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Inversion methods that do not model all of the physical events in the observed data lead to inconsistent sets of equations. This often results in serious artifacts in the inverted model. To mitigate this problem, I propose a misfit function that partly ignores the unexplainable arrivals in the data due to modeling limitation. This is tested on least squares migration of synthetic P–P arrivals, albeit P–S reflections exist in the observed data in addition, to demonstrate that in this case the new misfit is more robust than the standard L2 misfit.