Introduction

Preinstrumental information on earthquakes is important in seismicity studies of New Mexico because it covers a time period, 1849 through 1961, which is three times as great as the period of instrumental recording. Prior to 1962, the strengths of earthquakes were expressed in terms of maximum earthquake intensity, Io; a quantity assigned on the basis of what people observe during an earthquake, damage to structures, etc. The scale used to rank intensities in the United States is the Modified Mercalli-1931 (Richter, 1958). Merging of preinstrumental and instrumental data requires conversion of the maximum reported intensities to magnitudes. Gutenberg and Richter (1956) derived the empirical relation

M = 1 + 2/3 Io. (1)

Because this relation is based exclusively on data from California, it cannot be used on New Mexico earthquakes without confirming its applicability.

Data

In October, 1987, I was able to find 24 New Mexico earthquakes with both intensity and magnitude estimates (data from National Geophysical Data Center). Table 1 summaries intensity and magnitude data for the 24 events. Four average magnitudes were calculated for the earthquakes with reported maximum intensities of IV, V, VI and VII. The standard deviations on these average magnitudes are quite large inasmuch as reported maximum intensity can be dependent on factors such as distance to the epicenter, depth of focus, crustal Q, type of ground, and fault mechanism. However, note that the average magnitudes are consistently lower than estimates based on the Gutenberg-Richter relation. For example, equation (1) yields a magnitude of 5.0 for an Io of VI, whereas the observed average magnitude for that intensity in New Mexico is 4.2. A linear regression on the magnitude/intensity data pairs in Table 1 yields

M = 0.51 + 0.67 Io, (2)

which is considerably different from the Gutenberg-Richter relation.

List below are possible explanations for the significant difference between the New Mexico and California based magnitude-maximum intensity empirical equations:

1. Crustal Q is higher in New Mexico than California. In New Mexico seismic waves from an earthquake are less attenuated in the crust and therefore produce stronger ground motions at the epicenter than in California.

2. The majority of earthquakes in New Mexico have normal fault mechanisms whereas the majority in California have strike-slip mechanisms. For earthquakes of equal strength and depth, the radiation pattern for a normal fault will produce stronger ground motion at the epicenter than a strike-slip fault.

3. Focal depths are shallower on average in New Mexico than California which produces higher intensities on average for New Mexico earthquakes.

An observation of some interest is that the coefficient of the Io term is the same for the California and New Mexico relations, equation (1) and (2). The agreement is fortuitous because the uncertainties in this term are large for both cases. The California relation is probably somewhat better constrained than the New Mexico relation because Gutenberg and Richter used about twice as many data pairs as were available for the New Mexico analysis. However, the spread in magnitudes for specific reported Io values is approximately the same for both data sets.

Summary

Magnitude and maximum intensities for 24 New Mexico earthquakes produced an empirical equation between these two quantities which is significantly different than the Gutenberg-Richter California based relation. Possible explanations for the observed difference are (1) higher crustal Q in New Mexico, (2) dominantly normal fault mechanisms in New Mexico versus strike-slip fault mechanisms in California, and (3) shallower focal depths on average in New Mexico.

My analysis clearly indicates that the use of the Gutenberg-Richter relation to convert observed New Mexico maximum intensities to magnitudes leads to over estimations on the order of 1/2 magnitude unit. The adoption of the relation obtained in this study is recommended in order not to overstate the hazard on the basis of the preinstrumental data for earthquakes in New Mexico.

References

Gutenberg, B. And C.F. Richter (1956) Earthquake magnitude, intensity, energy and acceleration, Bull. Seismol. Soc. Am., 46, 105-145.

Richter, C.F. (1958) Elementary Seismology, W.H. Freeman and Co., San Francisco, 768 p.

Table 1. Maximum Intensity and Average Magniutde for 24 New Mexico Earthquakes

Maximum Intensity Modified Mercalli	Number of Earthquakes	Average Magnitude	Standard Deviation
IV	9	3.49	0.84
V	8	3.56	0.59
VI	6	4.22	0.50
VII	1	5.5

Note: Data are from a listing of earthquakes obtained from the National Geophysical Data Center for the time period 1962-1982.