Abstract
We investigate bias in surface-wave magnitude using the complete ISC and NEIC datasets from 1978 to 1993. We conclude that although there are some small differences between the ISC and NEIC magnitudes, there is no major difference between these agencies for this presentation of the global dataset. The frequency-distance plot for reported surface-wave amplitude observations exhibits detailed structure of the body-wave amplitude-distance curve at all distances; the influence of the surface-wave amplitude decay with distance is much less apparent. This censoring via the body waves represents a large deficit in the number of potentially usable surface-wave amplitude observations, particularly in the P-wave shadow zone between
= 100° and
120°. We have obtained two new modified Ms
formulas based upon analysis of all ISC data between 1978 and 1993. In
the first, the conventional logarithmic dependence of the distance
correction is retained, and we obtain M
es = log(A/T)max + 1.155 log() + 4.269.
In the second, we make allowance for the theoretically known contribution of dispersion and geometrical spreading, to obtain
M
ts = log(A/T)max + 1/3 log() + 1/2 log(sin ) + 0.0046 + 5.370.
Comparison of these
formulas with other work confirms the inadequacy of the
distance-dependence term in the Gutenberg and Prague formulas, and we
show that our first formula, as well as that of Herak and Herak, gives
less bias at all epicentral distances to within the scatter of the
observed dataset. Our second formula provides an improved overall
distance correction, especially beyond = 145°. We show evidence that
Airy-phase distance decay predominates at shorter distances ( 
30°), but for greater distances, we are unable to resolve whether
this or non-Airy-phase decay predominates. Assuming 20-sec surface waves
with U = 3.6 km/sec, we obtain a globally averaged apparent
Q -1 of 0.00192 +/- 0.00026 (Q 
500). We argue that our second
formula not only improves the distance correction for surface-wave
magnitudes but also promotes the analysis of unexplained amplitude
anomalies by formally allowing for those contributions that are
theoretically predictable. We conclude that there remains systematic
bias in station magnitudes and that this includes the effects of source
depth, different path contributions, and differences in seismometer
response. For intermediate magnitudes, M ts
shows less scatter against log M0 than does
Ms calculated using the Prague formula.