A digital low-frequency geophone based on 4th-order sigma-delta modulator and single-coil velocity feedback

Widely deployed conventional moving-coil geophones lack the responses needed at low frequencies for detecting long-period seismic waves, and rely heavily on the A/D conversion chips for data acquisition. This work reports on a digital low-frequency geophone based on the PID force balancing technique and a single loop 4th-order sigma-delta modulator. The system is studied by Simulink modeling and is designed to satisfy demanding bandwidth and stability requirements. In addition, the hardware implementation adopts a readout interface for a geophone that consists of two parts: the analog part picks off the coil voltage while driving a control balancing force; and the digital part performs a real-time time DF integrators filtering in an FPGA for high-order noise shaping. The experimental results confirm the design concept of the proposed digital geophone. The balancing loop extends the low-frequency response of a commercial 4.5 Hz geophone down to 0.16 Hz. Within a 200 Hz bandwidth, the sigma-delta modulator achieves an equivalent acceleration noise floor of 4.3 ng/√Hz @ 1.0 Hz and shapes the in-band quantization noise to a level below other noises in the system. This investigation shows its potential to detect low-frequency seismic waves for efficient and high precision deep Earth exploration and hazard predictions.