Conditional Simulation of Spatially Varying Multicomponent Nonstationary Ground Motions: Bias and Ill Condition

The application of the spectral representation method to the conditional simulation of ground motions can break down because of nonconvergence in inverting the conditioning covariance matrix, and the time-averaged power spectral density (PSD) functions of simulated records can deviate significantly from the target PSD functions. These two issues are discussed and explained. A procedure is proposed to overcome the two observed drawbacks. Its application can result in a close approximation of the means of the PSD functions of the conditionally simulated nonstationary ground motions to those estimated from observed ground motions. The close approximation becomes equality if the stationary processes are considered.