Abstract

A careful analysis of the concepts of earthquake intensity (I) and magnitude (M) shows that no straight line (obtained, for example, by fitting a catalog of observed {I, M} pairs) can adequately represent the intensity-magnitude relationship throughout the whole range of (theoretically) possible values. The remedy is straight-forward: fit the data (M versus I) with a nonlinear function (precisely, the inverse of a sigmoid curve) instead of a straight line.

This recipe has been applied to two data sets (from California and Italy) with satisfactory results, which are compared with those obtained from a sigmoid (I versus M) and from three alternative linear regression methods (I versus M, M versus I, and orthogonal regression line). It appears that this method works well not only for interpolation purposes but also for extrapolation; hence, it should be of interest to seismic engineering for exploring extreme, unprecedented scenarios.

Moreover, the abundance and statistical dispersion of middle-range observed data is an independent source of error as far as magnitudes corresponding to high-intensity events are to be estimated. This can be obviated by averaging, before fitting, the magnitude data that correspond to the same intensity. However, this procedure affects more the straight lines than the inverse sigmoid curve (M versus I), which shows great robustness.

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