Radiation impedance of torsionally vibrating seismic sources

Abstract

The thickness and shear‐wave velocity of a surface layer can theoretically be determined from seismic radiation impedance measurements using a torsional vibrator. These studies also provide physical insight into vibrator‐earth interaction. The radiation impedance of a circular disk vibrating torsionally on an anelastic half‐space has resonance peaks with a spacing that is a function of the ratio between baseplate radius and seismic wavelength. At low frequencies the shape of the impedance function is nearly independent of the baseplate flexure, although the magnitude is affected. At high frequencies the impedance depends strongly on the flexibility of the baseplate. The mass of the baseplate introduces an additional resonant effect, the frequency of which is a function of the baseplate mass. The presence of a surface layer produces an impedance curve which oscillates around the half‐space response. The amplitude of the oscillations is a function of the acoustic impedance contrast and depends upon the radiation pattern of the source. The oscillations are resonances caused by reflections within the surface layer, and both the period and amplitude of the oscillations are inversely proportional to the layer thickness. The amplitude of the layer resonance decreases rapidly as material damping increases. With impedance measurements over a sufficiently broad frequency range (up to about 500 Hz), it may be feasible to use half‐space oscillations and the layer resonances to determine the shear velocity and thickness of the layer of material beneath the baseplate.