Speaker
Description
Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. The traditional full waveform inversion (FWI) formulation estimates the unknown coefficients via minimization of the nonlinear, least squares data fitting objective function. For typical band-limited and high frequency data, this objective function has spurious local minima near and far from the true coefficients. Thus, FWI implemented with gradient based optimization algorithms may fail, even for good initial guesses, a phenomenon known as cycle skipping. Recently, it was shown that data driven reduced order models (ROMs) can be used to obtain a better behaved objective function for wave speed estimation. We introduce ROMs for waves obeying a first order hyperbolic system. They are defined via Galerkin projection on the space spanned by the wave snapshots, evaluated on a uniform time grid with an appropriately chosen time step. The proposed ROMs are data driven, as they are computed directly from the sensor measurements. The ROM computation applies to any linear waves in lossless and non-dispersive media. We present an example of acoustic waveform inversion in a medium with both wave speed and density unknown. Numerical examples show that both quantities can be estimated efficiently via minimization of an objective function that employs ROM based approximation of the wave field inside the unknown medium.