Analytical method for the kinematic response and signal error of a downhole seismometer subjected to P-waves

Abstract

This paper presents an analytical method for the steady-state kinematic response of downhole seismometers to vertically incident P-waves, based on a modified Vlasov model. The governing equations and boundary conditions of a soil–well system were obtained using Hamilton's principle. The three unknown functions were then decoupled using an iterative algorithm. The accuracy of the proposed method was validated by placing a downhole seismometer in the well and comparing the responses with previously reported results. A parametric study was performed to investigate the effects of the soil–well system properties on the kinematic response and monitoring errors of the downhole seismometer. Results indicated that the incident frequency, thickness of the foundation of the downhole seismometer, soil–well modulus ratio Ew/Es, and slenderness ratio of the downhole seismometer considerably influence the monitoring error, whereas soil damping has little effect on it.