  Full waveform inversion (FWI) aims at estimating subsurface medium properties
from measured seismic data. It is usually cast as a non-linear least-squares
problem that incorporates uncertainties in the measurements. In exploration
seismology, extended formulations of FWI that allow for uncertaties in the
physics have been proposed. Even when the physics is modelled accurately, these
extensions have been shown to be beneficial because they reduce the non-lineary
of the resulting data-fitting problem. In this note, I derive an alternative
(but equivalent) formulation of extended full waveform inversion. This
re-formulation takes the form of a conventional FWI formulation that includes a
medium-dependent weight on the residuals. I discuss the implications of this
re-formulation and illustrate its properties with a simple numerical example.
