The standard assumption of modelling the vertical component by vertically propagating P waves underestimates the spatial variability of the vertical ground motion over the dimension of the foundation of large structures, which can lead to very large vertical floor spectra at high frequencies. Modelling the vertical ground motion as inclined P-SV waves and including stochastic variability to the velocity structure for the Soil-Structure Interaction (SSI) analysis adds complexity to the vertical wave field, but it is not enough to match the complexity in observed vertical ground motions as measured by the spatial coherency from dense seismic arrays. The coherency between two stations is controlled by the standard deviation of the phase differences between the seismograms at the two stations. The complexity in the input motions can be increased by adding separation-distance-dependent and frequency-dependent variability of the phase angles to the phase of the input motions so that the empirical coherency is recovered. The additional phase variability is added to the seismogram over multiple short time windows to maintain the nonstationary characteristics of the input motion. This allows the physics-based P-SV wave propagation to be combined with empirical adjustments on the input motion to both preserves the deterministic wave propagation features of the SSI as well as being consistent with the empirical coherency models for the vertical component. The result is greater spatial variability in the motions at the foundation of the structure which should reduce the overestimation of the vertical floor spectra at high frequencies.

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