Convergence and physical interpretability of full waveform inversion updates are key issues as we contemplate practical FWI. One aspect of standard FWI updates that has been only superficially broached thus far is the idea that the sensitivity or Frechet kernel used in the gradient calculation could be re-tuned to increase convergency by accommodating more than the first order model/field variations. We present and analyze an approach to the construction of a second order sensitivity, and demonstrate its natural accommodation of for instance nonlinear reflection amplitudes, of the type encountered when contrasts causing reflections are large. In a companion paper we show how second order data-model interactions are properly incorporated in the inverse Hessian, but those do not appear in the updates we study here, and evidently do not adversely affect the treatment of second-order reflectivity.
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