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Waveform inversion via reduced order modeling

Liliana BorceaJosselin GarnierAlexander V. MamonovJ\\"orn Zimmerling
摘要
We introduce a novel approach to waveform inversion, based on a data drivenreduced order model (ROM) of the wave operator. The presentation is for theacoustic wave equation, but the approach can be extended to elastic orelectromagnetic waves. The data are time resolved measurements of the pressurewave at the sensors in an active array, which probe the unknown medium withpulses and measure the generated waves. The ROM depends nonlinearly on the databut it can be constructed from them using numerical linear algebra methods. Weshow that the ROM can be used for the inverse problem of velocity estimation.While the full-waveform inversion approach of {nonlinear least-squares} datafitting is challenging without low frequency information, due to multipleminima of the objective function, the minimization of the ROM misfit functionhas a better behavior, even for a poor initial guess. In fact, the ROM misfitfunction is demonstrably a convex function for low-dimensional parametrizationsof the unknown velocity. We give the construction of the ROM, introduce theinversion approach based on the ROM misfit and assess its performance withnumerical simulations.
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