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This paper focuses on an elastic dislocation problem that is motivated byapplications in the geophysical and seismological communities. In our model,the displacement satisfies the Lam\'e system in a bounded domain with a mixedhomogeneous boundary condition. We also allow the occurrence of discontinuitiesin both the displacement and traction fields on the fault curve/surface. By thevariational approach, we first prove the well-posedness of the directdislocation problem in a rather general setting with the Lam\'e parametersbeing real-valued $L^\infty$ functions and satisfy the strong convexitycondition. Next, by considering the scenario that the Lam\'e parameters areconstant and the fault curve/surface possesses certain corner singularities, weestablish a local characterisation of the slip vectors at the corner pointsover the dislocation curve/surface. In our study the dislocation isgeometrically rather general and may be open or closed. For both cases, weestablish the uniqueness results for the inverse problem of determining thedislocation curve/surface and the slips.

Dislocations with corners in an elastic body with applications to fault detection