Entire solutions of a variation of the eikonal equation and related PDEs
Sign Up to like & getrecommendations! Published in 2020 at "Proceedings of the Edinburgh Mathematical Society"
DOI: 10.1017/s0013091520000103
Abstract: Abstract The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or… read more here.
Keywords: solutions variation; variation eikonal; eikonal equation; equation ... See more keywords
The response of laser interferometric gravitational wave detectors beyond the eikonal equation
Sign Up to like & getrecommendations! Published in 2021 at "Classical and Quantum Gravity"
DOI: 10.1088/1361-6382/ac15db
Abstract: The response of Michelson interferometers to weak plane gravitational waves is computed at one order of accuracy beyond the eikonal equation. The modulation of the electromagnetic field amplitude and polarisation are taken into account by… read more here.
Keywords: response laser; laser interferometric; beyond eikonal; eikonal equation ... See more keywords
Upwind, No More: Flexible Traveltime Solutions Using Physics-Informed Neural Networks
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Geoscience and Remote Sensing"
DOI: 10.1109/tgrs.2022.3218754
Abstract: The eikonal equation plays an important role across multidisciplinary branches of science and engineering. In geophysics, the eikonal equation and its characteristics are used in addressing two fundamental questions pertaining to seismic waves: what paths… read more here.
Keywords: informed neural; physics; eikonal equation; upwind flexible ... See more keywords
Properties of C1-solutions to the eikonal equation
Sign Up to like & getrecommendations! Published in 2017 at "Lobachevskii Journal of Mathematics"
DOI: 10.1134/s1995080217040217
Abstract: In this paper we investigate geometrical properties of singular sets of approximated sets, and received results are used for research of smooth solution to the eikonal equation. read more here.
Keywords: properties solutions; equation; solutions eikonal; eikonal equation ... See more keywords
An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis
Sign Up to like & getrecommendations! Published in 2017 at "Geophysics"
DOI: 10.1190/geo2016-0160.1
Abstract: ABSTRACTSeismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because… read more here.
Keywords: equation; transversely isotropic; attenuation; attenuating transversely ... See more keywords