The Volume 27 of the serial Seismic Waves in Complex 3-D Structures of the annual reports of research project "Seismic waves in complex 3-D structures" (SW3D) summarizes the work done towards the end of the twenty-third year and during the twenty-fourth year of the project, in the period June, 2016 - May, 2017. 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.
In spite of its name, the serial Seismic Waves in Complex 3-D Structures (ISSN 2336-3827) is also devoted to the ray methods for electromagnetic waves studied by our group simultaneously with the ray methods for elastic or viscoelastic waves. The reason for the name is that we cannot change the name of our already registered serial.
Our group working within the project during the twenty-fourth year has consisted of six research workers: Vaclav Bucha, Petr Bulant, Vlastislav Cerveny, Ludek Klimes, Ivan Psencik and Bohuslav Ruzek. Ivan Psencik is the supervisor of PhD studies of Milosz Wcislo, with the PhD thesis on "Seismic waves in inhomogeneous, weakly dissipative, anisotropic media".
Veronique Farra (Institut de Physique du Globe de Paris, France), Petr Jilek (BP-America, Houston, USA), Tijmen Jan Moser (Zeehelden Geoservices, 's-Gravenhage, The Netherlands) and Mirko van der Baan (University of Alberta, Edmonton, Canada) visited us during the last year since June, 2016.
Ivan Psencik served as a member of the technical committee of the 17th International Workshop on Seismic Anisotropy in Horseshoe Bay, Texas, USA in 2016, and as a guest editor of the special part of Geophysics devoted to the workshop proceedings. Petr Bulant and Ivan Psencik served as two of four guest editors of the special issue of Studia Geophysica et Geodaetica with the proceedings from international workshop "Active and passive seismics in laterally inhomogeneous media" held at the Loucen Castle in Czech Republic on June 8-12, 2015. The proceedings were published in summer 2016.
This Introduction is followed by the Research Programme for the current, twenty-fourth year of the SW3D research project. More detailed information regarding the SW3D research project is available online at "http://sw3d.cz".
All 12 papers of the Volume 27 are related to seismic anisotropy or electromagnetic bianisotropy. The Volume 27 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.
The contribution "Determination of rock-sample anisotropy from P- and S-wave traveltimes" by I. Psencik, B. Ruzek, T. Lokajicek & T. Svitek is an extension of the work presented by B. Ruzek & I. Psencik in the Volume 26 of Seismic Waves in Complex 3-D Structures. There are, however, several important differences. First, instead of travel-time data collected during a synthetic vertical seismic profiling experiment, the contribution is devoted to the inversion of travel times measured on a spherical rock sample. In addition to the approximate equation for calculation of P-wave travel times expressed in terms of the weak-anisotropy parameters, an approximate equation for a common S wave (an artificial wave propagating with the ray velocity whose square is an average of squares of the S1- and S2-wave ray velocities) is also used.
Ivan Psencik participates in the Norwegian project Petromaks2: "Bayesian inversion of 4D seismic waveform data for quantitative integration with production data". He spent a week at the University of Bergen in the framework of this project. During his visit, his Norwegian colleagues and him prepared contribution "On the parametrization of seismic anisotropy for ray-Born inversion". The paper, whose authors are M. Jakobsen, I. Psencik, E. Iversen & B. Ursin is an extension of the Expanded Abstract submitted and accepted for the presentation at this year's EAGE conference in Paris. The main goal of the contribution is to test suitability of two parametrizations of anisotropic media for the use in the ray-Born inversion. The two tested parametrizations are the standard density-normalized elastic parameters in the Voigt notation and the weak-anisotropy parameters.
In their contribution "Reflection moveout approximation for a converted P-SV wave in a moderately anisotropic homogeneous VTI layer", V. Farra & I. Psencik continue their study of the non-hyperbolic reflection moveout (approximation of travel time of reflected waves) in anisotropic media. After formulae for P and SV waves in weakly or moderately anisotropic transversely isotropic media with the vertical axis of symmetry (Volume 23), for P waves in monoclinic media whose planes of symmetry coincide with the reflector (Volume 25), and for P waves in anisotropic media of arbitrary symmetry and orientation (Volume 26), they propose an approximate formula for the reflection moveout of converted waves in a homogeneous, transversely isotropic layer with the vertical axis of symmetry.
The second part, Elastic waves in anisotropic media, addresses the problems relevant to heterogeneous anisotropic elastic media.
As the present volume of Seismic Waves in Complex 3-D Structures illustrates, the weak-anisotropy parameters become an important tool for the parametrization of media of arbitrary anisotropy, symmetry and orientation in various forward and inverse modelling schemes. They are used in all three previously discussed contributions. In his contribution "Transformation rules for weak-anisotropy parameters", I. Psencik summarizes, at one place, important and useful formulae for the work with the weak-anisotropy parameters.
In the Volume 25, V. Bucha used ray-based Kirchhoff prestack depth migration for reflected S waves and converted waves in the two-layer velocity model with homogeneous triclinic anisotropy in the upper layer. V. Bucha now plans to extend his migration studies to inhomogeneous weakly anisotropic media and test the coupling ray theory. The SW3D software has no code to calculate coupling-ray-theory S waves in velocity models with interfaces. Hence, V. Bucha in his contribution "Comparison of Fourier pseudospectral method seismograms and ray-theory travel times in a simple triclinic model" tests the 3-D anisotropic seismic modelling code by Ekkehart Tessmer and shows the first results.
The third part, Viscoelastic waves in anisotropic media, is devoted to waves propagating in heterogeneous anisotropic viscoelastic media.
As mentioned above, Milosz Wcislo started his PhD studies under the supervision of Ivan Psencik. The first results of Milosz Wcislo's project are presented in the contribution "Seismic waves in inhomogeneous, weakly dissipative, anisotropic media; preliminary tests with P waves". Its authors, M. Wcislo & I. Psencik present the first results obtained with the generalized version of the SW3D software package ANRAY.
The representation theorem for elastic waves with a symmetric stiffness matrix is well known. Since it has not been proved that the stiffness matrix for viscoelastic waves is symmetric, L. Klimes derives the "Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix".
Crude oil with its long organic molecules often exhibits an optical activity which is described by a non-symmetric biisotropic constitutive matrix. We may thus ask whether crude oil can exhibit an analogous "acoustical activity" described by a non-symmetric isotropic stiffness matrix. This question represented one of motivations of study "Rotationally invariant viscoelastic medium with a non-symmetric stiffness matrix" by L. Klimes. The discovered answer is negative.
The fourth part, Electromagnetic waves in bianisotropic media, is devoted to electromagnetic waves propagating in heterogeneous bianisotropic media, i.e., in media where both permittivity and permeability depend on the direction of propagation.
The field equivalence principle for electromagnetic waves is analogous to the representation theorem for elastic waves. It has already been derived by various authors in various special cases of electromagnetic media. L. Klimes now derives the "Field equivalence principle for electromagnetic waves in a heterogeneous generally bianisotropic medium". Note that the author has not found the field equivalence principle for electromagnetic waves in such a general form in the literature.
Analogously to the determination of a general form of a rotationally invariant viscoelastic medium with a non-symmetric stiffness matrix which may be compared with a transversely isotropic elastic medium, L. Klimes also studies a general form of a "Rotationally invariant bianisotropic electromagnetic medium" which may be compared with an uniaxial bianisotropic electromagnetic medium.
In recent years, P. Bulant and L. Klimes extensively studied behaviour of rays and wave fields in elastic media with split intersection singularities. They wished to know to which extent are their studies relevant to electromagnetic waves. L. Klimes now finds an example of an "Uniaxial bianisotropic electromagnetic medium with a split intersection slowness-surface singularity".
P. Bulant and L. Klimes also defined and determined the reference symmetry axis of a generally anisotropic elastic medium which could be approximately transversely isotropic, and advantageously used this reference symmetry axis to trace the SH (ordinary) and SV (extraordinary) reference rays for the coupling ray theory in order to improve its accuracy. L. Klimes now analogously proposes the "Determination of the reference symmetry axis of a generally bianisotropic electromagnetic medium which could be approximately rotationally invariant.
The fifth and final part, DVD-ROM with SW3D software, data and papers, contains the DVD-R compact disk SW3D-CD-21.
Compact disk SW3D-CD-21, edited by V. Bucha & P. Bulant, contains the revised and updated versions of 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-21 also contains over 510 complete papers from journals and previous volumes of the serial Seismic Waves in Complex 3-D Structures in PostScript, PDF, GIF or HTML, and 3 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-21 is included in the Volume 27 in two versions, as the UNIX disk and DOS disk. The versions differ just by the form of ASCII files.
Prague, June 2017
Vlastislav Cerveny
Ludek Klimes
Ivan Psencik