Abstract: In this paper, we investigate the attenuation of maximum amplitude of S-waves of near earthquakes with epieentral distance and the damping of coda waves of near earthquakes with time in the Beijing-Tianjin and Sichuan-Yunnan regions. These attenuation features indicate an apparent difference in crustal media between these two regions. It is suggested that respective calibrating functions R(A), should be used in estimating near earthquake magnitudes. Some other aspects of magnitude determination for near earthquakes are also discussed.