References related to individual models of package DATA

Model with a lenticular inclusion (LEN)

• 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.
  Model with a lenticular inclusion is designed as an example of constructing a velocity model.
• Klimes, L. (1995): Examples of seismic models. In: Seismic Waves in Complex 3-D Structures, Report 3, Dep. Geophys., Charles Univ., Prague, pp. 5-35, online at "http://sw3d.cz".
  Detailed description of the model with a lenticular inclusion and of input data.
• Bulant, P. (1996): Two-point ray tracing in 3-D. Pure appl. Geophys., 148, 421-447.
  Two-point ray tracing in the model with a lenticular inclusion.
• 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 two-point diffracted rays in the model with a lenticular inclusion.

Preliminary Reference Earth Model (PREM)

Model with homogeneous layers (ELF1, MI)

• Klimes, L. (1995): Examples of seismic models. In: Seismic Waves in Complex 3-D Structures, Report 3, Dep. Geophys., Charles Univ., Prague, pp. 5-35, online at "http://sw3d.cz".
  Detailed description of the model with homogeneous layers and of input data.

Salt dome models (SD1 and SD2)

• Klimes, L. (1995): Examples of seismic models. In: Seismic Waves in Complex 3-D Structures, Report 3, Dep. Geophys., Charles Univ., Prague, pp. 5-35, online at "http://sw3d.cz".
  Detailed description of salt dome models SD1 and SD2 and of input data.

Model with interface slitted by a curved vertical fault (SLIT)

• Bulant, P. and Klimes, L. (1996): Examples of seismic models. Part 2. In: Seismic Waves in Complex 3-D Structures, Report 4, Dep. Geophys., Charles Univ., Prague, pp. 39-52, online at "http://sw3d.cz".
  Detailed description of the model with interface slitted by a curved vertical fault and of input data.

Western Bohemia a priori model (WB2)

• Klimes, L. (1995): Examples of seismic models. In: Seismic Waves in Complex 3-D Structures, Report 3, Dep. Geophys., Charles Univ., Prague, pp. 5-35, online at "http://sw3d.cz".
  Detailed description of the Western Bohemia a priori model and of input data.
• Bulant, P. (1996): Two-point ray tracing in 3-D. Pure appl. Geophys., 148, 421-447.
  Two-point ray tracing in the Western Bohemia a priori model.

Model of a real geological structure (L7)

• Bulant, P. and Klimes, L. (1996): Examples of seismic models. Part 2. In: Seismic Waves in Complex 3-D Structures, Report 4, Dep. Geophys., Charles Univ., Prague, pp. 39-52, online at "http://sw3d.cz".
  Detailed description of this velocity model and of input data.
• 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.
  Two-point ray tracing in this velocity model.

Gridded 2-D Marmousi model (MAR)

• Klimes, L. (1996): Travel times in the INRIA Marmousi models. In: Seismic Waves in Complex 3-D Structures, Report 4, Dep. Geophys., Charles Univ., Prague, pp. 53-60, online at "http://sw3d.cz".
  Ray tracing and calculation of travel times in two continuous INRIA versions of the Marmousi model. Demonstration of ray chaos.
• Klimes, L. (2000): Smoothing the Marmousi model for Gaussian-packet migrations. In: Seismic Waves in Complex 3-D Structures, Report 10, Dep. Geophys., Charles Univ., Prague, pp. 63-74, online at "http://sw3d.cz".
  Preparation of a 2-D velocity model by smoothing the discrete Marmousi model using Sobolev scalar products.
• Zacek, K. (2002): Smoothing the Marmousi model. Pure appl. Geophys., 159, 1507-1526.
  Preparation of a 2-D velocity model by smoothing the discrete Marmousi model using Sobolev scalar products.
• Zacek, K. (2006): Optimization of the shape of Gaussian beams. Stud. geophys. geod., 50, 349-366.
  Optimization of the shape of Gaussian beams in the smooth 2-D velocity model.
• Zacek, K. (2006): Decomposition of the wave field into optimized Gaussian packets. Stud. geophys. geod., 50, 367-380.
  Decomposition of the wave field into optimized Gaussian packets in the smooth 2-D velocity model.
• Zacek, K. (2005): Gaussian packet prestack depth migration. In: Seismic Waves in Complex 3-D Structures, Report 15, Dep. Geophys., Charles Univ., Prague, pp. 29-48, online at "http://sw3d.cz".
  Gaussian packet prestack depth migration with uniform Gaussian packets in the smooth 2-D velocity model.
• Bucha, V. (2008): Gaussian packet prestack depth migration. Part 2: Optimized Gaussian packets. In: Seismic Waves in Complex 3-D Structures, Report 18, Dep. Geophys., Charles Univ., Prague, pp. 129-138, online at "http://sw3d.cz".
  Gaussian packet prestack depth migration with optimized Gaussian packets in the smooth 2-D velocity model.

Unconformity 2-D model (U2D)

• 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".
  Ray-theory synthetic seismograms in 2-D model UNCONFORMITY without attenuation and with attenuation.
• Cerveny, V., Klimes, L. & Psencik, I. (2007): Seismic ray method: Recent developments. Advances in Geophysics, 48, 1-126.
  Ray-theory synthetic seismograms in 2-D model UNCONFORMITY without attenuation and with attenuation (Fig. 40).
• Bucha, V. and 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.

1-D model (RM)

• 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".
  Comparison of ray-matrix and finite-difference synthetic seismograms in simple 1-D model RM.
• Cerveny, V., Klimes, L. & Psencik, I. (2007): Seismic ray method: Recent developments. Advances in Geophysics, 48, 1-126.
  Comparison of ray-matrix and finite-difference synthetic seismograms in simple 1-D model RM (Fig. 41).

Weakly anisotropic model (QI)

• Psencik, I. & Dellinger, J. (2001): Quasi-shear waves in inhomogeneous weakly anisotropic media by the quasi-isotropic approach: a model study. Geophysics, 66, 308-319.
  Description of weakly anisotropic model QI (model WA rotated by 45 degrees). Comparison of quasi-isotropic coupling-ray-theory synthetic seismograms and reflectivity synthetic seismograms in weakly anisotropic model QI.
• Bulant, P. & Klimes, L. (2002): Numerical algorithm of the coupling ray theory in weakly anisotropic media. Pure appl. Geophys., 159, 1419-1435.
  Comparison of coupling-ray-theory synthetic seismograms calculated along isotropic reference rays and quasi-isotropic coupling-ray-theory synthetic seismograms in weakly anisotropic model QI.
• Klimes, L. & Bulant, P. (2004): Errors due to the common ray approximations of the coupling ray theory. Stud. geophys. geod., 48, 117-142.
  Coupling-ray-theory synthetic seismograms calculated along isotropic reference rays in weakly anisotropic models QI, QI2, QI4.
• 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.
  Coupling-ray-theory synthetic seismograms calculated along common S-wave anisotropic reference rays in weakly anisotropic models QI, QI2, QI4. Comparison with coupling-ray-theory synthetic seismograms calculated along isotropic reference rays.
• Cerveny, V., Klimes, L. & Psencik, I. (2007): Seismic ray method: Recent developments. Advances in Geophysics, 48, 1-126.
  Example of development of S-wave splitting with increasing anisotropy in models QIH, QI, QI2, QI4 (Fig. 21). Comparison of quasi-isotropic coupling-ray-theory synthetic seismograms and Chebyshev spectral method synthetic seismograms in weakly anisotropic model QI (Fig. 22).

Sample synthetic 3-D model (98)

• Bulant, P. and 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".
  Construction of the velocity model. Calculation of travel times by interpolation within ray cells. Two-point ray tracing. Ray-theory synthetic seismograms.

1-D anisotropic "twisted crystal" model (TC)

• Klimes, L. (2004): Analytical one-way plane-wave solution in the 1-D anisotropic "simplified twisted crystal" model. Stud. geophys. geod., 48, 75-96.
• 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.

Simple smooth 3-D model (N2)

• Klimes, L. & Kvasnicka, M. (1994): 3-D network ray tracing. Geophys. J. int., 116, 726-738.

2-D representation of the Kummer random medium (RAN)

• Klimes, L. (2002): Correlation functions of random media. Pure appl. Geophys., 159, 1811-1831.
  Example of the Kummer random medium (Fig. 8).
• Cerveny, V., Klimes, L. & Psencik, I. (2007): Seismic ray method: Recent developments. Advances in Geophysics, 48, 1-126.
  Example of the Kummer random medium (Fig. 38). First-arrival travel times in the 2-D representation of the Kummer random medium (Fig. 39).

2-D model with a salt body (HES)

• 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.
  Preparation of a 2-D velocity model by smoothing the discrete 2-D model with a salt body using Sobolev scalar products. Calculation of travel times by interpolation within ray cells.

1-D constant velocity gradient model (VGR)

• Klimes, L. & Kvasnicka, M. (1994): 3-D network ray tracing. Geophys. J. int., 116, 726-738.
• Klimes, L. (1996): Grid travel-time tracing: second-order method for the first arrivals in smooth media. Pure appl. Geophys., 148, 539-563.

SEG/EAGE Salt Model (SAL)

• 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.
  Preparation of a 2-D velocity model by smoothing the discrete 3-D SEG/EAGE Salt Model using Sobolev scalar products. Ray tracing.
• Bulant, P. (2004): Constructing the SEG/EAGE 3-D Salt Model for ray tracing using Sobolev scalar products. Stud. geophys. geod., 48, 689-707.
  Preparation of a 2-D velocity model by smoothing the discrete 3-D SEG/EAGE Salt Model using Sobolev scalar products. Ray tracing.
• Bucha, V. (2006): Ray tracing in the smoothed acoustic SEG/EAGE Salt Model. Part 1: Seismograms. J. seism. Explor., 15, 15-24.
  Two-point ray tracing and synthetic seismograms in the 3-D velocity model with interfaces.
• Bucha, V. (2006): Ray tracing in the smoothed acoustic SEG/EAGE Salt Model. Part 2: Maps of reflections. J. seism. Explor., 15, 153-164.
  Two-point ray tracing, points of reflection and corresponding amplitudes in the 3-D velocity model with interfaces.
• 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.
  Comparison of finite-difference seismograms calculated in the elastic SEG/EAGE Salt Model with travel times calculated in the 3-D velocity model with interfaces.

2-D model Pluto 1.5 (PLU)

• Bulant, P. (2001): Sobolev scalar products in the construction of velocity models - application to model Hess, to SEG/EAGE Salt Model, and to model Pluto 1.5. In: Seismic Waves in Complex 3-D Structures, Report 11, Dep. Geophys., Charles Univ., Prague, pp. 133-159.
  Preparation of a 2-D velocity model with interfaces by smoothing the discrete 2-D model with salt bodies using Sobolev scalar products. Ray tracing.

Computation of R/T coefficients

• Klimes, L. (2003): Weak-contrast reflection-transmission coefficients in a generally anisotropic background. Geophysics, 68, 2063-2072.

Models of the Cotton Valley site (CV)

Model with planar interfaces (EX)

Correlation functions of random media (CORFUN)

• Klimes, L. (2002): Correlation functions of random media. Pure appl. Geophys., 159, 1811-1831.
  Examples of random media (Figs. 2-8).

2-D model P1I with reflection surfaces (P1I)

• Bulant, P. & Martakis, N. (2011): Constructing model P1I for reflection studies In: Seismic Waves in Complex 3-D Structures, Report 21, pp.17-25, Dep. Geophys., Charles Univ., Prague.

Smooth 2-D model P1

• Sachl, L. (2011): 2D computations of 3D synthetic seismograms using the ray-based Born approximation in heterogeneous model P1. In: Seismic Waves in Complex 3-D Structures, Report 21, pp.99-114, Dep. Geophys., Charles Univ., Prague.

Simple models to test the Born approximation

• Sachl, L. (2011): 2D and 3D computations of 3D synthetic seismograms using the ray-based Born approximation in simple models. In: Seismic Waves in Complex 3-D Structures, Report 21, pp.69-98, Dep. Geophys., Charles Univ., Prague.