A new local magnitude ML scale has been developed for Norway, based on a regression analysis of synthesized Wood-Anderson records. The scale is applicable for distances up to more than 1000 km, and the data used comprise 741 short-period recordings at 21 seismic stations from 195 earthquakes in the magnitude range 1 to 5 occurring in and around Norway over the last 20 years. Magnitude corrections for distance have been evaluated in terms of a geometrical spreading term a and an anelastic attenuation term b, and the significant regional crustal differences in the area under investigation made it desirable to develop these for several subsets of the data base. The results for a are generally found to be around the commonly found value of 1.0 (using the Lg phase), while the values of b are found to be around 0.0008, consistent with the weak, intraplate attenuation expected for Norway. Compared to interplate California, this difference in attenuation represents more than a factor of ten in amplitude at a distance of 1000 km.

New ML scales are commonly tied to Richter's original definition at the standard reference hypocentral distance of 100 km. The significantly weaker Lg wave attenuation in Norway, however, requires a smaller reference distance. We have chosen a value of 60 km, based on an overall assessment of regional coverage, focal depths, and quality of the data. The resulting ML formula for Norway reads 
where Awa is synthesized Wood-Anderson amplitude (in mm), R is hypocentral distance (in km), and S is a station correction term that for all 21 stations is found to lie within the range ± 0.22. When using the entire data base, the spreading term a equals 1.02 (± 0.09), and the anelastic attenuation term b equals 0.00080 (± 0.00009). When only strictly continental ray paths are selected, the a value decreases to 0.91 (± 0.11) while the value of b increases to 0.00087 (± 0.00011), a difference which on the average accounts for less than 0.1 magnitude units. While all values used in the regressions have been derived for vertical amplitudes, a separate analysis has shown that these are not significantly different from the horizontal ones, and the new scale is therefore applicable to both. In order to facilitate the practical use of this new ML scale, a relation has also been established between observed seismogram amplitudes in nanometers (corrected for instrument response) and the synthesized Wood-Anderson amplitudes. This relation reads log Awa = 0.925 log Aobs − 2.32.

The new ML magnitudes for the events analyzed are in good agreement with those calculated from a previously used relation developed by Båth for Sweden. The ML values have also regressively been related to a data set of Ms magnitudes, yielding the relation Ms = 0.83 ML + 1.09.

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