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 sixth
year of the programme started on October 1, 1998.

All future revisions of program packages MODEL, CRT, and NET, delivered to the sponsors in the previous years, 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 previous years, 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 and to the possibility of calculating the corresponding amplitudes and contributions to the synthetic seismograms.

Methods to calculate synthetic seismograms in complex structures will be studied, mutually compared and combined.

Theoretical investigation of the applicability and accuracy of coupling ray theory, and especially of perturbations from isotropic media. Extensive tests of accuracy with programs based on the quasi-isotropic approximation. Comparison with results of other methods for weakly anisotropic media and for singular regions.

Derivation and programming of formulae for R/T coefficients for weak contrast interfaces separating weakly anisotropic media.

Study of qS waves signatures in arbitrary weakly anisotropic media.

Comparison of exact computations with the anisotropic ray-theory computations (with approximately ten terms of the ray series), and with the computations based on the coupling ray theory for weakly anisotropic media. (Anisotropic model with a rotating axis of symmetry.)

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.

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 studied. Program package RMATRIX by C.J. Thomson, linked to the CRT package, will be used for numerical calculations in 3-D models.

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 within ray cells in 3-D models will be further studied and the relevant numerical algorithms will be improved or new ones 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 and the possibility of a future extension to 3-D will be considered.

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. The main attention will be devoted to the estimation of the feasibility and costs of ray tracing and to the estimation of the Lyapunov exponents for the macromodels.

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

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

sMain attention will be paid to the development of a new 3-D elastic code, based on the 1998 update of the 2-D code with which we were able to solve some previously unstable models.

Hybrid Ray-FD method should be finished. Validation experiments will use comparison with the well tested DW-FD method, where DW is the Discrete Wavenumber method.

A new version of the elastic FD program, interfaced to the MODEL package, will be prepared. The innovation will mainly include the non-planar free surface topography, treated by the vacuum formalism, providing much simpler handling than the other recently available methods. Also included will be a spatially varying Q factor, linearly dependent on frequency. It is also intended to include the option that some blocks are filled with water, but the latter needs further numerical experiments.

An extended and revised version of the textbook on Seismic Ray Theory will be distributed to the consortium members as a special report (approximately 800 pages). The textbook describes the propagation of high-frequency seismic body waves in complex 3-D, laterally varying, isotropic, anisotropic or weakly anisotropic, elastic structures with curved interfaces. The pressure waves in liquid structures are also considered. Arbitrary elementary multiply-reflected waves are discussed, including the converted waves. Ray-theory Green functions are derived and discussed for all possible waves and structures under consideration. The construction of ray-synthetic seismograms and ray-synthetic particle ground motions is described in detail.

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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