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.*Revisions of packages MODEL, CRT and NET*

#### Packages MODEL and CRT:

**Model:**General 3-D layered and block isotropic structure, containing isolated bodies, pinchouts, etc. Inside the layers and blocks, the velocity and density varies laterally in all the three dimensions. Dissipation may be considered.

**Type of waves:**Arbitrary type of elementary seismic body wave corresponding to the zero order ray theory (P,S, converted). Arbitrary position of the source.

**Computations:**Initial value ray tracing by numerical integration of ray equations, travel time computation, dynamic ray tracing, ray propagator matrix, geometrical spreading, vectorial amplitudes, polarization vectors. The package may be applied to the evaluation of the elastodynamic ray-theory Green functions, and to the computations of the particle ground motions.

**Applications:**Reflection methods, refraction methods, VSP, hole-to-hole.

**Next versions:**The MODEL and CRT packages will be available to the consortium members in the middle of the third year of the project.

#### Package NET:

**Model:**General 3-D layered and block isotropic model. The medium parameters are specified at grid points of a 3-D rectangular mesh. The same model as in the complete seismic ray tracing may also be used.

**Types of waves:**First arrivals, constrained first arrivals.

**Computations:**First arrival travel times in the whole model are computed. The computations include also travel time of all non-ray waves (such as the first arriving diffracted waves in shadow zones, head waves, etc.). Arbitrary type and position of the source may be considered (point source, plane wave source, etc.). The algorithm of computation is independent on a model complexity.

**Applications:**Tomography, for an arbitrary source-receiver configuration. Seismic migration. Wavefront reconstruction. Etc.

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.*Ray tracing and synthetic wavefields in 3-D inhomogeneous anisotropic structures*

#### Package ANRAY:

**Model:**3-D laterally varying structure containing isotropic and anisotropic nonvanishing layers.

**Types of waves:**Arbitrary type of elementary seismic body wave (P, S, qP, qS1, qS2, any converted wave). Arbitrary position of the source.

**Computations:**Numerical integration of ray tracing and dynamic ray tracing equations, calculation of ray vectorial amplitudes, ray Green function, ray synthetic seismograms, particle ground motions.

**Applications:**Reflection methods, refraction methods, VSP and/or crosshole configuration.

**Updated version:**The program package ANRAY will be available to the consortium members at the end of the third year of the project.

**Main innovations:**a) Specification of elastic parameters in individual layers in a 3-D rectangular grid with a B-spline interpolation of parameters in the grid; b) Further debugging, removing inconsistencies in the extensive description of the package.

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

Seismic ray tracing code CRT described above (see point 1) will be supplemented with coding of the two-point ray tracing algorithm. The two-point ray tracing code will be universal, applicable not only to the point source (common-shot) initial conditions, but also to other initial conditions, e.g., zero-offset rays or diffracted rays. Moreover, the code will be, to some extent, applicable to other initial-value ray tracing codes than CRT.*Two-point ray tracing in complex isotropic structures*

Two methods may be used to compute synthetic seismograms in complex isotropic 3-D structures: the ray method and the method of summation of Gaussian beams. The computations of ray synthetic seismograms require the solution of the two-point ray tracing problem, see point 3. Compressional, shear and converted waves will be optionally considered.*Synthetic seismograms in 3-D isotropic complex structures*

Study of wave propagation in weakly anisotropic media using the first-order perturbation theory with emphasize on study of effects of weak anisotropy on radiation from point sources, on AVO experiments, and on travel-time fields.*Seismic wave propagation in weakly anisotropic inhomogeneous media*

Importance of incorporating the first-order additional terms of the ray method into the ray computations in isotropic media has been studied during the first two years of the project. An attempt will be made to extend this concept to anisotropic media. Final aim of these attempts is to provide a version of the ANRAY package containing an option to calculate the first-order additional terms both in isotropic and anisotropic layers.*Higher-order terms of the ray method*

The investigation of radiation patterns of seismic point sources situated at the Earth's surface or close to it, performed during the first two years of the project, will be extended. The extension will consist in the computation of synthetic seismograms corresponding to such sources.*Synthetic seismograms for sources and receivers situated at the Earth's surface or close to it*

In addition, also the following positions of point sources and receivers will be considered: a) The sources and receivers situated at inner structural interfaces or close to them, b) The sources and receivers situated close to a thin low-velocity surficial layer, c) The sources and receivers situated close to inner thin layers.

Algorithms of fast calculation of ray-theory travel times in dense rectangular grids will further be investigated. Various kinds of interpolation and extrapolation methods using the results of dynamic ray tracing will be considered. Attention will also be devoted to the multi-source/multi-receiver surface configurations, to the multi-valuedness of travel times, and to the application of the fast Fourier transform to interpolate course migrated sections.*Fast computation of ray-theory travel times*

The new, second order method to evaluate travel times in smooth media will further be investigated.*Second-order methods in grid travel-time tracing*

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

Development of theory and algorithms applicable in seismic travel-time tomography. Examples: evaluation of travel-time variations with respect to model parameters. Computation of the Sobolev scalar products of basis functions corresponding to model parameters. Study of a priori information on the model smoothness. Application of the above travel-time variations of Sobolev scalar products within the inversion algorithms and procedures.*Seismic tomography*

The program development of the FD speed-up, combining the independent ray calculations of the first arrival times, and the FD calculations of the waveforms of the first arrivals, will be finished. The test examples on model PICROCOL will be produced.*Finite-difference solutions of elastodynamic equations*

A new elastic FD code on (still rectangular, but) spatially irregular grids will be tested, with the intention to efficiently treat small localized heterogeneities, and a non-planar free surface.

Visualisation of the 2-D wavefields will be improved, including animation by IDL.

The development of the*Hybrid methods based on finite differences**hybrid DW - FD method*(DW = discrete wavenumber) will continue with the intention to efficiently treat 2-D heterogeneities in 1-D background media. The attention will be focused on solving problems arising from the inconsistencies between 2-D calculations and the source wavefields generated by 3-D (point) sources.

First attempts to build a new*hybrid ray - FD method*will be made.