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 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.
RESEARCH PROGRAMME FOR THE ELEVENTH YEAR
October 1, 2003 - September 30, 2004
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
including fitting and smoothing GOCAD models,
conversion of model parametrization, structural interface triangulation,
VRML and GOCAD visualization.
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.
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
Properties of the projection of ray coordinates onto Cartesian
coordinates within individual ray histories will be studied. New
applications of ray histories to numerical algorithms will be proposed.
The two-point ray tracing code will further be tested and applied
to various models.
4. Paraxial Fresnel edge waves
Contributions of single diffractions to the Green function may be
approximated by paraxial approximations of Fresnel edge waves in
vicinities of boundary rays between ray histories.
5. Synthetic seismograms in 3-D isotropic
and anisotropic complex structures
Methods to calculate synthetic seismograms in complex structures will
be studied, mutually compared and combined.
Calculation of synthetic seismograms by coupling ray theory
in layered models will further be tested.
Emphasis will be put on numerical implementation of Gaussian beams.
6. Seismic wave propagation in weakly anisotropic inhomogeneous media
Anisotropic common ray approximation of the coupling ray theory.
Derivation of coupling ray theory from the elastodynamic equation
concentrated on the study of errors due to neglected terms.
Theory of coupling S--wave Gaussian packets.
Definition of coupling ray theory travel times and amplitudes,
and study of frequency dispersion of S--wave coupling.
Study of accuracy of coupling ray theory in
a vicinity of S-wave singularities by comparison with more precise
methods like finite differences, reflectivity, etc.
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.
Study of models obeying ellipsoidal P--wave weak anisotropy.
Development of a P--wave ray tracer for inhomogeneous
weakly anisotropic media.
7. 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.).
8. Seismic wave propagation in anisotropic dissipative media
Computation of slowness vectors, polarisation vectors, energy and
pseudoenergy fluxes of P, S1 and S2 plane waves propagating
in general anisotropic viscoelastic media.
Both homogeneous and inhomogeneous plane waves will be considered.
Behaviour of attributes of these waves in various types
of viscoelastic anisotropic media will be studied both analytically
and numerically. Perturbation method will be used to find approximate
formulae for the attributes.
9. 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,
and the relevant numerical algorithms will be improved,
or new ones will be proposed.
Attention will also be devoted to the interpolation
between different shot and receiver positions.
10. 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 definition and high-frequency validity of velocity models.
11. Sensitivity of seismic waves to the structure
We shall study how the perturbations of a generally heterogeneous
isotropic or anisotropic structure manifest themselves
in the wavefield, and which perturbations can be detected
within a limited aperture and a limited frequency band.
12. 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.
13. 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 the accuracy of the
resulting model compared to the geological structure.
14. Local anisotropy parameter estimation from VSP measurements
Development of algorithms for the local determination of elastic
parameters from the VSP measurements. Use of P- and S-wave data.
Inversion for parameters of TI media with tilted axis of symmetry and
for the angles specifying the axis.
Attempts to answer the question whether is it possible to discriminate
between VTI and TI with tilted axis of symmetry.
Study of possibility to use NMO or AVO data to constrain the inversion.
15. 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.
16. 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
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.
17. Finite-difference solutions of elastodynamic equations
The main attention will be paid to the hybrid DW-FD and Ray-FD methods.
18. 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
prog04.ps (47 kB) with the Research Programme.
SW3D
- main page of consortium Seismic Waves in Complex 3-D Structures .