We propose a possible model for the origin of the spatial fluctuations of the stress field along faults and test our model in the case of the Nojima fault, Japan where unique estimates of the absolute stress field have been obtained. The model consists of two parts: an up-scaling of the fault morphology measured at laboratory scales and a numerical computation using a boundary element approach of the influence on the stress field along the fault of an elastic squeeze of the fault asperities. Accordingly, fluctuations of the stress field along the fault would be dominated by quenched fault properties rather than dynamical stress fluctuations produced during earthquakes.