Fault geometry invariance and dislocation potential in antiplane crustal deformation: physics-informed simultaneous solutions

Earthquake-induced crustal deformation provides valuable insights into the mechanisms of tectonic processes. Dislocation models offer a fundamental framework for comprehending such deformation, and two-dimensional antiplane dislocations are used to describe strike-slip faults. Previous earthquake deformation analyses observed that antiplane dislocations due to uniform fault slips are influenced predominantly by fault tips. Here, we state a general principle of fault geometry invariance in antiplane dislocations and exploit its theoretical consequence to define dislocation potentials that enable a streamlined crustal deformation analysis. To demonstrate the benefits of this theory, we present an analytical example and construct a rapid numerical solver for crustal deformation caused by variable fault slip scenarios using physics-informed neural networks, whose mesh-free property is suitable for modeling dislocation potentials. Fault geometry invariance and the dislocation potential may further the analysis of antiplane crustal deformation, particularly for uncertainty quantification and inversion analysis regarding unknown fault geometries in realistic crustal structures.