Magnitude-Recurrence Relationship and its Effect on Uniform Hazard Spectra: A Current Assessment

Gutenberg and Richter showed that magnitude-recurrence relationship may be represented by a linear relationship when the log of annual rate of exceedance was plotted against magnitude. This type of recurrence model has been in use because of its simplicity and because it fits the data reasonably well over a useful range of magnitudes of engineering interest. A quadratic log frequency relationship between magnitude and the mean annual rate has been proposed by others and shown to fit the available data well in the high magnitude range of the magnitude-recurrence relationship. UHS (Uniform Hazard Spectra) using a quadratic log frequency and the linear relationship, has been developed and compared. It is shown that using a linear relationship would result in a more conservative design when defining UHS for ductility level earthquakes (DLE) (return periods > 5,000 years). However, UHS for strength level earthquakes (SLE) (return periods <1000 years) are not affected greatly by the use of a linear relationship.