The Characteristics of Vibrations Produced by SH Type Torque in Multi-Layered Elastic Ground

Abstract

The vibrational characteristics of multi-layered elastic ground are theoretically investigated in the case of the stationary harmonic vibration of the surface of the ground. As the first step we treat the vibration generated by SH torque that emits the pure SH torque wave of axial symmetry with respect to the vertical axis. Integral expressions for the displacement fields are derived by using a technique applied first by N. A. Haskell to seismological problems. These expressions are transformed to complex integrals on the complex plane for ease of computation. As the points of computation of the displacement are near the origin, the branch line integrals become comparable with the contribution from the pole. The numerical results are compared with the spectra in a case where an infinite train of harmonic plane waves is vertically transmitted to the surface layers. When the depth of the points is several times as large as the thickness of the surface layer, the peak and dip of the spectral curve approximately agree with those in the incidence of SH plane waves.