Higher-order Hamilton-Jacobi perturbation theory for anisotropic heterogeneous media : Dynamic ray tracing in Cartesian coordinates
Iversen, E., Ursin, B., Saksala, T., Ilmavirta, J., & Hoop, M. V. D. (2019). Higher-order Hamilton-Jacobi perturbation theory for anisotropic heterogeneous media : Dynamic ray tracing in Cartesian coordinates. Geophysical Journal International, 216(3), 2044-2070. https://doi.org/10.1093/gji/ggy533
Published in
Geophysical Journal InternationalDate
2019Copyright
© The Authors 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
With a Hamilton–Jacobi equation in Cartesian coordinates as a starting point, it is common to use a system of ordinary differential equations describing the continuation of first-order derivatives of phase-space perturbations along a reference ray. Such derivatives can be exploited for calculating geometrical spreading on the reference ray and for establishing a framework for second-order extrapolation of traveltime to points outside the reference ray. The continuation of first-order derivatives of phase-space perturbations has historically been referred to as dynamic ray tracing. The reason for this is its importance in the process of calculating amplitudes along the reference ray. We extend the standard dynamic ray-tracing scheme to include higher-order derivatives of the phase-space perturbations. The main motivation is to extrapolate and interpolate amplitude and phase properties of high-frequency Green’s functions to nearby (paraxial) source and receiver locations. Principal amplitude coefficients, geometrical spreading factors, geometrical spreading matrices, ray propagator matrices, traveltimes, slowness vectors and curvature matrices are examples of quantities for which we enhance the computation potential. This, in turn, has immediate applications in modelling, mapping and imaging. Numerical tests for 3-D isotropic and anisotropic heterogeneous models yield clearly improved extrapolation results for the traveltime and geometrical spreading. One important conclusion is that the extrapolation function for the geometrical spreading must be at least third order to be appropriate at large distances away from the reference ray.
...
Publisher
Oxford University PressISSN Search the Publication Forum
0956-540XKeywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/28810421
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
Postdoctoral Researcher, AoFAdditional information about funding
MVdH gratefully acknowledges support from the Simons Foundation under the MATH + X program, the National Science Foundation under grant DMS-1815143 and the corporate members of the Geo-Mathematical Group at Rice University. TS gratefully acknowledges support from the Simons Foundation under the MATH + X program. JI has been supported by the Academy of Finland (decision 295853). BU has received support from the Research Council of Norway through the ROSE project. EI and BU are grateful for being invited to meetings at Rice University. In this work we have used academic software licenses from NORSAR and MATLAB. ...License
Related items
Showing items with similar title or keywords.
-
Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
Giesbertz, Klaas J. H.; Uimonen, Anna-Maija; van Leeuwen, Robert (Springer, 2018)We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential ... -
Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems
Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey (Springer International Publishing, 2018)The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. ... -
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey (Elsevier, 2021)The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing ... -
Approximation of functions over manifolds : A Moving Least-Squares approach
Sober, Barak; Aizenbud, Yariv; Levin, David (Elsevier BV, 2021)We present an algorithm for approximating a function defined over a d-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not ... -
Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals
Haslinger, Jaroslav; Blaheta, Radim; Mäkinen, Raino A. E. (Elsevier, 2021)The paper deals with the identification of material parameters characterizing components in heterogeneous geocomposites provided that the interfaces separating different materials are known. We use the optimal control ...