Fault weakening process controls earthquake rupture propagation and is of great significance to impact the final earthquake size and seismic hazard. Critical slip-weakening distance (Dc) is one of the key parameters, which however is of difficult endeavours to be determined on natural faults, mainly due to its strong trade-off with the fault strength drop. An estimation method of Dc value proposed by Fukuyama et al (2003, 2007) provides a simple and direct reference of Dc on real faults from the near-fault ground displacement at the peak of ground velocity (Dc”). However, multiple factors may affect the observed near-fault ground velocity and thus need to be considered when estimating Dc. In this work we conduct 3D finite element numerical simulations to examine the effects of finite seismogenic width and near-fault low velocity zones (LVZ) on the results of Dc”. In uniform models with constant prescribed Dc, the derived Dc” values increase with seismogenic width. With a near-fault LVZ, Dc” values show significant magnification. The width of the LVZ plays a more important role in enlarging Dc estimation compared to the depth of LVZ. Complex wavefields and multiple wiggles introduced by LVZ could lead to delay pick and then cause large deviation. Overestimation should be considered when using Dc” from limited station to infer Dc on fault. Furthermore, the scaling between Dc” and final slip in models with a constant Dc indicates that the scale-dependent feature of Dc” might not be related to variations in friction properties.