A Low-Frequency Extension Method for Geophone Based on Force Balance and Approximate Integrator

To address the issue of receiving extremely low-frequency weak signals in ultra-deep oil and gas seismic exploration, a low-frequency extension method for geophone based on Force Balance and Approximate Integrator (FB-AI) is proposed in this paper. Based on electromagnetic dynamics principles for moving-coil geophone, a Force Balance Closed-Loop (FBCL) model is established. After analyzing the closed-loop damping and frequency response characteristics of this model’s transfer function, a highly stable, gain-compensated negative resistance conversion circuit is designed. Thereafter, a low-frequency extended accelerometer with high consistency is developed. For designing a high-sensitivity low-frequency velocity sensor, an approximate integrator suitable for this extended accelerometer is constructed based on the least squares algorithm. The problem of inconsistent sensitivity caused by component tolerance is solved by independent adjustment of gain resistors. A cost-effective, compact, and alloy waterproof housing is designed to meet the requirements of large-scale field applications. Laboratory tests show a sensitivity of 200\; \textV/\left( \textm\cdot\texts^-1\right) with an operational bandwidth of 0.25 - 100\; \textHz , while field validation confirms the system fully meets the requirements for low-frequency signal detection.