We introduce a novel framework for seismic imaging and inversion based on model order reduction. The reduced order model (ROM) is an orthogonal projection of the wave equation propagator on the subspace of discretely sampled time domain wavefield snapshots. It can be computed entirely from the knowledge of the measured time domain seismic data using the block Cholesky factorization. Once the ROM is computed, its use is trifold.
First, the ROM can be used as a nonlinear "preconditioner" for full waveform inversion (FWI). Instead of conventional minimization of the least squares data misfit we propose to minimize the ROM misfit. Such objective is more convex and thus optimization is much less prone to common issues like getting stuck in local minima (cycle skipping), multiple reflection artifacts, slow convergence, etc.
Second, if a background kinematic model is available, the projected propagator can be backprojected to obtain a seismic image. ROM computation implicitly orthogonalizes the wavefield snapshots. This nonlinear procedure differentiates our approach from the conventional linear migration methods (Kirchhoff, RTM). It allows to resolve the nonlinear interactions between reflectors. As a consequence, multiple reflection artifacts are almost completely suppressed.
Third, the ROM can be used to generate the Born data, i.e. the data that the measurements would produce if the propagation of waves in the medium obeyed Born approximation instead of the wave equation. Consecutively, existing linear inversion and imaging techniques can be applied to Born data to obtain reconstructions in a direct, non-iterative manner.
(Joint with L. Borcea, V. Druskin, A. Thaler, M. Zaslavsky)