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 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 both forward numerical modelling and inversion
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.

**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 based on ray histories,
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).
Least-square travel-time tomography with smoothing using Sobolev
scalar products.

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

*Planned innovations*:
Anisotropic common-ray approximation of the coupling ray theory for S waves.
The package will be extended to solve various inverse problems,
travel-time tomography in particular.

**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.
Possibility of VRML visualization.

*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 including 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) Common ray approximation based on a ray in an anisotropic medium.
(b) Generalization of the quasi-isotropic approximation for layered media.
(c) Weak attenuation.
(d) Calculation of KMAH index in anisotropic media.
(e) Stabilization of ray tracing in a vicinity of shear-wave singularities.
(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).

**Package FORMS:**

*Computations*:
Subroutines used by other program packages including
data input and output subroutines,
management and plotting of synthetic seismograms,
2-D and 3-D graphics including 3-D virtual reality
with VRML and GOCAD visualization,
manipulation and calculation with gridded data (data cubes),
programs for matrix and vector operations necessary for inversion,
other general-purpose seismic software.

Study of models obeying ellipsoidal P--wave weak anisotropy. Development of a P--wave ray tracer for inhomogeneous weakly anisotropic media.

Algorithm of the Gaussian-packet prestack depth migration is being developed. Gaussian packets should be very efficient and offer explicit correspondence between the time and depth sections. Attention is paid to the optimization of the shape of Gaussian packets.

Study of possibilities to include coupling ray theory in seismic imaging.

Amplitude preserving Kirchhoff migration in anisotropic media: Synthetic study of possibilities and limitations to recover reflection coefficients from data measured in inhomogeneous anisotropic media.

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