Additive versus multiplicative regularization with Sobolev space norm stabilizer: application to FWI

Additive versus multiplicative regularization with Sobolev space norm stabilizer: application to FWI

Full-waveform inversion (FWI) is an efficient tool for obtaining high-resolution estimates of the subsurface properties. Existing some errors in the data makes FWI to be ill-posed and the problem needs to be regularized. In additive regularization (AR), the balancing factor needs to be adjusted during the inversion which is more costly for computationally expensive problem such as FWI. While in multiplicative regularization (MR), the data term of objective function, somehow, plays a role of this regularization balancing factor and there is no need to set this factor. In this study, we introduced MR method with Sobolev space norm as a regularization term and used a type of regularization term that has both Tikhonov and total variation regularization functionality. We compared MR with equivalent AR method by application on 2D synthetic noisy datasets. The results show the applicability of MR method for large-scale problems where it can provide more robust solution for the inversion.

Full-waveform inversion (FWI) is an efficient tool for obtaining high-resolution estimates of the subsurface properties. Existing some errors in the data makes FWI to be ill-posed and the problem needs to be regularized. In additive regularization (AR), the balancing factor needs to be adjusted during the inversion which is more costly for computationally expensive problem such as FWI. While in multiplicative regularization (MR), the data term of objective function, somehow, plays a role of this regularization balancing factor and there is no need to set this factor. In this study, we introduced MR method with Sobolev space norm as a regularization term and used a type of regularization term that has both Tikhonov and total variation regularization functionality. We compared MR with equivalent AR method by application on 2D synthetic noisy datasets. The results show the applicability of MR method for large-scale problems where it can provide more robust solution for the inversion.