Summary.

About a quarter of the local earthquakes recorded at Boulder City are from focal distances of five miles or less, and approximately another quarter are from distances between five and ten miles. As these earthquakes are so close to the Lake Mead stations, they are studied in somewhat different fashion from those which are so far away that focal depth of ten miles becomes negligible. It has been possible with a new formula to make an extrapolation of the Gutenberg-Richter Magnitude Scale down to one mile focal distance. With this extended scale the magnitudes of more than 1,000 local earthquakes are collected into frequency distribution tables and frequency polygons for the years 1941–1942. These tables show increase of efficiency or locating power of the Lake Mead seismograph system with better coverage and decrease of distance between stations when a fourth station is added. They show the increase of efficiency with an increase of instrumental magnification. The mode or the magnitude of the most frequently located shocks dropped from magnitude 3.0 in early 1941 to magnitude 2.5 when distances were cut between stations and probable epicenters by the station added at Boulder Dam. The magnitude dropped to 2.0 in the last half of 1942 after Benioff seismographs were placed in operation at the three other stations.

More than half the total local energy released annually is in the largest shock or group of shocks of maximum magnitude. The energy released in 1942 by local earthquakes is approximately equal to that released in 1941. The magnitude and perceptibility range of small shocks appears to be a linear function at local distances. Under exceptional circumstances, very small shocks are felt, apparently following the equation  
Δ=6M2
where M is the magnitude and Δ the distance in miles. More generally, there is an equal chance that an earthquake will be felt and reported if the following equation is used:  
Δ=8M11
This holds for local shocks of less than destructive magnitude. To extend approximately to earthquakes of large magnitude the following equation is derived:  
logΔ=0.5+0.25M1/M

This is for earthquakes of shallow focus.

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