Georgia Institute of Technology
Ali Siahkoohi is currently pursuing a Ph.D. in Computational Science and Engineering under the supervision of Dr. Felix J. Herrmann at Georgia Institute of Technology. He completed his B.Sc. in Electrical Engineering before obtaining his M.Sc. in Geophysics. Ali's research is mainly focused on applications of deep learning in inverse problems and uncertainty quantification.
The posterior probability distribution provides a comprehensive description of the solution in ill-posed inverse problems. Sampling from the posterior distribution in the context of seismic imaging is challenged by the high-dimensionality of the unknown and the expensive-to-evaluate forward operator. These challenges limit the applicability of Markov Chain sampling methods due to the costs associated with the forward operator. Moreover, explicitly choosing a prior distribution that captures the true heterogeneity exhibited by the Earth's subsurface further complicates casting seismic imaging into a Bayesian framework. To handle this situation and to assess uncertainty, we propose a data-driven variational inference approach based on conditional normalizing flows (NFs). The proposed scheme leverages existing data, which are in the form of low- and high-fidelity migrated image pairs, to train a conditional NF capable of characterizing the posterior distribution. After training, the NF can be used to sample from the posterior distribution associated with a previously unseen seismic survey, which is in some sense close, e.g., data from a neighboring survey area. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding band-limited noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image's reliability.
This is joint work with Gabrio Rizzuti, Mathias Louboutin, Philipp A. Witte, and Felix J. Herrmann.