Abstract
Seismic acquisition can be costly and inefficient when using spiked geophones. In most cases, such as the desert, the most practical solution is the use of flat bases, where geophone-ground coupling is based on an optimal choice of the mass and area of contact between the receiver and the ground. This optimization is necessary since areas covered by sand are loose sediments and poor coupling occurs. Other cases include ground coupling in stiff pavements, for instance urban areas and ocean-bottom nodes. We consider three different approaches to analyse coupling and model the geophone with a flat base (plate) resting on an elastic half-space. Two existing models, based on the full-wave theory, which we refer to as the Wolf and Hoover-O'Brien models, predict a different behaviour with respect to the novel method introduced in this work. This method is based on the transmission coefficient of upgoing waves impinging in the geophone-ground contact, where the ground is described as an anelastic half-space. The boundary conditions at the contact have already been used to model fractures and are shown here to provide the equation of the damped oscillator. This fracture-contact model depends on the stiffness characteristic of the contact between the geophone base plate and the ground. The transmission coefficient from the ground to the plate increases for increasing weight and decreasing base plate area. The new model predicts that the resonant frequency is independent of the geophone weight and plate radius, while the recorded energy increases with increasing weight and decreasing base plate area (as shown from our own experiments and measurements by Krohn) which is contrary to the theories developed by Wolf and Hoover-O'Brien. The transient response is obtained by an inverse Fourier transform. Optimal geophone-ground coupling and energy transmission are required, the first concept meaning that the geophone is following the motion of the ground and the second one that the signal is detectable. As a final example, we simulate seismic acquisition based on the novel theory, showing the differences between optimal and poor ground-to-geophone energy transmission.