In order to draw geological structures such as faults, interpolation is generally needed between scattered data. The use of an approximation criterion integrating the kinematic properties of the faults helps to document the fault surfaces by adding a compatibility criterion to the data set. Assuming that two jointed blocks of rocks slipping on each other generate a thread surface, an approximation method has been developed which integrates a thread criterion. This approximation method is used to solve an inverse problem with least-squares criteria including proximity to data points, smoothness and thread criteria. The aim is to find a smooth surface which is as close as possible to a thread and as close as possible to the observed data set. Applications to two corrugated fault surfaces with a dense data set, located in the Western Alps (France) and in the Transverse Ranges (California), confirm the validity of the thread assumption. Despite their difference in mean corrugation wavelength (5 m and 10 km respectively), in the type of fault (strike-slip and thrust fault respectively), and in the nature of the faulted rocks (limestones and sandstones respectively), very similar results are obtained. In both cases the observed data fit well with a thread surface and the computed fault displacement fits well with the measured displacement on the fault (striae, seismic focal mechanism, geodetic data, restoration). The conclusion is that treating a fault as a thread is a valid physical description which gives the slip direction independently of other kinematic indicators. The advantage of using a thread criterion in addition to classical proximity and smoothness criteria is that this physical insight allows information from areas where data are relatively dense to help constrain areas where data are relatively sparse, these last areas being those that are usually not well constrained by proximity and smoothness criteria.
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