Spectral analysis of the rotational component of seismic ground motion

An algorithm for the spectrum of the rotational component of surface ground motion during earthquake is derived. To obtain the rotation the total motion is decomposed into the wave components. Then the rotational motion is obtained in terms of the horizontal and vertical components treated as non-stationary random processes. The evolutionary spectrum of the rotational acceleration is a function of respective translational spectra, their co-spectrum and respective wave parameters. The analysis shows a shift of the higher frequency components in the rotational spectrum. The rotation is a function of the time derivative of translational components.