To better characterize seismic hazard, particularly, for induced seismicity, there is an increasing interest in methods to estimate moment magnitude (⁠Mw⁠) for small earthquakes. Mw is generally preferred over other magnitude types, but, it is difficult to estimate Mw for earthquakes with local magnitude (⁠ML⁠) <3–3.5⁠, using conventional moment tensor (MT) inversion. The 2020 Mww 5.7 Magna, Utah, seismic sequence provides an opportunity to illustrate and evaluate the value of spectral methods for this purpose. Starting with a high‐quality seismic catalog of 2103 earthquakes (⁠ML<5.6⁠), we estimate Mw using two independent spectral methods—one based on direct waves, yielding Mw,direct⁠, and the other based on coda waves, yielding Mw,coda⁠. For the direct‐wave method, we present a non‐parametric (NP) inversion scheme that solves for apparent geometrical spreading, G(R), and site effects (S), similar to other NP procedures that have been used to calibrate regional ML scales. The NP inversion is constrained using Mws derived from MTs for nine events in the Magna sequence. We recover statistically robust and physically reasonable G(R) and S and compute Mw,direct for 635 Magna earthquakes down to ML 0.7. For the coda‐wave method, we consider two separate calibration schemes involving previous MT solutions and compute Mw,coda for 311 earthquakes down to ML 1.0. For 280 of the events that were processed with both methods—Mw,direct and Mw,coda—are strongly correlated (r = 0.98), with a mean difference of only 0.05. We compare Mw,direct and Mw,coda with ML and find reasonably good agreement for ML<3.6 with the theoretically predicted relationship of Mw=(2/3)ML+C⁠, in which C is a regional constant. Our results imply that seismic network operators can use spectral‐based Mw estimates to replace ML estimates for events with ML≥1.0⁠, and possibly smaller. The main requirement is the existence of a small number of MT solutions for calibration purposes.

中文翻译：

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对小地震的Mw进行稳健而常规的确定：在2020 Mw 5.7 Magna（犹他州）地震序列中的应用

为了更好地表征地震危险性，特别是对于诱发地震活动，人们越来越希望对小地震的矩量值（Mw⁠）进行估算。一般而言，Mw比其他震级类型更可取，但是，使用传统的矩张量（MT）反演很难估计局部震级（？ML⁠）<3-3.5？的地震的Mw。2020年Mww 5.7犹他州麦格纳的地震序列为说明和评估频谱方法的价值提供了机会。从2103地震的高质量地震目录开始（⁠ML<5.6⁠），我们使用两种独立的频谱方法估算Mw：一种基于直接波，产生Mw，直接，另一种基于尾波，产生Mw。 ，尾声。对于直接波法，我们提出了一种非参数（NP）反演方案，该方案可解决表观几何扩展，G（R）和位点效应（S），类似于已用于校准区域ML比例的其他NP程序。使用麦格纳序列中9个事件的，来自MT的Mws来限制NP反转。我们恢复了统计上健壮且物理上合理的G（R）和S，并计算了635级至ML 0.7级的Magna地震的直接Mw。对于尾波法，我们考虑了涉及先前MT解决方案的两个单独的校准方案，并针对ML 1.0以下的311次地震计算了Mw，coda。对于这两种方法处理的280个事件-Mw，直接和Mw，尾气-高度相关（r = 0.98），平均差异仅为0.05。我们将Mw，direct和Mw，coda与ML进行了比较，发现ML <3具有相当好的一致性。具有理论预测关系Mw =（2/3）ML +C⁠的图6，其中C是区域常数。我们的结果表明，地震网络运营商可以使用基于频谱的Mw估计值来代替ML≥1.0？甚至可能更小的事件的ML估计值。主要要求是存在少量用于校准的MT解决方案。