To solve the problem that the Houfeng Seismograph’s directional function’s historical record was generally questioned. The analysis concludes that the spherical pendulum seismic measurement scheme may be a feasible restoration scheme with Rayleigh wave（the main component of non-local earthquakes） as wave source. A nonlinear complete mechanical model of the spherical pendulum under Rayleigh wave excitation is established. The equation of motion was derived. The approximate solution is obtained using the perturbation method. The results show that: the spherical pendulum restoration model has a directional response to Rayleigh waves. The magnitude of the directional response is related to the amplitude of the Rayleigh wave, as well as the frequency ratio and damping of the system. Combined with historical records to study the restoration models of the weather seismograph, the spherical pendulum model is the best restoration model for Zhang Heng’s Hou Feng seismograph in many aspects. This conclusion is an important theoretical basis to prove the historical authenticity of the Houfeng Seismograph.