@presentation {witte2016SINBADFpve,
	title = {Phase velocity error minimizing scheme for the anisotropic pure P-wave equation},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Pure P-wave equations for acoustic modeling in transverse isotropic media are derived by approximating the exact pure P-wave dispersion relation. In this work, we present an alternative to the common Taylor expansion based equations, in which we approximate the exact dispersion relation through a polynomial expansion and determine its coefficients by solving a least squares problem that minimizes the phase velocity error over the complete range of phase angles. We show that this approach is up to an order of magnitude more accurate than other pure P-wave equations at a comparable computational cost.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/witte2016SINBADFpve/witte2016SINBADFpve.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/witte2016SINBADFpve/witte2016SINBADFpve.mov},
	author = {Philipp A. Witte and Christiaan C. Stolk 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}
}
