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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. 

Abstract The magnitude‐frequency distribution (MFD) describes the relative proportion of earthquake magnitudes and provides vital information for seismic hazard assessment. Theb‐value, derived from the MFD, is commonly used to estimate the probability that a future earthquake will exceed a specified magnitude threshold. Improved MFD andb‐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 recalculate the magnitudes of 8,775 events for the 2011 Prague, Oklahoma sequence using a relative magnitude approach that depends only on waveform data to calculate magnitudes. We also compare the distribution of successive magnitude differences to the MFD and show that a combination of the magnitude difference distribution (MDFD) and relative magnitudes yields a reliable estimate ofb‐value. Using the MDFD and relative magnitudes, we examine the temporal and spatial variations in theb‐value and show thatb‐value ranges between ∼0.6 and 0.85 during the aftershock sequence for at least 5 months after theM5.7 mainshock, though areas surrounding the northeast part of the sequence experience higherb‐values (0.7–0.85) than the southwestern part of the Meeker‐Prague fault whereb‐value is the lowest (0.6–0.7). We also identify a cluster of off‐fault events with the highestb‐values in the catalog (0.85). These new estimates of MFD andb‐value will contribute to understanding of the relations between induced and tectonic earthquake sequences and promote discussion regarding the use ofb‐value in induced seismic hazard estimation. 

The development and operation of Enhanced Geothermal Systems (EGS) can induce earthquakes during fluid injections, posing significant hazards for both local populations and the continued operation of EGS plants. An improved understanding of the interplay between the physical mechanisms affecting geothermal induced seismicity is important for current and future EGS projects. One way to analyze seismicity is with the b-value, which represents the slope of earthquake magnitude frequency distributions. Previous EGS studies suggest a pore-pressure driven induced seismicity model where spatially – the b-value is high near the injection point and temporally – the b-value decreases during later stages of injection. We evaluate the pore-pressure driven model by comparing the spatiotemporal b-value evolutions of nine different EGS induced seismicity scenarios including Basel and FORGE, along with injections from Soultzsous-Forêts and Cooper Basin. In our spatiotemporal analyses, we find that a majority of examined sequences have a period where the distal b-value is significantly higher than the b-value near the injection point. These sequences indicate that the pore-pressure driven model is inadequate for describing spatiotemporal b-value evolution, and that additional physical mechanisms, like aseismic slip, could have significant effects on EGS induced seismicity. Further characterization of the b-value in EGS induced seismicity sequences provides an opportunity to better constrain the degrees to which different physical mechanisms influence seismicity. 

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.