Won-Young Kim
The M _L scale in eastern North America
Bulletin of the Seismological Society of America (August 1998), 88(4):935-951

Abstract:
An attenuation curve for the local magnitude scale, M _L , of eastern North American (ENA) earthquakes was empirically determined using synthetic Wood-Anderson seismograms derived from newly available broadband recordings from the U.S. National Seismographic Network (USNSN) and from additional stations of comparable quality. Wood-Anderson peak amplitudes measured on approximately 210 three-component, broadband digital records from 38 earthquakes in the distance range of 50 to 800 km were inverted for the attenuation curve and magnitude of each event. The earthquakes ranged from M _L = 2.2 to 4.6 and were recorded at about 20 stations in the region. Separate attenuation curves were determined for the N-S, E-W, and vertical components, as well as for the mean of the two horizontal components. All curves had similar slopes indicating that M _L can be determined from any one of the three components available. The Wood-Anderson peak amplitude phases were predominantly Lg waves arriving with a mean group velocity of 3.40+ or -0.23 km/sec and a mean period of 0.50+ or -0.26 sec. M _L for earthquakes in ENA can be obtained from the horizontal-component Wood-Anderson peak amplitude in millimeters, A(Delta ), using the formula M _L = log ₁₀ A(Delta ) (in mm)+1.55 log ₁₀ Delta (in km)-0.22+C, for distances 100 to 800 km and 2.2< or =M _L < or =4.6 and where C = station magnitude correction. The M _L is tied to Richter's (1935) M _L scale for southern California. A similar formula is given to determine M _L from the vertical-component synthetic Wood-Anderson seismograms. M _L is related to Nuttli's m _b (Lg) by M _L = 0.976 m _b (Lg)-0.05 for earthquakes with 2.2< or =M _L < or =4.6 in ENA. Analysis of six additional large earthquakes with M _L > or =5 indicates that M _L nearly equal m _b (Lg)-0.15 in a wide magnitude range of 2< or =M _L < or =6.5 in ENA.