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Tutorial on Surface Rotations from Wave Passage Effects: Stochastic Spectral Approach

Opole University of Technology, ul.Mikolajczyjka 5, 45-271 Opole, Poland z.zembaty{at}po.opole.pl www.zet.po.opole.pl

This article presents a concise review of the methods to obtain spectral densities of the rotational components of seismic ground motion from the spectral densities of both the translational components and wave propagation parameters. The rotational components are obtained by decomposing ground motion at the site into body and surface wave contributions with random amplitudes. To obtain rotation the resulting stochastic fields of body and surface waves are differentiated with respect to spatial coordinates. Assumption of plane waves radiating from a point source leads to two rotational components: rocking around a horizontal axis perpendicular to the source-site direction and torsion around a vertical axis. Construction of the rocking acceleration spectral density from P-, SV-, and Rayleigh-wave contributions as well as torsional spectral density from SH and Love waves (in terms of translational spectral densities and wave parameters) are discussed in detail. A short numerical analysis illustrates the proposed approach. A shift of the rotational spectra into higher frequencies compared to respective translational spectra is observed.

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