Report 22 of the Consortium project "Seismic Waves in Complex 3-D Structures" (SW3D) summarizes the work done towards the end of the eighteenth year and during the nineteenth year of the project, in the period June, 2011 - May, 2012. It also includes the DVD compact disk with updated and extended versions of computer programs distributed to the sponsors, with brief descriptions of the programs, and with the copy of the SW3D WWW pages containing papers from previous reports and articles from journals.

Consortium project "Seismic Waves in Complex 3-D Structures" has a new and simple address of its WWW pages since November 13, 2007.

Our group working within the project during the nineteenth year has consisted of five research workers Vaclav Bucha, Petr Bulant, Vlastislav Cerveny, Ludek Klimes and Ivan Psencik. MSc student Libor Sachl, who worked on the ray-based Born approximation, defended his MSc thesis on September 20, 2011.

Amir Askari (Tehran, Iran), Andrej Bona (Curtin University, Perth, Australia), Veronique Farra (Inst. Physique du Globe de Paris, France), Bjorn Ursin (Tech. University Trondheim, Norway), Umair bin Waheed (King Abdullah University of Science and Technology, Thuwal, Saudi Arabia) and Matthew Yedlin (University of British Columbia, Vancouver, Canada) visited us during the period May, 2011 - May, 2012.

Ivan Psencik was a member of the technical committee preparing the 15th International Workshop on Seismic Anisotropy in Bahrain in 2012, and served as the editor of the special issue of Studia Geophysica et Geodaetica (No. 1/2012) with the proceedings from international workshop "Seismic waves in laterally inhomogeneous media VII" held at the Tepla Premonstratensian Monastery in Czech Republic on June 21-26, 2010. Ivan Psencik also served as the editor of the special issue of Studia Geophysica et Geodaetica (No. 2/2012) dedicated to Vlastislav Cerveny on the occasion of his eightieth birthday. These special issues are distributed to the Consortium members together with this Report 22.

This Introduction is followed by the list of members of the SW3D Consortium during the nineteenth year of the project.

The Research Programme for the current, nineteenth year of the Consortium project comes after the list of members. The Research Programme for the next year will be prepared after the discussion at the Consortium meeting, June 11-12, 2012. More detailed information regarding the SW3D Consortium project is available online at "".

Research Report 22 contains mostly the papers related to seismic anisotropy (7 of 10 papers). Report 22 may roughly be divided into five parts, see the Contents.

The first part, Velocity models and inversion techniques, is devoted to various kinds of inverse problems, to the theory developed for application to their solution, and to the construction of velocity models suitable for ray tracing and for application of ray-based high-frequency asymptotic methods.

In paper "Effects of 1-D versus 3-D velocity models on moment tensor inversion in the Dobra Voda locality at the Male Karpaty region, Slovakia", Z. Jechumtalova and P. Bulant show their results obtained during the cooperation with Slovak industrial partner ProgSeis within the framework of the European Commission's FP7 consortium project "Advanced Industrial Microseismic Monitoring". They apply the software developed within the SW3D Consortium to smoothing 1-D and 3-D velocity models of the Dobra Voda locality, and to the calculation of ray-theory amplitudes which they then use within the moment tensor inversion using the software developed by the group lead by Jan Sileny at the Institute of Geophysics, Academy of Sciences of the Czech Republic.

In paper "Kirchhoff prestack depth migration in velocity models with and without gradients: Comparison of triclinic anisotropy with simpler anisotropies" V. Bucha shows the behaviour of the 3-D Kirchhoff prestack depth migration in the presence of triclinic anisotropy and vertical or horizontal velocity gradients. V. Bucha then studies the effects of incorrectly estimated anisotropy and of simple heterogeneity upon the migrated image.

In paper "Moveout approximation for P waves in a homogeneous VTI medium", V. Farra and I. Psencik use the formulae, which they derived in their previous works on wave propagation in weakly anisotropic media. They apply them to the derivation of the P-wave moveout approximation. The resulting formulae have a simple character, depend on four parameters with clear physical or geometrical meaning and yield results whose accuracy is comparable or better than most of commonly used moveout approximations. The authors are developing the theory applicable in migration or inversion, rather than performing inversion itself.

The second part, Ray-based Born approximation, is devoted to the first-order Born approximation.

L. Sachl continued his work on the ray-based Born approximation towards the end of the nineteenth year of the project, and prepared two new papers, the revised versions of which are presented in this report. Paper "Effect of caustics on the ray-based Born approximation", is devoted to (a) the problems with caustics corresponding to the incident ray-theory wavefield or to the ray-theory Green tensor from a receiver; (b) the considerable improvement of the accuracy of the reflected wave containing a caustic if the reflected wave is calculated by the Born approximation. L. Sachl then presents his final P-P Born scattering seismograms in paper "Born and ray-theory seismograms in 2D heterogenous isotropic models".

The third part, Paraxial ray methods in anisotropic media, is devoted to two-point paraxial travel times, which represent the travel times between two points chosen in a paraxial vicinity of the reference ray situated in inhomogeneous anisotropic media. The approximate formulae for these paraxial travel times have recently been derived in paper "Cerveny, V., Iversen, E. & Psencik, I. (2012): Two-point paraxial traveltimes in an inhomogeneous anisotropic medium. Geophys. J. int., 189, 1597-1610".

In paper "Tests of two-point paraxial traveltime formula in inhomogeneous anisotropic media" U. bin Waheed, V. Cerveny, E. Iversen and I. Psencik test efficiency and accuracy of the two-point paraxial travel time formula on models of smoothly varying isotropic and also anisotropic media. It is shown that for sufficiently distant two points in the studied models, the formula yields accurate results to a great distance from the reference ray. Application of the formula to the problem of perturbation of the source and receivers solved recently by the method based on numerical solution of the eikonal equation leads to increased efficiency and accuracy.

In paper "Two-point paraxial travel times using dynamic ray tracing in wavefront orthonormal coordinates", V. Cerveny, E. Iversen and I. Psencik generalize the above mentioned formulae for the two-point paraxial travel times to the situation in which the paraxial ray propagator matrix is computed along the reference ray by dynamic ray tracing in wavefront orthonormal coordinates.

The fourth part, Waves in weakly anisotropic elastic media, addresses the problems relevant to wave propagation in heterogeneous weakly anisotropic elastic media.

Paper "Second-order traveltimes and first-order spreading of reflected/transmitted P waves in inhomogeneous, weakly anisotropic media" by I. Psencik and V. Farra is the expanded abstract presented at the 15th International workshop on seismic anisotropy (IWSA) in Bahrain. The paper represents partial extension of the authors' work on first-order ray tracing in inhomogeneous weakly anisotropic media to laterally varying layered media.

After many years of their effort, P. Bulant and L. Klimes at last proposed the approximation of the coupling-ray-theory Green tensor by two S waves described by the coupling-ray-theory travel times and the coupling-ray-theory amplitudes in paper "Single-frequency approximation of the coupling ray theory". This approximation enables to interpolate the coupling ray theory results within ray cells and to use the coupling ray theory in all applications where we have used the standard ray theory up to now.

The fifth and final part, DVD-ROM with SW3D software, data and papers, contains the DVD-R compact disk SW3D-CD-16 and a related paper.

Since 1992, P. Bulant worked on developing a reliable 3-D two-point ray tracing algorithm based on previously developed initial-value ray tracing algorithm. Since 1997, P. Bulant worked on the interpolation within ray tubes, based on his algorithm of controlled initial-value ray tracing. In review paper "Interpolation within ray tubes - state of the art", P. Bulant summarizes the present algorithms and codes for controlled initial-value ray tracing and interpolation within ray tubes, and describes their applicability, especially with respect to velocity models.

Compact disk SW3D-CD-16, edited by V. Bucha and P. Bulant, contains the revised and updated versions of the software developed within the Consortium research project, together with input data related to the papers published in the Consortium research reports. A more detailed description can be found directly on the compact disk. Compact disk SW3D-CD-16 also contains over 430 complete papers from journals and previous reports in PostScript, PDF, GIF or HTML, and 3 books by V. Cerveny in PDF. Refer to the copy of the Consortium WWW pages on the compact disk. Compact disk SW3D-CD-16 is included in Report 22 in two versions, as the UNIX disk and DOS disk. The versions differ just by the form of ASCII files.


We are very grateful to all our sponsors for the financial support. The research has also been partially supported by the Grant Agency of the Czech Republic under contracts P210/10/0736 and P210/11/0117, by the Grant Agency of the Academy of Sciences of the Czech Republic under contract IAA300120801, by the Ministry of Education of the Czech Republic within research project MSM0021620860, and by the European Commission within FP7 project 230669 "Advanced Industrial Microseismic Monitoring".

Prague, June 2012

Vlastislav Cerveny
Ludek Klimes
Ivan Psencik

In: Seismic Waves in Complex 3-D Structures, Report 22, pp. 5-8, Dep. Geophys., Charles Univ., Prague, 2012.
This Introduction to Report 22 is also available in PDF (42 kB).