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 and inverse numerical modelling of seismic wave fields in 3-D inhomogeneous, isotropic and anisotropic structures. Considerable attention is also devoted to applications involving S waves, converted waves, S-wave splitting and coupling in anisotropic media, particle ground motions, etc. Much more detailed information can be obtained at "http://sw3d.mff.cuni.cz".

The research programme was begun on October 1, 1993.
The programme will go into its seventh year on October 1, 1999.

**Package CRT:**

*Model*: Using package MODEL.

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

*Computations*: Arbitrary position and shape of the source,
initial-value ray tracing by numerical integration of ray equations,
two-point ray tracing by the shooting method, travel-time computation,
dynamic ray tracing, paraxial-ray propagator matrix,
geometrical spreading, vectorial amplitudes, polarization vectors.
The package may be applied to the
evaluation of the elastodynamic ray-theory Green function, and to
the computation of synthetic seismograms,
including the coupling ray theory for weak anisotropy and the
response of fine layers at receiver sites
(program package RMATRIX by C.J. Thomson, linked to the CRT package).

*Aquisition schemes*: Surface seismics (land and marine),
VSP, cross-hole, OBS, OBC.

*Planned innovations*:
The package will be extended to solve various inversion problems.

**Package ANRAY:**

*Model*: 3-D laterally varying structures containing isotropic and
anisotropic non-vanishing layers. Specification of elastic parameters
inside individual layers either by linear interpolation between
isosurfaces of elastic parameters, or by B-spline interpolation
within a 3-D rectangular grid of elastic parameters.

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

*Computations*: Numerical integration of ray tracing and dynamic
ray tracing equations, calculation of ray vectorial amplitudes,
ray-theory Green function (also the Green function in the quasi-isotropic
approximation for qS waves), ray synthetic seismograms, particle
ground motions.

*Aquisition schemes*: Surface seismics (land and marine),
VSP, cross-hole, OBS, OBC.

*Planned innovations*:
(a) Further development of the quasi-isotropic approximation
(introduction of reflection and transmission into the QI computations,
implementation of the QI approximation for qP waves).
(b) Calculation of KMAH index in anisotropic media.
(c) Checks of stability of the anisotropic stiffness tensor in interpolated
data.
(d) Ray tracing tests with RHS specified by the polarization vectors.
(e) Modifications of outputs so that the graphical software
developed for the MODEL and CRT packages can be used.
(f) Further debugging, removal of inconsistencies in the description
of the package.

**Package NET:**

*Model*: Using package MODEL or using gridded velocities.

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

*Computations*: Arbitrary position and shape of the source.
First-arrival travel times in the whole model are computed.
The algorithm of computation is independent of the model's complexity.

*Aquisition schemes*: Surface seismics (land and marine),
VSP, cross-hole, OBS, OBC.

**Package FD:**

*Model*: Using package MODEL.

*Type of waves*: Complete elastic wave field.

*Computations*: Presently 2-D, without fluids.

*Aquisition schemes*: Surface seismics (land).

*Planned innovations*: 3-D, hybrid methods.

**Package FORMS:**

*Computations*:
Data input and output used by other packages,
management and plotting of synthetic seismograms,
2-D and 3-D graphics including 3-D virtual reality,
manipulation with gridded data (data cubes)
and other general-purpose seismic software.

*Planned innovations*:
Extension of manipulation with data cubes (e.g., 3-D FFT,
3-D random functions and correlation functions),
programs for matrix and vector operations necessary for inversion.

Study of the inaccuracy of the coupling ray theory due to the differences between the reference and exact rays. Estimation of frequencies at which the quasi-isotropic approximation should be replaced by the anisotropic ray theory, or by the coupling ray theory along the anisotropic ray theory rays.

Further development of algorithms for seismic travel-time tomography in anisotropic media (extensions to types of data other than VSP, extension to S-wave data, testing on synthetic examples). The theoretical investigation will also be aimed at the determination of the resolution of the elastic parameters with respect to the measurement geometry.

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