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Bias in surface-wave magnitude M_s due to inadequate distance corrections

Department of Geology and Geophysics University of Edinburgh Grant Institute, West Mains Road, Edinburgh EH9 3JW, United Kingdom

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 M_s 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

In the second, we make allowance for the theoretically known contribution of dispersion and geometrical spreading, to obtain

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^t_s shows less scatter against log M₀ than does M_s calculated using the Prague formula.

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