Scattering-Based Decomposition of Sensitivity Kernels for Full-Waveform Inversion

Abstract

With the increasing demand in complexity for subsurface models in environments such as subsalt, sub-basalt and pre-salt, full-waveform inversion (FWI) is quickly becoming one of the model-building methods of choice. While in principle capable of handling all of the nonlinearity in the data, in practice nonlinear gradient-based FWI is limited due to its notorious sensitivity to the choice of starting models. To help addressing model convergence issues in FWI, in this paper we analyze the role of nonlinearity in the so-called sensitivity kernels, which are the centerpiece of gradient-based FWI algorithms. Using a scattering-based approach and assuming acousticonly data, we start by reparameterizing the subsurface model in terms of smooth and singular 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 smooth and sharp model components. Focussing on the model backprojections from the scattered data only, we provide expressions for the Fr´echet-derivative sensitivity kernels of all four model parameters. Our results provide for the decomposition of current FWI kernels into no less than nine different sub-kernels which 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. We illustrate this by analyzing some of the sub-kernel terms in detail. The scattering-based FWI kernel decomposition we provide could have broad potential applications, such devising multiscale FWI algorithms, and improving velocity model building in the image domain using extended image gathers.