Magnitude of Earthquake Research Institute (ERI), University of Tokyo, ME, is determined using an empirical equation of Watanabe (1971). Based on the omega-square source model, constant stress drop scaling, constant Q, and instrumental response, we calculated a typical waveform for each event with a given seismic moment and MW to estimate its ME. This leads to theoretical relationships, which show 1)saturation for MW>6, 2)overestimation of ME for 3<MW<5, and 3) underestimation of ME for MW<2. Under MW 2, ME scales with 1.5MW, which may affect the estimation of b-value of the Gutenberg and Richter equation. Catalogue values of ME and MW for small and medium events show the predicted trend
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