Full waveform inversion (FWI) is used to reconstruct physical parameters of the sub-surface. In this report, we move towards a modified FWI scheme that iteratively solves for both source distribution uncertainty and velocity model uncertainty in the acoustic environment. The sensitivities are derived for these two parameters in both time and frequency domain. Additionally, to begin exploring the cross-talk between these two parameters, the Hessian is derived in the frequency domain. The paper concludes with an analytic example demonstrating the behaviour of this formulation and a discussion on the implications of these results.
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