@article{hj-high-2,
	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: transformation between Cartesian and ray-centred coordinates}},
	journal = {Geophysical Journal International},
	year = {2021},
	month = aug,
	volume = {226},
	number = {2},
	pages = {893--927},
	abstract = {Within the field of seismic modelling for anisotropic media, dynamic ray tracing is a powerful technique for computation of amplitude and phase properties of the high-frequency Green's function. Dynamic ray tracing is based on solving a system of Hamilton-Jacobi perturbation equations, which may be expressed in different 3-D coordinate systems. We consider two particular coordinate systems; a Cartesian coordinate system with a fixed origin and a curvilinear ray-centred coordinate system associated with a reference ray. For each system we form the corresponding 6-D phase spaces, which encapsulate six degrees of freedom in the variation of position and momentum. The formulation of (standard) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between the ray-centred and Cartesian phase spaces. Such transformation can also be used for defining initial conditions for dynamic ray tracing in Cartesian coordinates and for obtaining the coefficients involved in two-point traveltime extrapolation. As a step towards extending dynamic ray tracing in ray-centred coordinates to higher orders we establish detailed information about the higher-order properties of the transformation between the ray-centred and Cartesian phase spaces. By numerical examples, we 1) address the validity limits of the ray-centred coordinate system, and 2) demonstrate the transformation of higher-order derivatives of traveltime from Cartesian to ray-centred coordinates.},
	note = {PDF available upon request.}
}