Randomized full-waveform inversion: a dimenstionality-reduction approach

Full-waveform inversion relies on the collection of large multi-experiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem sizes numerically. Two main culprits can be identified. First, there is the so-called ‘‘curse of dimensionality’’ exemplified by Nyquist’s sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. Secondly, there is the recent ‘‘departure from Moore’s law’’ that forces us to develop algorithms that are amenable to parallelization. In this paper, we discuss different strategies that address these issues via randomized dimensionality reduction.