The paper by Thomas C. Hanks and Hiroo Kanamori introduces a moment magnitude scale, denoted as \(\mathbf{M}\), defined by the equation \(\mathbf{M} = \log M_{s} - 10.7\). This scale is uniformly valid for seismic moment \(M_{s}\) ranging from 3 to 7.5, magnitude \(M_{L}\) from 3 to 7, and magnitude \(M_{w}\) from 5 to 7. The authors explain that the widely used earthquake magnitude scales, such as \(M_{L}\), \(M_{s}\), and \(m_{b}\), are theoretically unbounded but are limited in practice due to the finite bandwidth of instrumentation. They demonstrate that these scales saturate at large magnitudes, similar to peak acceleration data at a fixed distance. Hanks and Kanamori propose a new magnitude scale based on the estimated radiated energy \(E_{s}\), which is derived from the earthquake stress drop \(\Delta \sigma\) and the shear modulus \(\mu\). This scale, denoted as \(M_{w}\), is shown to be similar to \(M_{s}\) for earthquakes with \(M_{s} \leq 8\). The moment magnitude scale \(\mathbf{M}\) is derived from the empirical relations between \(M_{s}\), \(M_{w}\), and \(M_{L}\), and it is found to be uniformly valid across a wide range of magnitudes. The paper includes tables presenting seismic moments and magnitudes for significant earthquakes in Southern California and historical large earthquakes in California. The results show good agreement between \(M_{s}\), \(M_{w}\), and \(\mathbf{M}\) for most earthquakes, with some deviations attributed to variable stress drop or saturation of the magnitude scales. The authors also discuss the implications of these findings for understanding the upper limits of seismic moment and the physical characteristics of major earthquakes in California.The paper by Thomas C. Hanks and Hiroo Kanamori introduces a moment magnitude scale, denoted as \(\mathbf{M}\), defined by the equation \(\mathbf{M} = \log M_{s} - 10.7\). This scale is uniformly valid for seismic moment \(M_{s}\) ranging from 3 to 7.5, magnitude \(M_{L}\) from 3 to 7, and magnitude \(M_{w}\) from 5 to 7. The authors explain that the widely used earthquake magnitude scales, such as \(M_{L}\), \(M_{s}\), and \(m_{b}\), are theoretically unbounded but are limited in practice due to the finite bandwidth of instrumentation. They demonstrate that these scales saturate at large magnitudes, similar to peak acceleration data at a fixed distance. Hanks and Kanamori propose a new magnitude scale based on the estimated radiated energy \(E_{s}\), which is derived from the earthquake stress drop \(\Delta \sigma\) and the shear modulus \(\mu\). This scale, denoted as \(M_{w}\), is shown to be similar to \(M_{s}\) for earthquakes with \(M_{s} \leq 8\). The moment magnitude scale \(\mathbf{M}\) is derived from the empirical relations between \(M_{s}\), \(M_{w}\), and \(M_{L}\), and it is found to be uniformly valid across a wide range of magnitudes. The paper includes tables presenting seismic moments and magnitudes for significant earthquakes in Southern California and historical large earthquakes in California. The results show good agreement between \(M_{s}\), \(M_{w}\), and \(\mathbf{M}\) for most earthquakes, with some deviations attributed to variable stress drop or saturation of the magnitude scales. The authors also discuss the implications of these findings for understanding the upper limits of seismic moment and the physical characteristics of major earthquakes in California.