submitted to Geophys. J. Int. Wavefield reconstruction for velocity-stress elastodynamic Full Waveform Inversion Ole Edvard Aaker ⋆ , Espen Birger Raknes ⋆† , Ørjan Pedersen ⋆ and Børge Arntsen ‡ ⋆ Aker BP ASA, Trondheim, Norway e-mail: ole.edvard.aaker@akerbp.com, espen.birger.raknes@akerbp.com, orjan.pedersen@akerbp.com † Norwegian University of Science and Technology, Department of Electronic Systems, Trondheim, Norway ‡ Norwegian University of Science and Technology, Department of Geoscience and Petroleum, Trondheim, Norway e-mail: borge.arntsen@ntnu.no SUMMARY Gradient computations in full waveform inversion (FWI) require calculating zero-lag cross-correlations of two wavefields propagating in opposite temporal directions. Loss- less media permit accurate and efficient reconstruction of the incident field from record- ings along a closed boundary, such that both wavefields propagate backwards in time. Reconstruction avoids storing wavefield states of the incident field to secondary storage, which is not feasible for many realistic inversion problems. We give particular atten- tion to velocity-stress modelling schemes and propose a novel modification of a con- ventional reconstruction method derived from the elastodynamic Kirchhoff-Helmholtz integral. In contrast to the original formulation (in a previous related work), the proposed approach is well-suited for velocity-stress schemes. Numerical examples demonstrate ac- curate wavefield reconstruction in heterogenous, elastic media. A practical example using three-dimensional elastic FWI demonstrates agreement with the reference solution. Key words: Full waveform inversion, elastic, reconstruction