The research is focused primarily on the fundamental issues of high-frequency seismic wave propagation in complex 3-D isotropic and anisotropic structures, which go beyond the traditional approaches. The ray method and its recent extensions as well as its combination with other methods are mainly applied and investigated. The emphasis is put on new, stable, more efficient and flexible algorithms for the forward numerical modelling of seismic wave fields in 3-D inhomogeneous, isotropic and anisotropic structures. Considerable attention is also devoted to applications involving shear waves, converted waves, shear wave splitting and coupling in anisotropic media, particle ground motions, etc.

The research programme started on October 1, 1993. The fifth
year of the programme started on October 1, 1997.

All future revisions of program packages MODEL, CRT, and NET, delivered to the sponsors in the first year of the project, will be delivered to the sponsors in the next years of the project.

All future revisions of program package ANRAY, delivered to the sponsors
in the second year of the project, will be delivered to the sponsors
in the next years of the project.

The examples of input data for the MODEL package, describing or approximating models delivered by the sponsors or other typical models, will be prepared. Upon request, also the sample data for programs CRT or NET to perform calculations in such models will be prepared. The examples of input data for the ANRAY package, for models delivered by the sponsors or other typical models, will be prepared too.

The two-point ray tracing code will further be tested and applied to various models. Attention will also be devoted to the calculation of two-point rays diffracted from edges and corner points.

The advantage of the two-point ray tracer will be taken for the computation of ray synthetic seismograms.

Programming quasi-isotropic formulae for qS waves as an independent program, which could be used along rays calculated in background inhomogeneous isotropic media. Purpose: To remove problems of the standard ray method for anisotropic media in regions, in which the qS waves propagate with nearly the same phase velocities.

Extension of the study of the R/T coefficients at a weak contrast interface separating two weakly anisotropic halfspaces to converted PS R/T coefficients. Study of possibilities to invert the R/T coefficients for the parameters of the surrounding media.

Study of qS waves signatures in arbitrary weakly anisotropic media.

Study of replenishing incomplete sets of anisotropic elastic parameters with default values. If all 21 real parts and 21 imaginary parts of the complex-valued components of the stiffness matrix are not known, the missing parameters may be supplied in such a way that the resulting anisotropic medium is in some sense the closest one to the isotropic medium.

Program COEF51, designed for the computation of reflection/transmission coefficients at structural interfaces and thin transition layers between two isotropic dissipative media will be further tested. The main attention will be devoted to frequency-independent reference R/T coefficients. Optionally, the program COEF51 works even for non-dissipative media. The program will be implemented to the program package CRT, where it will replace program COEF50 designed for the computation of R/T coefficients at structural interfaces between non-dissipative media.

Program SOURCE, designed for the computation of radiation patterns of point sources situated at the Earth's surface, at structural interfaces, at the sea bottom, at thin transition layers, and close to them, will be further tested. Both dissipative and non-dissipative models may be considered. The main attention will be devoted to explosive point sources and to arbitrarily oriented single force point sources. The program will be first implemented to the program package BEAM87 designed for the computation of synthetic seismograms in 2-D structures. Influence of radiation patterns on synthetic seismograms will be studied using this program package. After successful testing, the code will be implemented into the program package CRT (in the following years of the project).

Algorithms of fast calculation of ray-theory travel times in dense rectangular grids will further be investigated. Accuracy and efficiency of the interpolation of ray-theory travel times between rays in 3-D models will be studied and the relevant numerical algorithms will be proposed. If possible, attention will also be devoted to the interpolation between different shot and receiver positions.

Accuracy and efficiency of grid travel-time tracing methods to evaluate first-arrival travel times will further be studied.

The research will be concentrated mainly on the accuracy of travel-time calculations, on the accuracy of finite-difference modelling of seismic wavefields, and on the accuracy of other modelling methods designed or studied in the framework of the project.

Development of theory and algorithms applicable in seismic travel-time tomography with emphasis on the estimation of its accuracy.

Resolution and accuracy of migrations will be studied. Attention will be paid to the physical meaning of the migrated sections.

The first version of the 2D elastic FD code (with non-planar topography) will be prepared for distribution. This will include simplification of the presently existing data input/output, short description, and a test example.

Improvements of the hybrid Ray-FD code will be concentrated into removing numerical artifacts that, in some models, result from the excitation (coupling) lines. Study of the necessary degree of "completeness" of the Ray wave field will be accomplished for a set of generic models. Sources away from the FD plane will be studied, too. As a reference (more accurate) solution, the DW-FD method will be used.

Interface between the MODEL and FORMS packages, used also in ray-theory computations, and the finite-difference code.

The elastic FD modelling in models with topography will be carried out, including comparisons with independent methods, e.g. the ray method and the hybrid 2-D DW-FD code. The accuracy of the 2-D elastic FD code with non-planar topography will be tested against the finite element program.

The new hybrid (DW-FD) code, recently under development, in which a 3D elastic FD scheme is applied, will come through first numerical tests.

A "resolution test" will be performed on a realistic model derived from shallow reflection survey (reflector depth at about 50m). The true time sections, interpreted by means of 1D and acoustic synthetics, will be compared with the synthetic one obtained from 2D elastic FD modelling and or 2D elastic ray modelling.

In addition to this programme, we will certainly be responsive to specific technical suggestions and recommendations of sponsors within the general framework of the project. The research in most directions listed above will continue to the next years of the project.

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