Robust full‐waveform inversion using the Student's t‐distribution

Abstract

SUMMARYFull-waveform inversion (FWI) is a computational procedure to extract medium parameters from seismic data. Robust methods for FWI are needed to overcome sensitivity to noise and in cases where modeling is particularly poor or far from the real data generating process. We survey previous robust methods from a statistical perspective, and use this perspective to derive a new robust method by assuming the random errors in our model arise from the Student's t-distribution. We show that in contrast to previous robust methods, the new method progressively down-weighs large outliers, effectively ignoring them once they are large enough. This suggests that the new method is more robust and suitable for situations with very poor data quality or modeling. Experiments show that the new method recovers as well or better than previous robust methods, and can recover models with quality comparable to standard methods on noise-free data when some of the data is completely corrupted, and even when a marine acquisition mask is entirely ignored in the modeling. The ability to ignore a marine acquisition mask via robust FWI methods offers an opportunity for stochastic optimization methods in marine acquisition.

Waveform tomography in 2.5D: Parameterization for crooked‐line acquisition geometry

“…The sensitivity of the l 2 norm to data outliers (e.g., noise bursts or modeling errors) has been documented in research by several workers, who have argued for a variety of treatments to mitigate the problem. Some of these approaches make use of alternate norms, such as the l 1 norm [ Brossier and Operto , ], the logarithmic l 2 norm [ Shin and Min , ], and others [ Brossier et al ., ; Aravkin et al ., ] that reduce sensitivity to data outliers. Another approach involves processing of trace‐normalized seismic data under the l 2 norm and considers only the phase residuals [e.g., Operto et al , ; Bleibinhaus and Hilberg , ], which may yield significant benefits for stability because of reduced sensitivity to noise.…”

Suppressing non‐Gaussian noises with scaled receiver wavefield for reverse‐time migration: comparison of different approaches

“…When α = 0, it corresponds to the conventional imaging procedure; when α = 1, it is the L-1 norm case as in FWI; when combining the two above cases together, we can also obtain a hybrid solution as the Huber norm does. Also, when α = 2, it corresponds to the case of a student's t-distribution of the a posteriori distribution from a statistical point of view of the FWI minimizing functional (Aravkin, Leeuwen and Herrmann 2011). Logarithmic wavefield scaling used in frequency-domain FWI (Shin and Min 2006) can also be used here for RTM with the migration approach described as follows:…”

Seismic deconvolution and inversion with erratic data

“…Recently, Gholami and Sacchi () presented a deconvolution method including a mixed L p ‐L1 measure for the data misfit function and for the model regularization term. Aravkin, van Leeuwen and Herrmann (), Aravkin et al . (), Kumar et al .…”