Quasi-Newton optimization methods have been shown to provide considerable improvements in the convergence rate of full waveform inversion (FWI). These methods use approximate Hessian matrices to generate an update direction. The DFP method uses an approximate Hessian which predicts observed changes in the gradient, while remaining nearest in a least-squares sense to the previous approximate Hessian. By using a low-resolution approximation to the Hessian to initialize the method, we attempt to increase the rate of convergence. This work is ongoing, currently there are significant challenges in using the inverse of the Hessian on the low-resolution scale to provide a meaningful inverse on the high-resolution scale.
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