by Einar Iversen, Bjørn Ursin, Teemu Saksala, Joonas Ilmavirta, Maarten V. de Hoop
Abstract:
Dynamic ray tracing is a robust and efficient method for computation of amplitude and phase attributes of the high-frequency Green's function. A formulation of dynamic ray tracing in Cartesian coordinates was recently extended to higher orders. It was demonstrated that the higher-order approach yields a much better extrapolation of traveltime and geometrical spreading into the paraxial region of a reference ray -- for isotropic as well as anisotropic heterogeneous 3-D models of an elastic medium. This is of value in mapping, modelling, and imaging, where kernel operations are based on extrapolation or interpolation of Greens function attributes to densely sampled 3-D grids. As a next step, we introduce higher-order dynamic ray tracing in ray-centred coordinates, which has clear advantages: 1) Such coordinates fit naturally with the wave-propagation problems we study; 2) they lead to a reduction of the number of ordinary differential equations; 3) the initial conditions are simple and intuitive; 4) numerical errors due to redundancies are less likely to influence the results. In a numerical example, we demonstrate that paraxial extrapolation based on higher-order dynamic ray tracing in ray-centred coordinates yields results highly consistent with those obtained using Cartesian coordinates.
Reference:
Higher-order Hamilton-Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in ray-centred coordinates (Einar Iversen, Bjørn Ursin, Teemu Saksala, Joonas Ilmavirta, Maarten V. de Hoop), Geophysical Journal International, volume 226, number 2, pp. 1262–1307, 2021. (PDF available upon request.)
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Dynamic ray tracing is a robust and efficient method for computation of amplitude and phase attributes of the high-frequency Green's function. A formulation of dynamic ray tracing in Cartesian coordinates was recently extended to higher orders. It was demonstrated that the higher-order approach yields a much better extrapolation of traveltime and geometrical spreading into the paraxial region of a reference ray – for isotropic as well as anisotropic heterogeneous 3-D models of an elastic medium. This is of value in mapping, modelling, and imaging, where kernel operations are based on extrapolation or interpolation of Greens function attributes to densely sampled 3-D grids. As a next step, we introduce higher-order dynamic ray tracing in ray-centred coordinates, which has clear advantages: 1) Such coordinates fit naturally with the wave-propagation problems we study; 2) they lead to a reduction of the number of ordinary differential equations; 3) the initial conditions are simple and intuitive; 4) numerical errors due to redundancies are less likely to influence the results. In a numerical example, we demonstrate that paraxial extrapolation based on higher-order dynamic ray tracing in ray-centred coordinates yields results highly consistent with those obtained using Cartesian coordinates.
Bibtex Entry:
@article{hj-high-3,
author = {Einar Iversen and Bj{\o}rn Ursin and Teemu Saksala and Joonas Ilmavirta and Maarten V. de Hoop},
title = {{Higher-order Hamilton-Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in ray-centred coordinates}},
year = {2021},
journal = {Geophysical Journal International},
month = aug,
volume = {226},
number = {2},
pages = {1262--1307},
gsid = {13708043032470600231},
abstract = {Dynamic ray tracing is a robust and efficient method for computation of amplitude and phase attributes of the high-frequency Green's function. A formulation of dynamic ray tracing in Cartesian coordinates was recently extended to higher orders. It was demonstrated that the higher-order approach yields a much better extrapolation of traveltime and geometrical spreading into the paraxial region of a reference ray -- for isotropic as well as anisotropic heterogeneous 3-D models of an elastic medium. This is of value in mapping, modelling, and imaging, where kernel operations are based on extrapolation or interpolation of Greens function attributes to densely sampled 3-D grids. As a next step, we introduce higher-order dynamic ray tracing in ray-centred coordinates, which has clear advantages: 1) Such coordinates fit naturally with the wave-propagation problems we study; 2) they lead to a reduction of the number of ordinary differential equations; 3) the initial conditions are simple and intuitive; 4) numerical errors due to redundancies are less likely to influence the results. In a numerical example, we demonstrate that paraxial extrapolation based on higher-order dynamic ray tracing in ray-centred coordinates yields results highly consistent with those obtained using Cartesian coordinates.},
note = {PDF available upon request.}
}