Abstract: A source spectrum model for stochastic synthesis of strong ground motion is introduced in order to eliminate the dependence of the motion on the size of sub-source. In the model, the domination of asperity on high-frequency motion is emphasized. The corner frequency is related with the slip of sub-source and decreases with the rupturing, i.e., number of ruptured sun-sources. Furthermore, an approach is presented to add a scaling factor into the source spectrum model to counterbalance the energy loss from the change of source spectrum parameters with the spreading of rupture area. By means of this approach, an obvious decrease of variation of the total radiated energy at far field is demonstrated by a case study .