A Scattering-based Reparameterization of Sensitivity Kernels for Full-waveform Inversion

With the increasing demand in complexity for subsurface models in environments such as subsalt, sub-basalt and pre-salt, full-waveform inversion (FWI) is becoming one of the model-building methods of choice. While it can, in principle, handle all of the nonlinearity in the data, in practice nonlinear gradient-based FWI is limited due to its sensitivity to the choice of starting models. To address model convergence issues in FWI, here we analyze the role of nonlinearity in sensitivity kernels, which are the centerpiece of gradient-based FWI algorithms. Using a scattering-based approach, we reparameterize the subsurface model in terms of smooth and sharp components for both compressibility and density. This leads to a decomposition of the data into a reference field that is sensitive only to the smooth model, and a scattered field sensitive to both model components. Focussing on the model backprojections from the scattered data, we provide expressions for the Frchet-derivative sensitivity kernels of all model parameters. Our results decompose current FWI kernels into several subkernels that have explicitly different levels of nonlinearity with respect to both data and model parameters. This capability to discern levels of nonlinearity within FWI kernels is key to understanding model convergence in gradient-based, iterative FWI.