We propose a novel approach to time domain full waveform inversion with reconstructed wavefield (RFWI). RFWI relaxes the constraint that the forward modeled data exactly solves the wave equation in conventional full waveform inversion (FWI) to an L2 approximation. RFWI estimates earth models and jointly reconstructs the wavefield by minimizing the data misfit and wave equation error. The potential benefits include avoiding cycle skipping and mitigating some of the problems with local minima. The applicability of RFWI will be illustrated on both synthetic and field examples.


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