Waveform inversion via reduced order modeling

We introduce a novel approach to waveform inversion based on data-driven reduced order model (ROM) of the wave operator. The presentation is for acoustic equation, but can be extended elastic or electromagnetic waves. data are time resolved measurements pressure gathered by an acquisition system that probes unknown medium with pulses and measures generated propose solve inverse problem velocity estimation minimizing square misfit between ROM computed from recorded modeled data, at current guess velocity. give step computation ROM, which depends nonlinearly yet obtained them in noniterative fashion, using efficient methods linear algebra. also explain how make robust inaccuracy. requires full array response matrix colocated sources receivers. However, we find deal approximation this matrix, towed-streamer interpolation reciprocity on-the-fly. Although full-waveform nonlinear least-squares fitting challenging without low-frequency information, due multiple minima fit objective function, function has better behavior, even poor initial guess. explicit functions simple setting convexity properties, whereas displays local minima.