A Hybrid Stochastic-deterministic Optimization Method for Waveform Inversion

Present-day high quality 3D acquisition can give us lower frequencies at longer offsets with which to invert. However, the computational costs involved in handling this data explosion are tremendous. Therefore, recent developments in full-waveform inversion have been geared towards reducing the computational costs involved. Recent attention has been drawn towards reducing the number of sources by randomly combining the sources in to a few supershots, but other strategies are also possible. In all cases, the full data misfit, which involves all the sequential sources, is replaced by a reduced misfit that is much cheaper to evaluate, but also less accurate. The optimization of such an inaccurate, or noisy, misfit is the topic of stochastic optimization. In this paper, we propose an optimization strategy that borrows ideas from this field. The strategy consists of starting with very few sources (low cost) and gradually increasing the accuracy of the misfit as the iterations proceed. We test the proposed strategy on a synthetic dataset. We achieve a very reasonable inversion result at the cost of roughly 13 evaluations of the full misfit and observe a speed-up of roughly a factor 20.