Finding a velocity model that produces simulated data that fits the observed one is the main objective of full waveform inversion (FWI). To meet such an objective we often need to solve for a high-resolution delineation of the subsurface medium. The current algorithms are usually implemented over the entire model space with a consistent discretization and physical assumptions, which can be both complex and costly in practice. Alternatively, we develop an FWI framework that utilizes a split model to an overburden, like the medium above a reservoir, and the underlying represented by data at a datum at the bottom of the overburden. We simultaneously invert for the velocity model above the datum level, which effects the redatuming process but often owns to more simple physics, and the corresponding data at that datum, which may represent a complex reservoir region. We formulate the redatuming operator using a modified expression of the extended Born representation, which is a multi-dimensional crosscorrelation. The resulting modeling needed in such an inversion includes wavefields from a source and those ignited at the datum level. We estimate the overburden velocity using low-wavenumber updates along the modeled reflection wavepaths. The dimensionality of the model extension and the retrieved data helps us match data on the surface, which results in a robust implementation. Tests on a simple model and the Marmousi show that our method can build a good velocity model and also obtain redatumed data with reasonable amplitude accuracy.