TY - JOUR

T1 - Deep preconditioners and their application to seismic wavefield processing

AU - Ravasi, Matteo

N1 - KAUST Repository Item: Exported on 2022-10-18
Acknowledgements: I thank KAUST for supporting this research. I am also grateful to Claire Birnie (KAUST) for insightful discussions. All numerical examples have been created using the PyLops (Ravasi and Vasconcelos, 2020) and PyTorch (Paszke et al., 2017) computational frameworks.

PY - 2022/9/26

Y1 - 2022/9/26

N2 - Seismic data processing heavily relies on the solution of physics-driven inverse problems. In the presence of unfavourable data acquisition conditions (e.g., regular or irregular coarse sampling of sources and/or receivers), the underlying inverse problem becomes very ill-posed and prior information is required to obtain a satisfactory solution. Sparsity-promoting inversion, coupled with fixed-basis sparsifying transforms, represent the go-to approach for many processing tasks due to its simplicity of implementation and proven successful application in a variety of acquisition scenarios. Nevertheless, such transforms rely on the assumption that seismic data can be represented as a linear combination of a finite number of basis functions. Such an assumption may not always be fulfilled, thus producing sub-optimal solutions. Leveraging the ability of deep neural networks to find compact representations of complex, multi-dimensional vector spaces, we propose to train an AutoEncoder network to learn a nonlinear mapping between the input seismic data and a representative latent manifold. The trained decoder is subsequently used as a nonlinear preconditioner for the solution of the physics-driven inverse problem at hand. Through synthetic and field data examples, the proposed nonlinear, learned transformations are shown to outperform fixed-basis transforms and converge faster to the sought solution for a variety of seismic processing tasks, ranging from deghosting to wavefield separation with both regularly and irregularly subsampled data.

AB - Seismic data processing heavily relies on the solution of physics-driven inverse problems. In the presence of unfavourable data acquisition conditions (e.g., regular or irregular coarse sampling of sources and/or receivers), the underlying inverse problem becomes very ill-posed and prior information is required to obtain a satisfactory solution. Sparsity-promoting inversion, coupled with fixed-basis sparsifying transforms, represent the go-to approach for many processing tasks due to its simplicity of implementation and proven successful application in a variety of acquisition scenarios. Nevertheless, such transforms rely on the assumption that seismic data can be represented as a linear combination of a finite number of basis functions. Such an assumption may not always be fulfilled, thus producing sub-optimal solutions. Leveraging the ability of deep neural networks to find compact representations of complex, multi-dimensional vector spaces, we propose to train an AutoEncoder network to learn a nonlinear mapping between the input seismic data and a representative latent manifold. The trained decoder is subsequently used as a nonlinear preconditioner for the solution of the physics-driven inverse problem at hand. Through synthetic and field data examples, the proposed nonlinear, learned transformations are shown to outperform fixed-basis transforms and converge faster to the sought solution for a variety of seismic processing tasks, ranging from deghosting to wavefield separation with both regularly and irregularly subsampled data.

UR - http://hdl.handle.net/10754/679901

UR - https://www.frontiersin.org/articles/10.3389/feart.2022.997788/full

UR - http://www.scopus.com/inward/record.url?scp=85139479235&partnerID=8YFLogxK

U2 - 10.3389/feart.2022.997788

DO - 10.3389/feart.2022.997788

M3 - Article

SN - 2296-6463

VL - 10

JO - Frontiers in Earth Science

JF - Frontiers in Earth Science

ER -