Statistical Sampling Enabled Full Waveform Inversion

Full-waveform Inversion has recently emerged as a promising method for refining seismic velocity models to achieve enhanced imaging. The algorithm involves iteratively updating the velocity model to improve the match between the recorded seismic data and the simulated waveforms, with the goal of estimating the true velocity structure. Each iteration typically requires multiple wavefield extrapolations. As a result the technique places significant computational burdens on even the largest computers when applied to commercial three-dimensional surface seismic datasets. This computational cost has been attacked previously by combining the processing of multiple physical shots into a single ';encoded-shot', using random encoding techniques (Krebs et al, 2009). The encoding can be based upon time shifts, polarity reversal or convolution with a short random series any of which may be changed between iterations. While this technique works well for geometries with fixed receiver arrays (e.g. ocean-bottom cables) additional steps are usually required when applied to moving arrays both because the area occupied by the encoded shot grows in comparison to a single shot, and because not every receiver registers data from every shot in the recorded data. This paper discusses an alternative approach using concepts from statistical sampling, proposed by van Leeuwen & Hermann 2012. Rather than using every shot, or encoding multiple shots, at each iteration we randomly select a different subset of shots as input to the inversion algorithm. The method promises a reduction in the computational costs while still ensuring that all the information in the data is utilized during the inversion. Furthermore, the method is applicable without modification to both fixed and moving geometries. Results are shown for a synthetic model and a real marine data set acquired with a multi-vessel coil geometry. Both examples show significant computational savings, compared to the conventional algorithm, without any detectable reduction in quality.