@techreport {witte2016OGHPClst,
	title = {A large-scale time-domain seismic modeling and inversion workflow in Julia},
	number = {TR-EOAS-2017-1},
	year = {2017},
	institution = {UBC},
	abstract = {We present our initial steps towards the development of a large-scale seismic modeling workflow in Julia that provides a framework for wave equation based inversion methods like full waveform inversion or least squares migration. Our framework is based on the Devito, a finite difference domain specific language compiler that generates highly optimized and parallel code. We develop a flexible workflow that is based on abstract matrixfree linear operators and enables developers to write code that closely resembles the underlying math, while at the same time leveraging highly optimized wave equation solvers, allowing us to solve large-scale three-dimensional inverse problems.},
	keywords = {HPC, inversion, Modelling},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/witte2016OGHPClst/witte2016OGHPClst.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Gerard Gorman and Felix J. Herrmann}
}
@techreport {louboutin2016OGHPCocp,
	title = {Optimizing the computational performance of time-domain modelling{\textendash}-leveraging multiple right-hand-sides},
	number = {TR-EOAS-2017-2},
	year = {2017},
	institution = {UBC},
	abstract = {Exploration geophysics heavily relies upon fast solvers for the wave-equation and its adjoint. The main computational cost of a wave-equation solver is to compute the Laplacian, or more complex finite-difference operators, at every time step. The performance of many discretizations is limited by the relatively low operational intensity (number of floating point operations divided by memory traffic) of the finite-difference stencil. Solving the wave-equation for multiple sources/right-hand-sides (RHSs) at once mitigates this problem by increasing the operational intensity. This is implemented by rewriting the classical matrix-vector product into a matrix-matrix product where each column of the second matrix represent the solution wavefield for each given source. This minor modification to the solver is shown to achieve a 2-4 times speedup compared to a single source solver. We concentrate in this paper on acoustic modelling, but our approach can easily be extended to anisotropic or elastic cases for both forward and adjoint modelling.},
	keywords = {finite differences, HPC, Modelling, time domain},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/louboutin2016OGHPCocp/louboutin2016OGHPCocp.pdf},
	author = {Mathias Louboutin and Gerard Gorman and Felix J. Herrmann}
}
@conference {louboutin2017SIAMras,
	title = {Raising the abstraction to separate concerns: enabling different physics for geophysical exploration},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	abstract = {Full-waveform inversion is a PDE-constrained optimisation problem involving massive amounts of data (petabytes) and large numbers of unknowns (O(10^9)). This well known compute-intensive and data-intensive is extremely challenging for several reasons. First, there is the complexity of having to handle extremely large data volumes with metadata related to experimental details in the field, and the discretization of the unknown earth parameters and approximate physics. Second, reduced or adjoint-state methods call for computationally intensive PDE solves for each source experiment (of which there are thousands) for each iteration of a gradient-based optimization scheme. The talks will give an overview how carefully chosen layers of abstraction can help manage both the complexity and scale of inversion while still achieving the high degree of computational performance required to make full-waveform a practical tool. Specifically, the presentations will focus on domain specific stencil language for time-stepping methods to solve various types of wave equations and on abstracts for large-scale parallel optimization frameworks.},
	keywords = {finite differences, HPC, Modelling, SIAM, time domain},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/louboutin2017SIAMras/louboutin2017SIAMras_pres.mov},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/louboutin2017SIAMras/louboutin2017SIAMras_pres.pdf},
	author = {Mathias Louboutin and Michael Lange and Navjot Kukreja and Fabio Luporini and Felix J. Herrmann and Gerard Gorman}
}
@techreport {louboutin2016SEGocp,
	title = {Optimizing the computational performance and maintainability of time-domain modelling{\textendash}-leveraging multiple right-hand-sides},
	number = {TR-EOAS-2016-2},
	year = {2016},
	month = {06},
	institution = {UBC},
	abstract = {Numerical solvers for the wave equation are a key component of Full-Waveform Inversion (FWI) and Reverse-Time Migration (RTM). The main computational cost of a wave-equation solver stems from the computation of the Laplacian at each time step. When using a finite difference discretization this can be characterized as a structured grid computation within Colella{\textquoteright}s Seven Dwarfs. Independent of the degree of parallelization the performance will be limited by the relatively low operational intensity (number of operations divided by memory traffic) of finite-difference stencils, that is so say that the method is memory bandwidth bound. For this reason many developers have focused on porting their code to platforms that have higher memory bandwidth, such as GPU{\textquoteright}s, or put significant effort into highly intrusive optimisations. However, these optimisations rarely strike the right performance vs productivity balance as the software becomes less maintainable and extensible. By solving the wave equation for multiple sources/right-hand-sides (RHSs) at once, we overcome this problem arriving at a time-stepping solver with higher operational intensity. In essence, we arrive at this result by turning the usual matrix-vector products into a matrix-matrix products where the first matrix implements the discretized wave equation and each column of the second matrix contain separate wavefields for each given source. By making this relatively minor change to the solver we readily achieved a $\times2$ speedup. While we limit ourselves to acoustic modeling, our approach can easily be extended to the anisotropic or elastic cases.},
	keywords = {3D, Modelling, time domain},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2016/louboutin2016SEGocp/louboutin2016SEGocp.html},
	author = {Mathias Louboutin and Gerard Gorman and Felix J. Herrmann}
}
@conference {witte2016SEGpve,
	title = {Phase velocity error minimizing scheme for the anisotropic pure P-wave equation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {452-457},
	abstract = {Pure P-wave equations for acoustic modeling in transverse isotropic media are derived by approximating the exact pure Pwave dispersion relation. In this work, we present an alternative approach to the approximate dispersion relation of Etgen and Brandsberg-Dahl, in which we approximate the exact dispersion relation through a polynomial expansion and determine its coefficients by solving a linear least squares problem that minimizes the phase velocity error over the entire range of phase angles. The coefficients are also optimized over a pre-defined range of Thomsen parameters, so that the phase error is small for models with spatially varying anisotropy. Phase velocity error analysis shows that the optimized pure P-wave equation is up to one order of magnitude more accurate than other popular pure P-wave equations, even for highly non-elliptic anisotropy. The optimized equation can be easily turned into a time-domain forward modeling scheme and comparisons of the modeled waveforms with analytical travel times once more illustrate its high accuracy. We also provide an efficient implementation of our approach for 3D tilted TI media that limits the count of fast Fourier transforms per time step to a number that is comparable to other pure P-wave equations.},
	keywords = {anisotropy, least squares, Modelling, SEG, TTI},
	doi = {10.1190/segam2016-13844850.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/witte2016SEGpve/witte2016SEGpve.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/witte2016SEGpve/witte2016SEGpve_poster.pdf},
	author = {Philipp A. Witte and Christiaan C. Stolk and Felix J. Herrmann}
}
@conference {zheglova2014EAGEams,
	title = {Application of matrix square root and its inverse to downward wavefield extrapolation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {In this paper we propose a method for computation of the square root of the Helmholtz operator and its inverse that arise in downward extrapolation methods based on one-way wave equation. Our approach involves factorization of the discretized Helmholtz operator at each depth by extracting the matrix square root after performing the spectral projector in order to eliminate the evanescent modes. The computation of the square root of the discrete Helmholtz operator and its inverse is done using polynomial recursions and can be combined with low rank matrix approximations to reduce the computational cost for large problems. The resulting square root operator is able to model the propagating modes kinematically correctly at the angles of up to 90 degree. Preliminary results on convergence of iterations are presented in this abstract. Potential applications include seismic modeling, imaging and inversion.},
	keywords = {EAGE, extrapolation, Modelling, one-way wave equation, square root},
	doi = {10.3997/2214-4609.20141184},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/zheglova2014EAGEams/zheglova2014EAGEams.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/zheglova2014EAGEams/zheglova2014EAGEams_pres.pdf},
	author = {Polina Zheglova and Felix J. Herrmann}
}
@article {herrmann2009GEOPcsf,
	title = {Compressive simultaneous full-waveform simulation},
	journal = {Geophysics},
	volume = {74},
	number = {4},
	year = {2009},
	month = {07-08},
	pages = {A35-A40},
	abstract = {The fact that computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem{\textendash}-where simulated data is recovered from a relatively small number of independent simultaneous sources{\textendash}-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield{\textquoteright}s sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.},
	keywords = {Compressive Sensing, full-waveform, Modelling, SLIM},
	doi = {10.1190/1.3115122},
	url = {http://library.seg.org/doi/abs/10.1190/1.3115122},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcsf/herrmann2009GEOPcsf.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@article {lin2007GEOPcwe,
	title = {Compressed wavefield extrapolation},
	journal = {Geophysics},
	volume = {72},
	number = {5},
	year = {2007},
	month = {08},
	pages = {SM77-SM93},
	publisher = {SEG},
	abstract = {An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Modelling, SLIM, wave propagation},
	doi = {10.1190/1.2750716},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2007/lin07cwe/lin07cwe.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@article {herrmann2005ICAEsdb,
	title = {Seismic deconvolution by atomic decomposition: a parametric approach with sparseness constraints},
	journal = {Integrated Computer-Aided Engineering},
	volume = {12},
	number = {1},
	year = {2005},
	month = {01},
	pages = {69-90},
	publisher = {IOS Press},
	address = {Amsterdam, The Netherlands},
	abstract = {In this paper an alternative approach to the blind seismic deconvolution problem is presented that aims for two goals namely recovering the location and relative strength of seismic reflectors, possibly with super-localization, as well as obtaining detailed parametric characterizations for the reflectors. We hope to accomplish these goals by decomposing seismic data into a redundant dictionary of parameterized waveforms designed to closely match the properties of reflection events associated with sedimentary records. In particular, our method allows for highly intermittent non-Gaussian records yielding a reflectivity that can no longer be described by a stationary random process or by a spike train. Instead, we propose a reflector parameterization that not only recovers the reflector{\textquoteright}s location and relative strength but which also captures reflector attributes such as its local scaling, sharpness and instantaneous phase-delay. The first set of parameters delineates the stratigraphy whereas the second provides information on the lithology. As a consequence of the redundant parameterization, finding the matching waveforms from the dictionary involves the solution of an ill-posed problem. Two complementary sparseness-imposing methods Matching and Basis Pursuit are compared for our dictionary and applied to seismic data.},
	keywords = {deconvolution, Modelling, Processing, SLIM},
	issn = {1069-2509},
	url = {http://dl.acm.org/citation.cfm?id=1238980.1238986},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/IntegratedComputerAidedEngineering/2005/herrmann2005ICAEsdb/herrmann2005ICAEsdb.pdf},
	author = {Felix J. Herrmann}
}
@article {herrmann2004GJIssa,
	title = {Seismic singularities at upper-mantle phase transitions: a site percolation model},
	journal = {Geophysical Journal International},
	volume = {159},
	number = {3},
	year = {2004},
	month = {12},
	pages = {949-960},
	abstract = {Mineralogical phase transitions are usually invoked to account for the sharpness of globally observed upper-mantle seismic discontinuities. We propose a percolation-based model for the elastic properties of the phase mixture in the coexistence regions associated with these transitions. The major consequence of the model is that the elastic moduli (but not the density) display a singularity at the percolation threshold of the high-pressure phase. This model not only explains the sharp but continuous change in seismic velocities across the phase transition, but also predicts its abruptness and scale invariance, which are characterized by a non-integral scale exponent. Using the receiver-function approach and new, powerful signal-processing techniques, we quantitatively determine the singularity exponent from recordings of converted seismic waves at two Australian stations (CAN and WRAB). Using the estimated values, we construct velocity{\textendash}depth profiles across the singularities and verify that the calculated converted waveforms match the observations under CAN. Finally, we point out a series of additional predictions that may provide new insights into the physics and fine structure of the upper-mantle transition zone.},
	keywords = {Modelling, percolation, SLIM},
	doi = {10.1111/j.1365-246X.2004.02464.x},
	author = {Felix J. Herrmann and Y. Bernab{\'e}}
}
