The magnitude, MJMA, estimated by the Japan Meteorological Agency (JMA) is generally referred to in Japan for the regional seismicity in the area. MJMA is determined from maximum displacement amplitudes of the total seismic wave traces. For earthquakes shallower than 60 km, MJMA is determined by Tsuboi's formula, and for earthquakes deeper than 60 km, by Katsumata's formula. These relations were designed to give almost the same magnitude value as that of Gutenberg and Richter. We compared MJMA with moment magnitude, MW, which can be calculated from the centroid moment tensor (CMT) solutions. It was found that the average difference between MJMA and MW is not significant for shallow earthquakes in the magnitude range from 5 to 7, but it is significant at a low level for the earthquakes of deeper foci. The averaged difference reaches about 0.4 magnitude units for the focal depth of 600 km. We derived an attenuation function for the maximum displacement amplitude assuming the validity of the moment magnitude. This relation between epicentral distance and amplitude for shallow earthquakes is almost identical to the one calculated from Tsuboi's formula. It is suggested that the estimated attenuation function for deep-focus earthquakes reflects the specific Q and velocity structure that is peculiar to the subduction zone.