  A novel approach to full waveform inversion (FWI), based on a data driven
reduced order model (ROM) of the wave equation operator is introduced. The
unknown medium is probed with pulses and the time domain pressure waveform data
is recorded on an active array of sensors. The ROM, a projection of the wave
equation operator is constructed from the data via a nonlinear process and is
used for efficient velocity estimation. While the conventional FWI via
nonlinear least-squares data fitting is challenging without low frequency
information, and prone to getting stuck in local minima (cycle skipping),
minimization of ROM misfit is behaved much better, even for a poor initial
guess. For low-dimensional parametrizations of the unknown velocity the ROM
misfit function is close to convex. The proposed approach consistently
outperforms conventional FWI in standard synthetic tests.
