The elastic wave equation with the seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with sources on the plane surface of a half-space, which have the form of abrupt walls with a long tail, propagating in the interior and on the surface of the half-space. These secondary waves are associated to the seismic mainshock. The results, previously reported, are re-derived by using Fourier transformations and specific regularization procedures. The relevance of this seismic motion for the ground motion, the seismographs' recordings and the effect of the inhomogeneities in the medium are discussed.

The paper highlights the performance of the seismic isolation devices, installed on retrofitted buildings in reducing the seismic response when subjected to earthquakes. Two buildings from the beginning of the XX-th century in Bucharest are chosen from many more, monitored over the city area. We discuss the response of these base-seismic isolated structures, relying on good quality data acquired from the recent strong earthquake (03.11.2022, MW = 5.0). Elastic response spectra computed from recordings at two levels of each structure are used, placed under and right above the isolating layer. At one building the existence of previous recordings and the particularity of the sensors allow a comparison with other two relatively recent medium intensity earthquakes. The assessment is carried out in terms of maximum acceleration amax, measured at certain levels in each structure, spectral acceleration amplitude SAmax and spectral-peak corresponding period. We find that the base-isolation methodology is effective in reducing the response of the building right above the isolating layer, an observation valid for both structures, all components of the recordings, and spectral acceleration values. Moreover, the outcomes from the modal evaluation performed prior to rehabilitation and seismic isolation process are presented, by pointing out a higher newly acquired fundamental period of the isolated structures.