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A large proportion of the land mass of the world is classified as Stable Continental Regions, these are generally regions where the seismic activity is low. Consequently there is little instrumentally recorded strong-motion data available from which to build robust models for seismic hazard evaluation for these regions. Recourse is therefore made to using spatial events as a surrogate for temporal events, on the assumption that the regions selected spatially have similar tectonic characteristics. Even this approach requires the addition to the database of historic events, these are events that have been recorded pre-instrumentally using macroseismic intensity records as the basis. This leads to a key objective of the analysis of historic seismic data is the determination of a relationship between an events macroseismic intensity records and its magnitude through regression analysis of a large set of known data. An important part of regression analysis for this type of data is the development of a functional form that matches the nature of the data and models the physical processes that gives rise to it. The equations which are considered and compared in this paper are those of Frankel, Johnston, Ambraseys, Murphy and O’Brien and Kövesligethy. In addition, to explain how these equations relate to the physical process, Frankel’s equation is compared with the equation from Boore’s Stochastic Method. The paper then compares, in detail, the magnitude-intensity relationships developed by Johnston and Ambraseys, the interest focusing on the different regression techniques used. This is followed by an exploration of the merits of each approach with the analysis using Johnston’s global dataset of Stable Continental Region events. The discussion between these models provides the basis for the development of a typical value for the attenuation quality factor Q for Stable Continental Regions in the frequency range 1 to 5 Hz. Together the findings in this paper provide the opportunity for developing ground motion prediction equations from a mixed macroseismic and instrumented approach. It also provides a means to further improve the knowledge of macroseismic data and notes potential uncertainties in the values of the derived magnitudes.

AN ANALYSIS OF METHODS FOR DERIVING MAGNITUDES OF HISTORIC EARTHQUAKES THAT ARE BASED ON PHYSICAL PRINCIPLES