An Improved Planar Wavefront Model To Estimate Rocking Seismic Motion Spectra Using Translational Spectra At A Single Station

It is convenient to synthesize the Fourier spectra of the rocking ground motions at a station from the recorded translational motions at the same station. The conventional models in this approach assume (1) the seismic source to be a point source, (2) the medium to be a horizontally stratified elastic half-space, and (3) the translational motions to be caused primarily by the planar wavefronts of the body waves. An improved 'planar wavefront' model is proposed under this approach such that (1) the model applies also to near the epicenter, with the hypocentral distance of the station assumed to be much larger than the wavelengths of the incident waves, (2) the information on the underlying focal mechanism is accounted for, and (3) both in-plane and out-of-plane rocking spectra can be estimated. The proposed model assumes the material properties of the stratified medium to vary smoothly with depth. Further, it considers the spatial variations of both the amplitudes and the incidence angles of the incoming waves. The spatial variation of the amplitudes is formulated by considering the physics of (1) the radiation of body waves emitted by a kinematic shear dislocation point source and (2) the propagation of those waves through the stratified medium. A numerical study shows that the proposed model leads to more accurate rocking spectra over a large range of fault parameters and frequencies. Further, a few example nearepicenter records of translational ground motions illustrate the disparities between the time-domain estimates of the proposed model with those of the conventional models as well as between the responses of simple structures subjected to the two sets of motions.