Measurements (9,941) of peak amplitudes on Wood-Anderson instruments (or simulated Wood-Anderson instruments) in the Southern California Seismographic Network for 972 earthquakes, primarily located in southern California, were studied with the aim of determining a new distance correction curve for use in determining the local magnitude, ML. Events in the Mammoth Lakes area were found to give an unusual attenuation pattern and were excluded from the analysis, as were readings from any one earthquake at distances beyond the first occurrence of amplitudes less than 0.3 mm. The remaining 7,355 amplitudes from 814 earthquakes yielded the following equation for ML distance correction, log A0
where r is hypocentral distance in kilometers. A new set of station corrections was also determined from the analysis. The standard deviation of the ML residuals obtained by using this curve and the station corrections was 0.21. The data used to derive the equation came from earthquakes with hypocentral distances ranging from about 10 to 700 km and focal depths down to 20 km (with most depths less than 10 km). The log A0 values from this equation are similar to the standard values listed in Richter (1958) for 50 < r < 200 km (in accordance with the definition of ML, the log A0 value for r = 100 km was constrained to equal his value). The Wood-Anderson amplitudes decay less rapidly, however, than implied by Richter's correction. Because of this, the routinely determined magnitudes have been too low for nearby stations (r < 50 km) and too high for distant stations (r > 200 km). The effect at close distances is consistent with that found in several other studies, and is simply due to a difference in the observed ≈ 1/r geometrical spreading for body waves and the 1/r2 spreading assumed by Gutenberg and Richter in the construction of the log A0 table.
ML's computed from our curve and those reported in the Caltech catalog show a systematic dependence on magnitude: small earthquakes have larger magnitudes than in the catalog and large earthquakes have smaller magnitudes (by as much as 0.6 units). To a large extent, these systematic differences are due to the nonuniform distribution of data in magnitude-distance space (small earthquakes are preferentially recorded at close distances relative to large earthquakes). For large earthquakes, however, the difference in the two magnitudes is not solely due to the new correction for attenuation; magnitudes computed using Richter's log A0 curve are also low relative to the catalog values. The differences in that case may be due to subjective judgment on the part of those determining the catalog magnitudes, the use of data other than the Caltech Wood-Anderson seismographs, the use of different station corrections, or the use of teleseismic magnitude determinations. Whatever their cause, the departures at large magnitude may explain a 1.0:0.7 proportionality found by Luco (1982) between ML's determined from real Wood-Anderson records and those from records synthesized from strong-motion instruments. If it were not for the biases in reported magnitudes, Luco's finding would imply a magnitude-dependent shape in the attenuation curves. We studied residuals in three magnitude classes (2.0 < ML ≦ 3.5, 3.5 < ML ≦ 5.5, and 5.5 < ML ≦ 7.0) and found no support for such a magnitude dependence.
Based on our results, we propose that local magnitude scales be defined such that ML = 3 correspond to 10 mm of motion on a Wood-Anderson instrument at 17 km hypocentral distance, rather than 1 mm of motion at 100 km. This is consistent with the original definition of magnitude in southern California and will allow more meaningful comparison of earthquakes in regions having very different attenuation of waves within the first 100 km.