An empirical scaling law that relates local magnitude (ML), epicentral distance (Δ), and strong horizontal ground-motion accelerations (Acc) was derived from the strong-motion accelerograms of Western U.S. earthquakes, in conjunction with the available local magnitude as determined by the seismological laboratories at Pasadena and Berkeley, and with those ML values determined by Kanamori and Jennings and by Espinosa. This law provides the basis for determining ML directly from accelerograms recorded at near and intermediate epicentral distances from earthquakes having local magnitudes in the 4.0 to 7.5 range. The empirical relations are given by
The values of ML determined from these relations are in excellent agreement with those values determined by other empirical techniques (Kanamori and Jennings, 1978; Espinosa, 1979). The Imperial Valley earthquake of October 15, 1979, with an ML = 6.6 (PAS), compares well with an ML = 6.66 ± 0.26 determined in this study. The procedure developed here is applied to the most significant earthquakes in the Western United States. The characteristics of the acceleration attenuation curves in the Western U.S. were compared with those for the Central United States and found to differ appreciably. The absorption coefficient for short-period waves is σ = 0.0278/km in the 10 ≦ Δ ≦ 60 km range, and σ = 0.0512/km in the 60 ≦ Δ ≦ 300 km range in Western United States. The procedure developed in this study allows the evaluation of ML directly from the accelerograms of moderate and larger earthquakes recorded at short epicentral distances. It also allows a rapid computation of the expected level of strong ground motions for distances greater than 10 km for a given size earthquake.