Full Waveform Inversion and the truncated Newton method: quantitative imaging of complex subsurface structures

SUMMARY Full Waveform Inversion (FWI) is a powerful tool for quantitative seismic imaging from wide-azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the resolution of a large-scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artifacts generated by energetic multiple reflections. Conventional preconditioned gradient-based minimization methods only roughly approximate the effect of this operator. We are interested in this study to another class of minimization methods, named as truncated Newton methods. These methods are based on the computation of the model update through a matrix-free conjugate gradient resolution of the Newton linear system. The aim of this study is to present a feasible implementation of this method for the FWI problem, based on a second-order adjoint state formulation for the computation of Hessian-vector products. We compare this method with the nonlinear conjugate gradient and the l-BFGS method within the context of 2D acoustic frequency FWI for the reconstruction of P-wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf Of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data-set from the Valhall oil field in North sea. These tests emphasize the interesting properties of the truncated Newton method regarding conventional optimization methods within the context of FWI.