A new elastic model for ground coupling of geophones with spikes

Ground coupling are terms that describe the transfer from seismic ground motion to the motion of a geophone. In previous models, ground coupling was mainly considered as a disk lying on top of a half-space, not considering the fact that in current practice geophones are spiked and are buried for optimal response. In this paper we introduce a new model that captures the spike added to the geophone and models the effect of geophone burial. The geophone is modeled as a rigid, movable cylinder embedded in a half-space near or at the surface. The coupling problem is then tackled by a scattering approach using the elastic form of reciprocity; we consider the vertical component only. The main feature in the coupling function is a resonance whose location and shape depend on the different parameters of the geophone and the soil. In accordance with previous models, adding mass reduces the frequency of resonance. However, we show that pure mass loading assumption is too restrictive for standard geophones. Our new model shows that increasing the spike radius and length decreases the frequency of resonance and the resonance is more peaked. Furthermore, burying the geophone decreases the frequency of resonance, but when one takes into account that the soil at depth is more compact, then the behavior is as observed in practice — namely, an increase in frequency of resonance. As for the properties of the soil, the shear-wave velocity has the largest effect; when increased, it shifts the frequency of resonance to the high-frequency end as desired.