@conference {louboutin2018SEGeow,
	title = {Effects of wrong adjoints for RTM in TTI media},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {331-335},
	abstract = {In order to obtain accurate images of the subsurface, anisotropic modeling and imaging is necessary. However, the twenty-one parameter complete wave-equation is too computationally expensive to be of use in this case. The transverse tilted isotropic wave-equation is then the next best feasible representation of the physics to use for imaging. The main complexity arising from transverse tilted isotropic imaging is to model the receiver wavefield (back propagation of the data or data residual) for the imaging condition. Unlike the isotropic or the full physics wave-equations, the transverse tilted isotropic wave-equation is not not self-adjoint. This difference means that time-reversal will not model the correct receiver wavefield and this can lead to incorrect subsurface images. In this work, we derive and implement the adjoint wave-equation to demonstrate the necessity of exact adjoint modeling for anisotropic modeling and compare our result with adjoint-free time-reversed imaging.},
	keywords = {Adjoint, anisotropy, finite-differences, Imaging, RTM, SEG, TTI},
	doi = {10.1190/segam2018-2996274.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/louboutin2018SEGeow/louboutin2018SEGeow.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/louboutin2018SEGeow/louboutin2018SEGeow_pres.pdf},
	author = {Mathias Louboutin and Philipp A. Witte 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}
}
@techreport {witte2015TRoam,
	title = {Overview on anisotropic modeling and inversion},
	number = {TR-EOAS-2015-6},
	year = {2015},
	month = {08},
	institution = {UBC},
	abstract = {This note provides an overview on strategies for modeling and inversion with the anisotropic wave equation. Since linear and non-linear inversion methods like least squares RTM and Full Waveform Inversion depend on matching observed field data with synthetically modelled data, accounting for anisotropy effects is necessary in order to accurately match waveforms at long offsets and propagation times. In this note, the two main strategies for anisotropic modelling by solving either a pseudo acoustic wave equation or a pure quasi-P-wave equation are discussed and an inversion workflow using the pure quasi-P-wave equation is provided. In particular, we derive the exact adjoint of the anisotropic forward modelling and jacobian operator and give a detailled describtion of their implementation. The anistropic FWI workflow is tested on a sythetic data example.},
	keywords = {anisotropy, full waveform inversion, Modeling},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/witte2015TRoam/witte2015TRoam.html},
	author = {Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
