The research project "Seismic waves in complex 3-D structures" (SW3D) started on October 1, 1993. The project reached the end of its twenty-seventh year on September 30, 2020, and still continues.

The Volume 30 of the serial Seismic Waves in Complex 3-D Structures of the annual reports of research project "Seismic waves in complex 3-D structures" summarizes the work done in the period December, 2019 - December, 2020. It also includes the DVD compact disk with updated and extended versions of computer programs, with brief descriptions of the programs, and with the copy of the SW3D research project WWW pages containing papers from previous volumes and articles from other journals.

Our group working within the project during the twenty-seventh year has consisted of five research workers: Vaclav Bucha, Petr Bulant, Vlastislav Cerveny, Ludek Klimes and Ivan Psencik. Ivan Psencik is the supervisor of PhD students Milosz Wcislo, with the PhD thesis on "Seismic waves in inhomogeneous, weakly dissipative, anisotropic media", and Han Xiao of Jilin University, China, who works on the inversion of reflection seismic data in anisotropic media.

Veronique Farra (Universite de Paris, France) visited us since the publication of the preceding Volume 29 in December, 2019.

The Research Programme for the twenty-fourth year of the SW3D research project, published in the Volume 27 of the serial Seismic Waves in Complex 3-D Structures, still holds. More detailed information regarding the SW3D research project is available online at "".

The Volume 30 contains mostly the papers related to seismic anisotropy (6 of 7 papers). Two papers are devoted to attenuation. The Volume 30 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 solving, and to constructing velocity models suitable for ray tracing and for application of ray-based high-frequency asymptotic methods.

H. Xiao & I. Psencik use in their contribution "Determination of P-wave anisotropic parameters and thickness of a single layer of arbitrary anisotropy from traveltimes of a reflected P wave" the approximate travel-time formula for a P wave reflected at the bottom of an anisotropic layer derived and presented by V. Farra and I. Psencik in previous Volumes 28 and 29. The authors of the present study use the formula for an estimate of nine of fifteen P-wave anisotropic parameters specifying anisotropy of the layer, and also for an estimate of the thickness of the layer. These anisotropic parameters represent an alternative to the elements of the stiffness tensor. Weak-to-moderate anisotropy of any symmetry and orientation can be considered. The inversion scheme is tested on several models with varying anisotropy symmetry and strength.

Paper "Kirchhoff prestack depth scalar migration of complete wave fields in a simple velocity model with triclinic anisotropy: PP, PS1 and PS2 waves" by V. Bucha continues and verifies promising imaging results presented in the related papers of previous Volumes 28 and 29, applying the prevailing-frequency approximation of the coupling ray theory to migrating S waves. V. Bucha now considers a homogeneous triclinic velocity model whereas he used inhomogeneous weakly anisotropic velocity models in his paper of the Volume 29. Moreover, he now calculates migrated sections for all three components of PP, PS1 and PS2 reflected waves.

The second part, Ray methods in isotropic media, is devoted to the development of ray methods and related numerical algorithms.

After we designed the interpolation within ray cells in the Volume 7, some researchers including consortium members were curious about the numerical efficiency of the proposed algorithm. P. Bulant thus numerically tested the efficiency in the Volumes 8 and 10. In his contribution "Two factors affecting the speed of interpolation within ray cells" P. Bulant synthesizes the latter two studies which are closely related.

The third part, Waves in anisotropic elastic media, addresses the problems relevant to heterogeneous anisotropic elastic media.

V. Farra & I. Psencik, in their contribution "Approximate P-wave reflection coefficient in weakly-to-moderately anisotropic media of arbitrary tilt" offer an approximate formula for the reflection coefficient of a P wave reflected at the interface between two half-spaces of arbitrary but weak-to-moderate anisotropy. Parameterization by weak-anisotropy parameters is applied. Advantage of this parameterization consists in its unique use for all types and orientations of anisotropy. Freedom in the choice of the velocities of the reference isotropic medium allows to increase the accuracy of the formula. It is illustrated by results of included synthetic tests.

In paper "Ray-velocity vectors of reflected S1S1 and S2S2 waves displayed on the ray-velocity surfaces in a simple homogeneous velocity model with triclinic anisotropy" V. Bucha reveals the ray-velocity vectors at the sources and receivers plotted together with the ray-velocity surfaces of S1S1 and S2S2 reflected waves. These plots, displayed for selected common shot gathers, are supplemented with ray diagrams.

The fourth part, Ray theory for anisotropic viscoelastic media, is devoted to the extension of ray theory from anisotropic elastic media to anisotropic viscoelastic media.

When extending the ray tracing algorithm from anisotropic elastic media to anisotropic viscoelastic media, L. Klimes encountered a problem with non-existing eigenvectors of the Christoffel matrix. He demonstrates this problem in contribution "Two S-wave eigenvectors of the Christoffel matrix need not exist in anisotropic viscoelastic media".

Since the equations for ray tracing and for geodesic deviation are usually expressed in terms of the eigenvectors of the Christoffel matrix, L. Klimes designed a new algorithm, which uses the eigenvalues of the Christoffel matrix but not its eigenvectors, in paper "Tracing real-valued reference rays in anisotropic viscoelastic media".

The fifth and final part, DVD-ROM with SW3D software, data and papers, contains the DVD-R compact disk SW3D-CD-24.

Compact disk SW3D-CD-24, edited by V. Bucha & P. Bulant, contains the software developed within the SW3D research project, together with input data related to the papers published in the serial Seismic Waves in Complex 3-D Structures. A more detailed description can be found directly on the compact disk. Compact disk SW3D-CD-24 also contains over 540 complete papers from journals and previous volumes of the serial Seismic Waves in Complex 3-D Structures in PostScript, PDF, GIF or HTML, and 2 older books by V. Cerveny and his coauthors in PDF. Refer to the copy of the SW3D research project WWW pages on the compact disk. Compact disk SW3D-CD-24 is included in the Volume 30 in two versions, as the UNIX disk and DOS disk. The versions differ just by the form of ASCII files.

Prague, December 2020

Vlastislav Cerveny
Ludek Klimes
Ivan Psencik

Seismic Waves in Complex 3-D Structures, 30, 5-7.
This Introduction to Report 30 is also available in PDF (34 kB).