Robust reconstruction methods were proposed for tangential dislocations on planar faults. It was assumed that only surface observations were available, and that a traction-free condition applied at that surface. The study made extensive use of an asymptotic estimate for the observed surface displacement. This estimate was first used to derive a so-called moments reconstruction method. It was then also used to find necessary conditions for a surface displacement field to be caused by a slip on a fault. These conditions led to the introduction of two parameters: the activation factor and the confidence index. These could be deduced from surface observations in a robust manner. They indicated whether a measured displacement field was due to an active fault. A second combined reconstruction technique was developed which blended least-squares minimization with the moments method. A careful assessment was made of how the present reconstruction method was affected by the sensitivity of the observation apparatus and the step-size of the grid of surface observation points. The maximum permissible step-size for such a grid was deduced for various values of fault-depth and orientation. Finally, numerical examples of fault reconstruction were presented. It was demonstrated that the present combined method was sharp robust and computationally inexpensive. It was also noted that this method performed satisfactorily for shallow faults; in spite of the fact that the asymptotic formula deteriorated in that case.

Detecting Tangential Dislocations on Planar Faults from Traction Free Surface Observations. I.R.Ionescu, D.Volkov: Inverse Problems, 2009, 25[1], 015012