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Non-stationary property in frequency content of horizontal ground motion vectors

The non-stationary properties of the strong ground motions are considered to have dominant influence on the dynamic response of structures. In this article, a new method is proposed to study the instantaneous frequency by constructing analytic signals with two orthogonal horizontal components of ground motion vectors directly. Comparing with the traditional method of constructing analytic signals based on Hilbert transforms, the new method is digestible and simple in calculation, and it can also avoid some associated limits of Hilbert transform. In this article, instantaneous frequency obtained from the new method is simulated with an exponential decay model, and its attenuation rules which can be used for synthesizing design ground motions are investigated. By comparing the attenuation rules between vector and unidirectional ground motions, the difference between new method and traditional method are investigated. The results show that the new method of constructing analytic signals is feasible, and the exponential decay model is effective to describe the change of instantaneous frequency with time.