Effect of the interfacial continuity on the elastic full-waveform inversion

Ourania Giannopoulou 

Full-waveform inversion (FWI) routinely assumes welded interfaces between subsurface layers, yet many geological and engineering targets including karst cavities, fractures, and unbonded soil-structure contacts exhibit interfacial slip. We show that this modelling assumption is not merely a geometric detail but introduces a systematic bias in the recovered physical parameters. Using a finite-element full-waveform-inversion framework implemented in FEniCS, we compare two interfacial treatments: a standard continuous Galerkin (CG) formulation that enforces welded continuity, and a discontinuous Galerkin (DG) formulation based on Nitsche's method that permits tangential slip at material boundaries. A synthetic "inversion crime" cross-test on a two-dimensional elastic inclusion model demonstrates that the CG solver absorbs the interfacial slip effects through biased density estimates, achieving a numerically lower misfit at the cost of parameter accuracy. The DG formulation, by contrast, maintains physical consistency and recovers more accurate parameter values. Our results highlight the need for practitioners to carefully consider interfacial continuity assumptions when inverting seismic data from environments where welded boundary conditions may not hold.