Abstract: The various useful source-parameter relations between seismic moment and common use magnitude lg(M0)and Ms, ML, mb; between magnitudes Ms and ML,MS and wb, ML and mb; and between magnitude Ms and lg (L) (fault length), lg (W) (fault width), lg (S) (fault area),lg (D) (average dislocation); ML and Ig (fc) (corner frequency)have been derived from the scaling law which is based on an average two-dimensional faultingmodel of a rectengularfault. A set of source-parameters can be estimated from only one magnitude by using these relations. The average rupturevelocityofthe fault Vr = 2.65 km/s, the total time of rupture T(s) = 0.35 (s/km) L (km) and the average dislocation slip rate D (t) = 114m/s are also obtained.There are four strong points to measure earthquake size with the seismic moment magnitude Mw.(1)The seismic moment magnitude shows the strain and rupture size. It is the best seal for the measurement of earthquake size.(2)It is a quantity of absolute mechanics, and has clear physical meaning. Any size of earthquake can be measured. There is no saturation. It can be used to quantify both shallow and deep earthquakes on the basis of the waves radiated.(3)It can link up the previous magnitude scales.(4)It is a uniform scale of measurement of earthquake size. It is suitable for statistics covering a broad range of magnitudes. So the seismic moment magnitude is a promising magnitude worth popularization.