References related to software package CRT

Detailed description of initial-value Complete Ray Tracing (CRT)

• Cerveny, V., Klimes, L. & Psencik, I. (1988): Complete seismic-ray tracing in three-dimensional structures. In: Doornbos, D.J. (ed.), Seismological Algorithms, pp. 89-168, Academic Press, New York.

Two-point ray tracing algorithm

• Bulant, P. (1996): Two-point ray tracing in 3-D. Pure appl. Geophys., 148, 421-447.
• Bulant, P. (1999): Two-point ray-tracing and controlled initial-value ray-tracing in 3-D heterogeneous block structures. J. seism. Explor., 8, 57-75.

Examples of two-point ray tracing

• Bulant, P. & Klimes, L. (1998): Computations in the model composed during the 1998 consortium meeting. In: Seismic Waves in Complex 3-D Structures, Report 7, Dep. Geophys., Charles Univ., Prague, pp. 33-56, online at "http://sw3d.cz".
• Bucha, V. (2006): Ray tracing in the smoothed acoustic SEG/EAGE Salt Model. Part 1: Seismograms. J. seism. Explor., 15, 15-24.
• Bucha, V. (2006): Ray tracing in the smoothed acoustic SEG/EAGE Salt Model. Part 2: Maps of reflections. J. seism. Explor., 15, 153-164.
• Bucha, V. (2006): Comparison of finite-difference seismograms and ray-theory travel times in the elastic SEG/EAGE Salt Model. J. seism. Explor., 15, 225-239.

Example of calculating two-point diffracted rays

• Bulant, P. (1999): Two-point ray-tracing and controlled initial-value ray-tracing in 3-D heterogeneous block structures. J. seism. Explor., 8, 57-75.

Calculation of travel times by interpolation within ray cells (program mtt.for)

• Bulant, P., & Klimes, L. (1999): Interpolation of ray-theory travel times within ray cells. Geophys. J. int., 139, 273-282.

Examples of interpolation within ray cells

• Bulant, P. & Klimes, L. (1998): Computations in the model composed during the 1998 consortium meeting. In: Seismic Waves in Complex 3-D Structures, Report 7, Dep. Geophys., Charles Univ., Prague, pp. 33-56, online at "http://sw3d.cz".
• Bulant, P. (2002): Sobolev scalar products in the construction of velocity models: Application to model Hess and to SEG/EAGE Salt Model. Pure appl. Geophys., 159, 1487-1506.
• Bulant, P. (2012): Interpolation within ray tubes - state of the art. In: Seismic Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles Univ., Prague, pp. 169-182, online at "http://sw3d.cz".

Calculation of synthetic seismograms (programs green.for, greenss.for)

• Klimes, L. (1996): Synthetic seismograms in 2-D model UNCONFORMITY. In: Seismic Waves in Complex 3-D Structures, Report 4, Dep. Geophys., Charles Univ., Prague, pp. 77-89, online at "http://sw3d.cz".

Examples of synthetic seismograms

• Bucha, V. & Klimes, L. (1999): Finite differences above the MODEL package. In: Seismic Waves in Complex 3-D Structures, Report 8, Dep. Geophys., Charles Univ., Prague, pp. 171-192, online at "http://sw3d.cz".
  Comparison of ray-theory and finite-difference synthetic seismograms in 2-D model UNCONFORMITY without attenuation.

Ray-Born synthetic seismograms

• Sachl, L. (2013): Validation of 3D synthetic seismograms based on the ray-Born approximation. Stud. geophys. geod., 57, 84-102. PDF

Ray tracing in anisotropic media

• Klimes, L. (2006): Ray-centred coordinate systems in anisotropic media. Stud. geophys. geod., 50, 431-447.
• Klimes, L. (2006): Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium. Stud. geophys. geod., 50, 449-461.

Coupling ray theory (program green.for with wan.for)

• Bulant, P. & Klimes, L. (2002): Numerical algorithm of the coupling ray theory in weakly anisotropic media. Pure appl. Geophys., 159, 1419-1435.
• Klimes, L. & Bulant, P. (2004): Errors due to the common ray approximations of the coupling ray theory. Stud. geophys. geod., 48, 117-142.
• Klimes, L. & Bulant, P. (2006): Errors due to the anisotropic-common-ray approximation of the coupling ray theory. Stud. geophys. geod., 50, 463-477.
• Klimes, L. & Bulant, P. (2012): Single-frequency approximation of the coupling ray theory. In: Seismic Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles Univ., Prague, pp. 143-167, online at "http://sw3d.cz".

Examples of coupling ray theory

• Bulant, P., Klimes, L., Psencik, I. & Vavrycuk, V. (2004): Comparison of ray methods with the exact solution in the 1-D anisotropic "simplified twisted crystal" model. Stud. geophys. geod., 48, 675-688.
• Bulant, P. & Klimes, L. (2004): Comparison of quasi-isotropic approximations of the coupling ray theory with the exact solution in the 1-D anisotropic "oblique twisted crystal" model. Stud. geophys. geod., 48, 97-116.
• Bulant, P. & Klimes, L. (2008): Numerical comparison of the isotropic-common-ray and anisotropic-common-ray approximations of the coupling ray theory. Geophys. J. int., 175, 357-374.

Calculation of synthetic seismograms by the ray-matrix method (program greenss.for, package RMATRIX)

• Klimes, L. (1998): Comparison of ray-matrix and finite-difference methods in a simple 1-D model. In: Seismic Waves in Complex 3-D Structures, Report 7, Dep. Geophys., Charles Univ., Prague, pp. 169-180, online at "http://sw3d.cz".
• Thomson, C.J. (1998): Notes on waves in layered media to accompany program Rmatrix. In: Seismic Waves in Complex 3-D Structures, Report 7, Dep. Geophys., Charles Univ., Prague, pp. 147-162, online at "http://sw3d.cz".
• Thomson, C.J. (1998): Notes on Rmatrix, a program to find the seismic plane-wave response of a stack of anisotropic layers. In: Seismic Waves in Complex 3-D Structures, Report 7, Dep. Geophys., Charles Univ., Prague, pp. 163-167, online at "http://sw3d.cz".

Kirchhoff prestack depth migration

• Bucha, V. (2012): Kirchhoff prestack depth migration in 3-D simple models: comparison of triclinic anisotropy with simpler anisotropies. Stud. geophys. geod., 56, 533-552.