@presentation {rizzuti2021ML4SEISMICdfw,
	title = {A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion},
	year = {2021},
	month = {11},
	abstract = {Many of the seismic inversion techniques currently proposed that focus on robustness with respect to the background model choice are not apt to large-scale 3D applications, and the methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously limited by convergence stagnation and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting models or inaccurate parameters (such as anisotropy) that are typically kept fixed during inversion. It is based on a dual reformulation of the classical wavefield reconstruction inversion, whose empirical robustness with respect to these issues is well documented in the literature. While the classical version is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation, our proposal allows the deployment of state-of-the-art time-domain finite-difference methods, and is potentially mature for industrial-scale problems.},
	keywords = {FWI, ML4SEISMIC, SLIM, wave-equation, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/rizzuti2021ML4SEISMICdfw/Tue-10-55-Rizzuti.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@conference {rizzuti2021SIAMGSwrid,
	title = {Time-domain Wavefield Reconstruction Inversion for large-scale seismic inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2021},
	note = {(SIAM GS, virtual)},
	month = {06},
	abstract = {Data fitting based on a wave equation model has driven the modern development in seismic imaging, and it is now relevant for large scale inversion. A wider adoption is currently being limited by available computational resources and the classical limitations of non-linear optimization, which often produces suboptimal local minima. A class of methods based on the inexact solution of the wave equation, known as wavefield reconstruction inversion, have shown remarkable robustness towards local minima, however the solvers required for the inexact wave equation scale badly to 3D problems. We propose a reformulation of wavefield reconstruction inversion which involves the solution of the classical time-domain wave equation, and it is practical for large-scale problems. Applications to tilted-transverse isotropy synthetic datasets clearly demonstrate the advantage over traditional full-waveform inversion.},
	keywords = {FWI, SIAM, time domain, WRI},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMGS/2021/rizzuti2021SIAMGSwrid/rizzuti2021SIAMGSwrid.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Felix J. Herrmann}
}
@conference {rizzuti2019SIAMGStwri,
	title = {A dual formulation for time-domain wavefield reconstruction inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2019},
	note = {(SIAM GS)},
	month = {03},
	abstract = {Wavefield reconstruction inversion (WRI) is based on the combination of data misfit and PDE-residual penalty terms, and it aims at the reconstruction of the optimal property model and field pair. A full-space optimization would require the storage of field variables for every frequency or time sample (and every source). Remedies via variable projection are well studied, but they entail the solution of a modified wave equation, which is costly both in frequency and time domain. Here, we explore an efficient alternative to WRI, where properties are complemented, instead, by elements of the dual data space. The starting point of our proposal is the denoising reformulation of WRI: the PDE compliance is optimized under the constraint of a given data fit. Since the field variable can be eliminated from the associated saddle-point problem, we obtain a new objective functional of only properties and Lagrange multipliers. Its evaluation, and gradient computation, involves the solution of the original wave equation, which is amenable to time-domain discretization. The optimization scheme of choice can now leverage on affordable storage of the iterates.},
	keywords = {WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMGS/2019/rizzuti2019SIAMGStwri/rizzuti2019SIAMGStwri.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@article {fang2017sewri,
	title = {Source estimation for wavefield-reconstruction inversion},
	journal = {Geophysics},
	volume = {83},
	number = {4},
	year = {2018},
	note = {(Geophysics)},
	pages = {R345-R359},
	abstract = {Source estimation is essential to all the wave-equation-based seismic inversions, including full-waveform inversion and the recently proposed wavefield-reconstruction inversion. When the source estimation is inaccurate, errors will propagate into the predicted data and introduce additional data misfit. As a consequence, inversion results that minimize this data misfit may become erroneous. To mitigate the errors introduced by the incorrect and pre-estimated sources, an embedded procedure that updates sources along with medium parameters is necessary for the inversion. So far, such a procedure is still missing in the context of wavefield-reconstruction inversion, a method that is, in many situations, less prone to local minima related to the so-called cycle skipping, compared to full-waveform inversion through exact data-fitting. While wavefield-reconstruction inversion indeed helps to mitigate issues related to cycle skipping by extending the search space with wavefields as auxiliary variables, it relies on having access to the correct source functions. In this paper, we remove the requirement of having the accurate source functions by proposing a source estimation technique specifically designed for wavefield-reconstruction inversion. To achieve this task, we consider the source functions as unknown variables and arrive at an objective function that depends on the medium parameters, wavefields, and source functions. During each iteration, we apply the so-called variable projection method to simultaneously project out the source functions and wavefields. After the projection, we obtain a reduced objective function that only depends on the medium parameters and invert for the unknown medium parameters by minimizing this reduced objective. Numerical experiments illustrate that this approach can produce accurate estimates of the unknown medium parameters without any prior information of the source functions.},
	keywords = {estimation, FWI, source, variable projection, WRI},
	doi = {10.1190/geo2017-0700.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/fang2017sewri/fang2017sewri.html},
	author = {Zhilong Fang and Rongrong Wang and Felix J. Herrmann}
}
@conference {wang2015SIAMwds,
	title = {Wavefield-denoising and source encoding},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2015},
	note = {(SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, California)},
	month = {06-07},
	keywords = {SIAM, source encoding, WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/wang2015SIAMwds/wang2015SIAMwds_pres.pdf},
	author = {Rongrong Wang and Ozgur Yilmaz and Felix J. Herrmann}
}
