SUMMARY MAGNITUDE (M)
[c6, p178]

To construct a single, summary-magnitude scale, M, to characterize the relative size of all the events listed in Table 6.1, I use each of the scales described above, being careful to consider such factors as the historical period and event location, as well as the quality of individual determinations. Where choices between several magnitude estimates are possible, the summary magnitude, M, 15 weighted toward long-period estimates of magnitude. Specifically, Ms and MG-R are selected when judged reliable (110 events). Many local magnitudes have thus been superseded by surface-wave magnitudes; this effect is most noticeable for the largest events, where saturation of ML becomes important. ML is the principal contributor to 20 summary magnitudes, half of which also have reported M values that agree well. For all but two events before 1898 (1857 and 1872) and for two 20th-century events, M is based on MI. In effect, the summary magnitude is an intensity magnitude before 1898 and a teleseismic surface-wave magnitude thereafter.

If M is to be uniformly validity across the entire timespan of the catalog, MI must be an unbiased estimator of Ms or MG-R. To test this absence of bias, the correlation between MI and the two surface-wave magnitudes has been examined for 23 events with reliable Ms or MG-R estimates, and an MI value determined from the isoseismal maps of Toppozada and others (1981) and Toppozada and Parke (1982). This comparison shows that although the two magnitude scales are well correlated, MI systematically underestimates Ms and MG-R by 0.3 +/- 0.3 units. If the sample is restricted to Ms=<6.5 (n=18), the bias is 0.2 +/ 0.3 units. To further investigate this apparent bias, ML was compared with MI for 10 common events, for which the bias was 0.25 +/- 0.2 units. As a final check, the difference between Ms or MG-R and MI for the 12 events listed in Table 6.1 also used by Toppozada (1975) to develop MI relations was found to be 0.10 +/- 0.19 units.

On the basis of these results, the summary magnitudes from MI values of Toppozada and others (1981) have been adjusted upward by 0.15 units and then rounded to the nearest quarter magnitude unit. Thus, events of MI=5.7 become M=5-3/4, and those of MI=5.8 become M=6. No magnitude adjustment exceeded a quarter unit. MI values from other sources have simply been rounded to the nearest quarter unit, because they average 0.2 units higher than the values of Toppozada and others (1981) and Toppozada and Parke (1982), where comparisons can be made. Summary magnitudes for events before 1850 have not been adjusted upward, owing to the imprecision of the original estimates.