Calculation formulas of linear geometrical spreading for ray tracing in a 3D block inhomogeneous gradient medium

Calculation formulas of linear geometrical spreading for ray tracing in a 3D block inhomogeneous gradient medium

Suitable recurrent formulas are derived for direct programming of linear geometrical spreading of a central field of seismic rays in a 3D block gradient medium. These formulas are needed to organize shooting for area observation systems. For recalculation formulas across an interface, a new represen...

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Veröffentlicht in:Numerical analysis and applications 2009-07, Vol.2 (3), p.260-271
Hauptverfasser: Tsetsokho, V. A., Belonosova, A. V., Belonosov, A. S.
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Mathematics
Mathematics and Statistics
Numerical Analysis
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Belonosova, A. V.
Belonosov, A. S.
description Suitable recurrent formulas are derived for direct programming of linear geometrical spreading of a central field of seismic rays in a 3D block gradient medium. These formulas are needed to organize shooting for area observation systems. For recalculation formulas across an interface, a new representation which involves a special nonorthogonal projection operator is found. This operator allows for additive separation of terms that depend only on the ray curvature, boundary curvature, and variable character of the velocity ratio along the boundary. Formulas which express partial derivatives of the eikonal via linear and angular geometrical spreadings are presented.
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subjects Mathematics
Mathematics and Statistics
Numerical Analysis
title Calculation formulas of linear geometrical spreading for ray tracing in a 3D block inhomogeneous gradient medium
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