Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.