We introduce a novel nonlinear imaging method for the acoustic wave equationbased on data-driven model order reduction. The objective is to image thediscontinuities of the acoustic velocity, a coefficient of the scalar waveequation from the discretely sampled time domain data measured at an array oftransducers that can act as both sources and receivers. We treat the waveequation along with transducer functionals as a dynamical system. A reducedorder model (ROM) for the propagator of such system can be computed so that itinterpolates exactly the measured time domain data. The resulting ROM is anorthogonal projection of the propagator on the subspace of the snapshots ofsolutions of the acoustic wave equation. While the wavefield snapshots areunknown, the projection ROM can be computed entirely from the measured data,thus we refer to such ROM as data-driven. The image is obtained bybackprojecting the ROM. Since the basis functions for the projection subspaceare not known, we replace them with the ones computed for a known smoothkinematic velocity model. A crucial step of ROM construction is an implicitorthogonalization of solution snapshots. It is a nonlinear procedure thatdifferentiates our approach from the conventional linear imaging methods(Kirchhoff migration and reverse time migration - RTM). It resolves alldynamical behavior captured by the data, so the error from the imperfectknowledge of the velocity model is purely kinematic. This allows for almostcomplete removal of multiple reflection artifacts, while simultaneouslyimproving the resolution in the range direction compared to conventional RTM.
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