@unpublished {rex2024IMAGEvc,
	title = {Velocity Continuation for Common Image Gathers with Fourier Neural Operators},
	year = {2024},
	month = {3},
	abstract = {Common-image gathers (CIGs) are pivotal in migration-velocity analysis (MVA). However, MVA is often hindered by the computational burden of traditional migration methods. To bypass these limitations, we introduce a neural-surrogate learning approach that utilizes Fourier Neural Operators (FNOs, Li et al. 2020) to accelerate MVA. Following the velocity-continuation scheme of Siahkoohi, Louboutin, and Herrmann (2022), we train a survey-specific FNO to map the CIGs associated with one migration-velocity model to another without remigration. This methodology leverages the capacity of FNOs to approximate complex PDE-based mappings, rendering computational cost at inference negligible, thereby expediting MVA. By enabling rapid generation and evaluation of CIGs across various velocity models, it offers a pathway to quickly examine velocity models according to preferred properties and to quantify uncertainties in imaged reflectivities at the same time. Additionally, this methodology paves the way for inverse design optimization, updating velocity models to produce CIGs with desirable characteristics.},
	keywords = {CIG, deep learning, FNO, Imaging, Uncertainty quantification, velocity continuation},
	url = {https://slimgroup.github.io/IMAGE2024/Rex2024SEG/paper.html},
	author = {Richard Rex and Ziyi Yin and Felix J. Herrmann}
}
@presentation {yin2022ML4SEISMICavc,
	title = {Amortized velocity continuation with Fourier neural operators},
	year = {2022},
	month = {11},
	abstract = {Velocity continuation aims to map the migration image using one background model to the image using another background model. It is of great importance to quantify the uncertainty in seismic imaging result from various background models. With Fourier neural operators as a learned surrogate, this continuation from a given background model to an unseen background model can be quite accurately estimated with near-zero cost. However, the limitation of the prior art is that the input background model and the survey area are assumed to be fixed. The main contribution of this work is to extend the Fourier neural operator surrogate to be amortized over different given background models and survey areas. We verify the effectiveness of our learned surrogates by a realistic example on different areas of Parihaka dataset against different background models.},
	keywords = {Fourier neural operators, ML4SEISMIC, SLIM, Uncertainty quantification, velocity continuation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yin2022ML4SEISMICavc/index.html},
	author = {Ali Siahkoohi and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGvcw,
	title = {Velocity continuation with Fourier neural operators for accelerated uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies{\textendash}-due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.},
	keywords = {Fourier neural operators, SEG, Uncertainty quantification, velocity continuation},
	doi = {10.1190/image2022-3750475.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/Tue-16-30-Siahkoohi.pdf},
	software = {https://github.com/slimgroup/fno4vc},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {kumar2018SEGlreiv,
	title = {Low-rank representation of extended image volumes{\textendash}{\textendash}applications to imaging and velocity continuation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {4418-4422},
	abstract = {In this paper, we present a cost-effective low-rank factorized form of computing the full subsurface extended image volumes without explicitly calculating the receiver wavefields. The propose approach is computationally feasible, which exploits the low-rank structure of full subsurface extended image volumes organized as a matrix, thus avoiding the customary loop over sources. Using carefully selected stylized examples, we show how conventional migration images can be extracted from the low-rank factorized form. We also present a velocity continuation procedure that uses the same low-rank form and allows us to map the extended image for one velocity model to another velocity model without recomputing all the source wavefields.},
	keywords = {image volume, low-rank, SEG, velocity continuation},
	doi = {10.1190/segam2018-2998404.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/kumar2018SEGlreiv/kumar2018SEGlreiv.html},
	author = {Rajiv Kumar and Marie Graff-Kray and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {vanleeuwen2012EAGEext,
	title = {Wave-equation extended images: computation and velocity continuation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {An extended image is a multi-dimensional correlation of source and receiver wavefields. For a kinematically correct velocity, most of the energy will be concentrated at zero offset. Because of the computational cost involved in correlating the wavefields for all offsets, such exteded images are computed for a subsurface offset that is aligned with the local dip. In this paper, we present an efficient way to compute extended images for all subsurface offsets without explicitly calculating the receiver wavefields, thus making it computationally feasible to compute such extended images. We show how more conventional image gathers, where the offset is aligned with the dip, can be extracted from this extended image. We also present a velocity continuation procedure that allows us to compute the extended image for a given velocity without recomputing all the source wavefields.},
	keywords = {EAGE, extended image, velocity continuation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/vanleeuwen2012EAGEext/vanleeuwen2012EAGEext.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/vanleeuwen2012EAGEext/vanleeuwen2012EAGEext_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59616},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
