SW3D Reasearch programme
October 1, 1995--September 30, 1996
Revisions of packages MODEL, CRT and NET
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.
Packages MODEL and CRT:
General 3-D layered and block isotropic structure,
containing isolated bodies,
pinchouts, etc. Inside the layers and blocks, the velocity and
laterally in all the three dimensions. Dissipation may be
Type of waves:
Arbitrary type of elementary seismic body wave
corresponding to the
zero order ray theory
Arbitrary position of the source.
Initial value ray tracing by numerical
integration of ray equations,
travel time computation, dynamic ray tracing, ray propagator matrix,
spreading, vectorial amplitudes, polarization vectors. The package
may be applied to the
evaluation of the elastodynamic ray-theory Green functions, and to
of the particle ground motions.
Reflection methods, refraction methods, VSP, hole-to-hole.
The MODEL and CRT packages will be available to
the consortium members in the middle of the third year of the
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
ray tracing may also be used.
Types of waves:
First arrivals, constrained first arrivals.
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.
Tomography, for an arbitrary source-receiver
migration. Wavefront reconstruction. Etc.
Ray tracing and synthetic wavefields in 3-D inhomogeneous
All future revisions of program package ANRAY, delivered to the
in the second year of the project, will be delivered to the sponsors
the next years of the project.
3-D laterally varying structure containing isotropic and
Types of waves:
Arbitrary type of elementary seismic body wave
(P, S, qP, qS1, qS2,
any converted wave). Arbitrary position of the source.
Numerical integration of ray tracing and dynamic
equations, calculation of ray vectorial amplitudes, ray Green
ray synthetic seismograms, particle ground motions.
Reflection methods, refraction methods, VSP
and/or crosshole configuration.
The program package ANRAY will be
available to the consortium members at the end of the third year of
a) Specification of elastic parameters in
individual layers in a 3-D rectangular grid with a B-spline
of parameters in the grid; b) Further debugging, removing
in the extensive description of the package.
Sample data for the program packages
The examples of input data for the MODEL package describing or
approximating typical models delivered by the sponsors will be
Upon request, also the sample input data for programs CRT, NET, or
to perform calculations in such models will be prepared.
Two-point ray tracing in complex isotropic structures
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
code will be universal, applicable not only to the point source
(common-shot) initial conditions, but also to other initial
e.g., zero-offset rays or diffracted rays. Moreover, the code will
some extent, applicable to other initial-value ray tracing codes than
Synthetic seismograms in 3-D isotropic complex structures
Two methods may be used to compute synthetic seismograms in complex
3-D structures: the ray method and the method of summation of
The computations of ray synthetic seismograms require the solution of
two-point ray tracing problem, see point 3. Compressional, shear and
converted waves will be optionally considered.
Seismic wave propagation in weakly anisotropic inhomogeneous
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,
on travel-time fields.
Higher-order terms of the ray method
Importance of incorporating the first-order additional terms of the
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
to provide a version of the ANRAY package containing an option to
calculate the first-order additional terms both in isotropic and
Synthetic seismograms for sources and receivers situated at
Earth's surface or close to it
The investigation of radiation patterns of seismic point sources
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
computation of synthetic seismograms corresponding to such sources.
In addition, also the following positions of point sources and
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
receivers situated close to inner thin layers.
Fast computation of ray-theory travel times
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
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.
Second-order methods in grid travel-time tracing
The new, second order method to evaluate travel times in smooth media
will further be investigated.
Accuracy of seismic modelling
The research will be concentrated mainly on the accuracy of travel
on the accuracy of finite-difference modelling of seismic wave
fields, and on
the accuracy of other modelling methods designed or studied in the
of the project.
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
to model parameters. Study of a priori information on the model
Application of the above travel-time variations of Sobolev scalar
within the inversion algorithms and procedures.
Finite-difference solutions of elastodynamic equations
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.
A new elastic FD code on (still rectangular, but) spatially
irregular grids will be tested, with the intention to efficiently
small localized heterogeneities, and a non-planar free surface.
Visualisation of the 2-D wavefields will be improved, including
animation by IDL.
Hybrid methods based on finite differences
The development of the 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
solving problems arising from the inconsistencies between 2-D
and the source wavefields generated by 3-D (point) sources.
First attempts to build a new hybrid ray - FD method will be