Seismic response to a prescribed seismogram of a body embedded in a multilayered half space

While the actual problem is composed of an active fault surface, a soil site and a body embedded at that site; the proposed method provides an alternative smaller linear problem by replacing the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. The Green's function for each of three fundamental problems of isotropic elastic and viscoelastic spaces undergoing harmonic vibration is derived. Infinite elements are adopted in the far field, and finite elements in the near field. The three fundamental problem solutions are used as the shape functions of infinite element nodal lines. The three concentrated orthogonal force components at the focal point are determined in such a way that the Fourier transforms of the three orthogonal acceleration components measured at a seismograph station are checked. For seismic analysis of a finite embedded body, consider the differential between the actual system and the seismic free field, which is the embedding half space without any embedment and being excited by the fictitious focal point forces. All along the analysis has been carried out in the frequency domain. An appropriate inverse Fourier transform algorithm will properly yield all results as time functions.