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Title: Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: transformation between Cartesian and ray-centred coordinates
SUMMARY Within the field of seismic modelling in 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 (conventional) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between Cartesian and ray-centred phase-space perturbations. 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 Cartesian and ray-centred phase-space perturbations. By numerical examples, we (1) visualize the validity limits of the ray-centred coordinate system, (2) demonstrate the more » transformation of higher-order derivatives of traveltime from Cartesian to ray-centred coordinates and (3) address the stability of function value and derivatives of volumetric parameters in a higher-order representation of the subsurface model. « less
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Publication Date:
Journal Name:
Geophysical Journal International
Page Range or eLocation-ID:
893 to 927
Sponsoring Org:
National Science Foundation
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