This work began with a discussion of the mechanics of seismic sensors, based on
the simple harmonic oscillator model. Both traditional analog geophones and MEMS
accelerometers can be viewed as harmonic oscillators, over the range of frequencies used
in seismic exploration. Where they differ is in the transduction used to record the motion
of the proof mass. Geophones use a coil/magnet inductor, while MEMS accelerometers
use capacitors. This defines the proof mass motion that they detect. Geophones detect
the velocity of the coil relative to the magnet, and MEMS accelerometers detect the
displacement of the central proof mass in the silicon sandwich. Due to the MEMS
accelerometers’ very high resonance, any residual displacement of the proof mass is
proportional to the acceleration of the case. For timescales on the order of the desired
signal frequencies, the digital feedback loop in the MEMS accelerometer effectively acts
as an additional analog restoring force. This effectively stiffens the suspension of the
proof mass, which further increases the resonance, and increases the range of frequencies
where the ‘high-frequency resonance’ approximation is true. For the useful seismic band,
MEMS accelerometer output is a direct representation of the case, and thus ground,
acceleration. Due to weight and sensitivity requirements, the resonance of a geophone is
neither very high nor very low relative to the frequencies of the desired signal. This
means no approximation can be made, and geophone output is not a direct representation
of any domain of ground motion.