@article {tu2014fis,
	title = {Fast imaging with surface-related multiples by sparse inversion},
	journal = {Geophysical Journal International},
	volume = {201},
	number = {1},
	year = {2015},
	note = {(Geophysical Journal International)},
	month = {04},
	pages = {304-317},
	abstract = {In marine exploration seismology, surface-related multiples are usually treated as noise mainly because subsequent processing steps, such as migration velocity analysis and imaging, require multiple-free data. Failure to remove these wavefield components from the data may lead to erroneous estimates for migration velocity or result in strong coherent artefacts that interfere with the imaged reflectors. However, multiples can carry complementary information compared to primaries, as they interact with the free surface and are therefore exposed more to the subsurface. Recent work has shown that when processed correctly multiples can improve seismic illumination. Given a sufficiently accurate background velocity model and an estimate for the source signature, we propose a new and computationally efficient linearized inversion procedure based on two-way wave equations, which produces accurate images of the subsurface from the total upgoing wavefield including surface-related multiples. Modelling of the surface-related multiples in the proposed method derives from the well-known surface-related multiple elimination method. We incur a minimal overhead from incorporating the multiples by having the wave-equation solver carry out the multiple predictions via the inclusion of an areal source instead of expensive dense matrix-matrix multiplications. By using subsampling techniques, we obtain high-quality true-amplitude least-squares migrated images at computational costs of roughly a single reverse-time migration (RTM) with all the data. These images are virtually free of coherent artefacts from multiples. Proper inversion of the multiples would be computationally infeasible without using these techniques that significantly bring down the cost. By promoting sparsity in the curvelet domain and using rerandomization, out method gains improved robustness to errors in the background velocity model, and errors incurred in the linearization of the wave equation with respect to the model. We demonstrate the superior performance of the proposed method compared to the conventional RTM using realistic synthetic examples.},
	keywords = {approximate message passing, Compressive Sensing, curvelet, inversion, Kaczmarz, multiples},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2014/tu2014fis/tu2014fis.pdf},
	url2 = {http://gji.oxfordjournals.org/cgi/content/full/ggv020?ijkey=pKzrSXbtxjlOjzd\&keytype=ref},
	author = {Ning Tu and Felix J. Herrmann}
}
@techreport {tschannen2014tdl,
	title = {Time domain least squares migration and dimensionality reduction},
	number = {TR-EOAS-2014-9},
	year = {2014},
	month = {06},
	institution = {UBC},
	abstract = {Least-squares seismic migration (LSM) is a wave equation based linearized inversion problem relying on the minimization of a least-squares misfit function, with respect to the medium perturbation, between recorded and modeled wavefields. Today{\textquoteright}s challenges in Hydrocarbon ex- ploration are to build high resolution images of more and more complicated geological reservoirs, which requires to handle very large systems of equations. The extreme size of the problem com- bined with the fact that it is ill-conditioned make LSM not yet feasible for industrial purposes. To overcome this "curse of dimensionality", dimension reduction and divide-and-conquer tech- niques that aim to decrease the computation time and the required memory, while conserving the image quality, have recently been developed. By borrowing ideas from stochastic optimiza- tion and compressive sensing, the imaging problem is reformulated as an L1-regularized, sparsity promoted LSM. The idea is to take advantage of the compressibility of the model perturbation in the curvelet domain and to work on series of smaller subproblems each involving a small ran- domized subset of data. We try two different subset sampling strategies, artificial randomized simultaneous sources experiments ("supershots") and drawing sequential shots firing at random source locations. These subsets are changed after each subproblem is solved. In both cases we obtain good migration results at significantly reduced computational cost. Application of these methods to a complicated synthetic model yields to encouraging results, underlining the usefulness of sparsity promotion and randomization in time stepping formulation.},
	keywords = {Compressive Sensing, sparsity promotion, Stochastic optimization, Wave equation migration},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/tschannen2014tdl/tschannen2014tdl.pdf},
	author = {Valentin Tschannen and Zhilong Fang and Felix J. Herrmann}
}
