Building a regularization toolbox for FWI

A versatile procedure has been developed in the framework to ADMM-based WRI to interface different regularizations with the optimization algorithm where WRI is broken down into two successive linear subproblems. We adapt this procedure to regularize classical nonlinear FWI. This procedure is reviewed in the WIND Technical Report 1 for a vast catalogue of regularizer. A regularization toolbox based upon this approach is under development.

Aghamiry H., A. Gholami and S. Operto (2020). A practical guide to implement smooth and nonsmooth regularization in Full Waveform Inversion with ADMM, Technical Report n 1 - version 1, WIND project, 29 pages .

Figure 1: Performance of different regularizer in IR-WRI for the 2004 BP salt model. (a) True velocity model/ (b) Starting velocity model. (c) Zero-order Tikhonov regularization. (d) TV regularization. (e) Sedond-order Tikhonov regularization. (f) Compund Tikhonov + TV regularization.

More details can be found in H. Aghamiry, A. Gholami and S. Operto. Compound Regularization of Full-waveform Inversion for Imaging Piecewise Media, IEEE Transactions on Geoscience and Remote Sensing, https://doi.org/10.1109/TGRS.2019.2944464, 58(2), pages 1192--1204, 2020.

References:

• H. Aghamiry, A. Gholami and S. Operto. Full Waveform Inversion by proximal Newton methods using adaptive regularization, Geophysical Journal International, Volume 224, Issue 1, January 2021, Pages 169–180, https://doi.org/10.1093/gji/ggaa434.
• H. Aghamiry, A. Gholami and S. Operto. Compound Regularization of Full-waveform Inversion for Imaging Piecewise Media, IEEE Transactions on Geoscience and Remote Sensing, 58(2): 1192--1204, 2020, https://doi.org/10.1109/TGRS.2019.2944464.
• H. Aghamiry, A. Gholami, and S. Operto, Attenuation imaging by wavefield reconstruction inversion with bound constraints and total variation regularization. Geophysics, 85(4)381--396, 2020, https://doi.org/10.1190/geo2019-0596.1 .
• H. Aghamiry, A. Gholami and S. Operto, ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization, Geophysical Journal International, 219, 1316--1333 , 2019, https://doi.org/10.1093/gji/ggz369 .
• H. Aghamiry, A. Gholami and S. Operto, Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media, Geophysical Journal International, 218(2), 855-872, 2019, https://doi.org/10.1093/gji/ggz189.