Abstract:With considering the earthquake motion as a stochastic process,based on the basic principles of dynamical analysis by using finite element method,formulas for the back-evaluating stochastic seismic characteristics of the bedrock from the stochastic seismic characteristics of the ground surface are derived by using the impulse-response function,the theories of random vibration,and the principles of Fourier transform. A method of finite element back analysis for this purpose is put forward. By using this method,the stochastic seismic characteristics of the bedrock could be calculated from the stochastic seismic characteristics of the ground surface. A numerical example shows that the ground changes the frequency composition of earthquake motion and has an obviously amplifying effect on seismic motion of the bedrock. The seismic motion of the bedrock should be input to earthquake motion during the analysis of earthquake resistance of underground structures.