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  • Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in ray-centred coordinates
Title: Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in ray-centred coordinates
SUMMARY 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. Extrapolation of traveltime and geometrical spreading was demonstrated to yield significantly higher accuracy—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 Green’s function attributes to densely sampled 3-D grids. We introduce higher-order dynamic ray tracing in ray-centred coordinates, which has certain advantages: (1) such coordinates fit naturally with wave propagation; (2) they lead to a reduction of the number of ordinary differential equations; (3) the initial conditions are simple and intuitive and (4) numerical errors due to redundancies are less likely to influence the computation of the Green’s function attributes. In a 3-D 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. Furthermore, in a 2-D example we show that interpolation of dynamic ray tracing quantities along a wavefront can be done with much better consistency in ray-centred coordinates than in Cartesian coordinates. In both examples we measure consistency by means of constraints on the dynamic ray tracing quantities in the 3-D position space and in the 6-D phase space.  more » « less
Award ID(s):
1815143
PAR ID:
10298820
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Geophysical Journal International
Volume:
226
Issue:
2
ISSN:
0956-540X
Page Range / eLocation ID:
1262 to 1307
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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