecrest sequence. The method also provides constraints on moment magnitude estimates for M <3 events, which are not routinely available using current methods. Although the relative magnitude method is advantageous because it can be applied uniformly in various regions and does not require empirical distance or attenuation corrections, there are several parameters that require subjective decision making and may introduce bias in the resulting magnitude estimates. These include acceptable thresholds for signal-to-noise ratios and cross correlation, filtering procedures, sampling windows, and station selection. Here, we not only calculate magnitude but also investigate how the subjective decision making affects the resulting magnitudes. Based on our analysis, we present recommendations to enhance the utility of this method for future users. 

A precise understanding of earthquake magnitudes is vital for accurate calculations of magnitude exceedance probabilities and seismic hazard assessment. However, characterization of earthquake magnitude, particularly for small events, is complicated by differences in network capabilities and procedures. Furthermore, the use of differing magnitude scales for events of various sizes introduces additional challenges and produces disparate magnitude estimates for the same events. To address the need for a consistent magnitude estimation procedure that can accurately estimate magnitude across a wide magnitude range and in diverse tectonic environments, we investigate the use of the relative magnitude method. This approach utilizes amplitude ratios of highly correlated waveforms among numerous interlinked event pairs to compute magnitude for a group of events. While the relative magnitude method is advantageous because it can be applied uniformly in various regions and does not require distance or attenuation corrections, there are several parameters that currently require human decision which may introduce bias. These include acceptable thresholds for signal-to-noise ratios and cross-correlation, filtering procedures, sampling windows, and station selection. Our research focuses on computing new relative magnitudes for events in southern California, including the 2019 Ridgecrest sequence. We investigate the uncertainty that human decision may impose on the resulting magnitudes and compare our results to other magnitude estimation methods. Finally, we present our recommendations for routine procedures that minimize uncertainty and variability in the relative magnitude method, aiming to enhance the utility of this method for future users. 

Accurate estimates of earthquake magnitude are necessary to improve our understanding of seismic hazard. Unbiased magnitudes for small earthquakes are especially important because magnitude exceedance probabilities for large earthquakes are derived from the behavior of small earthquakes. Also, accurate characterization of small events is becoming increasingly important for ground motion models. However, catalog magnitudes may vary for the same event depending on network procedures and capabilities. In addition, different magnitude scales are often used for events of varying sizes. For example, moment magnitude (Mw) is the widely preferred estimate for earthquake size but it is often not available for small earthquakes (M < 3.5). As a result, statistical measures such as magnitude frequency distribution (MFD) and b-value can be biased depending on magnitude type and uncertainties that arise during the measurement process. In this research we demonstrate the capability of the relative magnitude method to provide a uniform and accurate estimate of earthquake magnitude in a variety of regions, while only requiring the use of waveform data. The study regions include the Permian Basin in Texas, central Oklahoma, and southern California. We present results in which only relative magnitudes are used to estimate MFD and b-value as well as relative magnitudes that are benchmarked to an absolute scale using a coda-envelope derived Mw calibration for small events. We also discuss potential sources of uncertainty in the relative magnitude method such as acceptable signal-to-noise ratios, cross-correlation thresholds, and choice of scaling constant, as well as our attempts to mitigate those uncertainties.