Multiscale Newton-Krylov methods for inverse acoustic wave propagation

The objective of this work is to solve the inverse acoustic wave propagation problem. The goal is to determine the acoustic properties of a heterogenous medium, given a pressure source and measurements at receiver locations on the boundary. The inverse problem is formulated as partial differential equation (PDE) constrained optimization problem. The objective function is the L2 norm difference between the measured and the predicted acoustic response; the constraints are the wave propagation PDEs; and the optimization function to be determined is the material field. Problems of this type arise in a number of important applications including medical imaging and seismic inversion.; The inverse wave propagation problems have numerous challenges including extreme large scale, ill-posedness and numerous multiple minima of the objective function. We overcome the last two difficulties by developing a parallel Newton-Krylov least-squares optimization method.; To overcome ill-conditioning and multiple minima, we develop a multiscale algorithm that relies on separately determining spectral components of the material field: we sweep through the source frequencies, determining successively higher frequency components of the material field on successively finer grids. The multiscale strategy is based on inverting for low frequency components of the material profile by low frequency source excitation. For a given optimization grid the optimizer is discouraged from moving in finer frequency directions by applying regularization.; We demonstrate the performance of the algorithm through synthetic two- and three-dimensional acoustic inversion problems. We show that the algorithm has good parallel and algorithmic scalability, and successfully inverts for the targeted models.