RESEARCH PROGRAMME OF SEISMIC WAVES IN COMPLEX 3-D STRUCTURES
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 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.
The programme will go into its eighth year on October 1, 2000.
RESEARCH PROGRAMME FOR THE EIGHTH YEAR
October 1, 2000 - September 30, 2001
1. Program packages
Package MODEL:
Model: General 3-D layered and block isotropic or anisotropic
structures, containing isolated bodies, pinchouts, etc.
Inside the layers and blocks, the elastic parameters may vary
in all three dimensions.
Dissipation and non-planar topography can be considered.
Possibility of model smoothing, data fitting by inversion,
conversion of model parametrization, structural interface triangulation
and VRML visualization.
Planned innovations:
Interface from and to GOCAD.
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:
Anisotropic common-ray approximation of the coupling ray theory for S waves.
The package will be extended to solve various inversion 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.
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 S waves, ray synthetic seismograms, particle
ground motions.
Aquisition schemes: Surface seismics (land),
VSP, cross-hole.
Planned innovations:
(a) Further development of the quasi-isotropic (QI) approximation:
further evaluation of its validity by comparing the QI results with
results of more precise methods;
incorporation of reflection and transmission within the QI computations.
(b) Checks of stability of the anisotropic stiffness tensor with
respect to interpolation.
(c) Calculation of pressure in the surface liquid layer;
calculation of the conversion coefficients at the anisotropic
solid/liquid interface.
(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.
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 and calculation with gridded data (data cubes),
programs for matrix and vector operations necessary for inversion,
other general-purpose seismic software.
2. Sample data for the program packages
Examples of the input data describing or approximating models
delivered by the consortium members or other typical models
will be prepared.
Examples of the input data to perform calculations in such
models will also be prepared.
3. Two-point ray tracing in complex isotropic 3-D structures
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 synthetic seismograms (edge waves).
4. Synthetic seismograms in 3-D isotropic complex structures
Methods to calculate synthetic seismograms in complex structures will
be studied, mutually compared and combined.
5. Seismic wave propagation in weakly anisotropic inhomogeneous media
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 common-ray
or anisotropic common-ray approximation of the coupling ray theory
should be replaced by the anisotropic ray theory, or by the coupling
ray theory along the anisotropic ray theory rays.
Development of an efficient P-wave ray tracing for weakly anisotropic
inhomogeneous media.
6. Applicability of the high-frequency asymptotics in the
vicinity of S-wave singularities
Anisotropic S-wave ray tracing in a vicinity of singularities
in inhomogeneous anisotropic media. Investigation of accuracy
of various high-frequency approximations (zeroth-order anisotropic
ray approximation, quasi-isotropic approximation, higher-order
anisotropic ray approximations, Gaussian beams, etc.) for S waves,
propagating in strongly or weakly anisotropic homogeneous or
inhomogeneous media in the vicinity of singularities, by comparison
with other more precise methods (exact solutions, finite differences,
etc.).
7. R/T coefficients for inhomogeneous waves in dissipative elastic media
Computation of R/T coefficients at structural interfaces and
thin transition layers between two isotropic dissipative media will be
tested further. The main attention will be devoted to
frequency-independent reference R/T coefficients.
8. Computation of ray-theory travel times, amplitudes
and other quantities at the nodes of 3-D grids
Algorithms of fast calculation of ray-theory travel times in dense
rectangular grids will be investigated further.
The accuracy and efficiency of the interpolation of ray-theory
travel times within ray cells in 3-D models will be studied further,
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.
9. Accuracy of seismic modelling
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
within 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 high-frequency validity of velocity models.
10. Lyapunov exponents and model smoothing
Construction and smoothing of velocity macro models will further
be studied, with emphasis on the application of Sobolev scalar
products and Lyapunov exponents.
Attention will be paid to a possible extension of the estimation
of Lyapunov exponents to smooth 3-D models and to 2-D models with
structural interfaces.
11. Seismic tomography
Development of theory, algorithms and programs applicable
in seismic travel-time tomography and inversion of the coherency
panels, with emphasis on the estimation of their accuracy.
Further development of algorithms for seismic travel-time tomography in
anisotropic media, synthetic tests of possibility to discriminate
anisotropy from inhomogeneity. Extension to other types of data
acquisition, extension to shear wave data, study of effects of noise.
The theoretical investigation will also be aimed at the determination
of the resolution of the elastic parameters with respect to the
measurement geometry.
12. Decomposition of a wave field into Gabor wavelets
Discretized integral decomposition of a spatial wave field
at a fixed time or a time-dependent wavefield along a smooth
surface into Gabor wavelets in 2-D or 3-D.
The Gabor wavelets may be frequency-dependent and their
shape may be smoothly varying in space and time, which
requires much more general decomposition than the integral
Gabor transform.
The decomposition into Gabor wavelets may be useful for the
decomposition of a general wave field into Gaussian beams or packets.
13. Migrations
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 velocity model, including its anisotropy.
Algorithm of the Gaussian-packet prestack depth migration
will be developed.
Gaussian packets should be very efficient and offer explicit
correspondence between the time and depth sections.
Attention will be paid to the optimization of the shape of
Gaussian packets.
14. Gaussian-packet "finite elements"
In the beginning of each time interval of a given duration,
the wave field may be decomposed into Gaussian packets
propagating throughout the corresponding time interval and
yielding the wave field in the beginning of the next time interval.
15. Finite-difference solutions of elastodynamic equations
The main attention will be paid to the development of a new 3-D elastic
code and to the hybrid DW-FD and Ray-FD methods.
16. Concluding remarks
In addition to this programme, we will certainly be responsive to
specific technical suggestions and recommendations of the consortium
members within the general framework of the project.
The research in most directions listed above will continue into the
future years of the project.
You may download PostScript file
prog01.ps (65 kB) with the Research Programme.
SW3D
- main page of consortium Seismic Waves in Complex 3-D Structures .