Synthesis of Spatially Correlated Earthquake Ground Motions Based on Hilbert Transform

A simplified method for synthesizing spatially correlated earthquake ground motions is developed based on Hilbert transform and a reference earthquake record. In this method, one reference earthquake record is treated as the original ground motion, based on a series of generated ground motions. This procedure uses the instantaneous amplitude and the instantaneous phase of the record obtained using Hilbert transform to achieve the nonstationarity of ground motion. To establish the coherency between generated ground motions, an incoherence model is employed to describe the relation between the instantaneous phase at the present station and the instantaneous phases at previous stations. This type of phase is defined as the instantaneous coherence phase. In addition, time lag is included in the instantaneous coherence phase to prescribe the wave passage effect. The proposed Hilbert-transform-based method is efficient and avoids cumbersome parameter estimations as well as other drawbacks involved in some traditional synthesizing methods. Applications of this method demonstrate that the generated ground motions are statistically analogous with the reference record.

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