Abstract: Based on the traditianal strike-slip fault displacement formula, the time variable is introduced to study the dynamic relationship between surface displacement and time in motion of strike-slip fault. The dynamic evolution formula of surface displacement of strike-slip fault was obtained. When the fault is on the near-mid field or the seismogenic time is relatively long, the surface motion is approximately proportional to the logarithmic function of time. From the derived formula, we can get: ① The movement of the strike-slip fault over time is divergent, but the divergence rate is very slow; ② The good linear feature of most of the GPS time series is a local linear approximation in the mid-late stage of seismogenic; ③ At any moment in the mid-late stages of the seismogenic, the displacement of any point on the surface of the near-mid field of the fault is proportional to the distance from the fault. That is, the surface displacement curve perpendicular to the fault direction approximates a straight line. ④ Starting observing at a certain moment before the earthquake, the displacement of the station far from the fault before the earthquake is larger than the displacement from the station near the fault; the displacement from the station near the fault is larger than the displacement from the station far from the fault. The dynamic evolution formula of the surface displacement of the strike-slip fault is suitable for the near-mid field of the fault and the mid-late stage of the seismogenic. It can provide theoretical support for the determination of fault seismic hazard.

Key words: GPS time series, Linear approximation, Dynamic dislocation, Strike-slip fault