  We propose a formulation of full-wavefield inversion (FWI) as a constrained
optimization problem, and describe a computationally efficient technique for
solving constrained full-wavefield inversion (CFWI). The technique is based on
using a total-variation regularization method, with the regularization weighted
in favor of constraining deeper subsurface model sections. The method helps to
promote "edge-preserving" blocky model inversion where fitting the seismic data
alone fails to adequately constrain the model. The method is demonstrated on
synthetic datasets with added noise, and is shown to enhance the sharpness of
the inverted model and correctly reposition mispositioned reflectors by better
constraining the velocity model at depth.
