Gennady A. Ryzhikov and Vladimir N. Troyan
Table of contents
Introduction
1. Mathematical topics of remote sensing inverse problems
1.1 Basic principles of functional analysis
1.2 Ill-posed problems
1.3 Some aspects of mathematical statistics
2. Functional links between sounding signal fields and medium parameters
2.1 Seismology and seismics
2.2 Ocean acoustics
2.3 Electromagnetic waves in the Earth interior and ionosphere
2.4 Remote sensing of the atmosphere
3. Ray theory of sounding signal propagation
3.1 Basic concepts of ray theory
3.2 Ray approximation for scalar wave equation
3.3 WKBJ-method for 1D Helmholtz equation
3.4 Ray theory for elastic wave propagation
3.5 Ray approximation for stratified media
3.6 Surface waves in stratified media
3.7 Ray approximation for electromagnetic fields
3.8 Some aspects of the ray-tomography problem
4. Construction and interpretation of tomography functionals
4.1 Construction of linear functionals for a data set.
4.2 Tomography functional
4.3 Some examples of construction and interpretation of tomography functionals
4.4 Ray tomography functionals in dynamic-kinematic interpretation of remote sensing data
4.5 Construction of In- and Out- fields in stratified reference medium
5. Tomography interpretation of remote sensing problems
5.1 Some aspects of linear tomography
5.2 Generalized Radon inversion in diffraction tomography
5.3 Optimal algorithms in reconstructive tomography
5.4 Critical analysis of retrieval errors and the Bakus-Gilbert method
5.5 Back-projection in diffraction tomography
5.6 Regularization methods in 3D ray tomography
Appendix
References
TOMOGRAPHY AND REMOTE SENSING INVERSE PROBLEMS
.
G.A.Ryzhikov and V.N.Troyan
The book describes the state of the art in remote sensing inverse
problems and their interpretation in terms of computerized tomography.
The introductory chapter formulates some basic principles of functional
analysis, mathematical statistics and approaches to solving the ill-posed
problems. A special attention is paid to the presentation of different
methods of regularization. On the basis of the model of the sounding signal
propagation in an examined medium, the notion tomography
functional is introduced. Tomography functional maps the field of the
unknown medium parameters into the set of the experimental data.
Examples of tomography functionals are constructed for the scalar
wave equation, Lame equation, and for the transfer equation with isotropic
scattering. The main impact of the tomography experiment is relevant to
the overlapping of the tomography functional supports; that is in general
the information on a medium voxel is contained in the whole set of measurements.
The diffraction tomography algorithms are formulated, and it is
shown how a backprojection procedure in the generalized Radon transformation
relates to holography. The physical grounds are presented for applying
the proper regularization method to solve tomography problems of the remote
sensing. The optimal decision criterion is investigated and the physical
interpretation of the tomography functionals is performed. Information/statistical
characteristics of the recovery of the functional on the medium parameter
field are finally analyzed.
Mathematical Physics, Tomography, Geophysics
For researchers, students and engineers
219 pp, 17 Figs. , St. Petersburg University Press, 1994, ISBN 5-288-00773-X ( in Russian *)
Gennady
A. Ryzhikov is a Senior Researcher at the Institute of Physics of St.Petersburg
University
Vladimir
N. Troyan is a Professor of Physics, Vice-rector
for Researches of St. Petersburg University & Head of Department
of Terrestrial Physics :
198904 St.Petersburg
Petrodvorets,
Ulianovskaya 1
phone +7 812 4284322
fax +7 812 4287240
Some topics were published also in English :
Ryzhikov G.A. and Troyan V.N., 1988,
The solution of an inverse dynamic seismic
problem
for three-dimensional inhomogeneous media:
Revista de Geofisica 44, no.2, Madrid,
149-156.
Ryzhikov G.A. and Troyan V.N., 1993,
3D diffraction tomography. Part I:
construction and interpretation of tomography
functionals:
Proc. of Russian- Norwegian Oil Exploration
Workshop II
5.05-7.05.92, Norsk Hydro Research Centre,
Bergen, 41a
Ryzhikov G.A. and Troyan V.N., 1993,
3D diffraction tomography. Part II:
reconstruction algorithm with statistical
regularization.
Proc. of Russian- Norwegian Oil Exploration
Workshop II
5.05-7.05.92, Norsk Hydro Research Centre,
Bergen, 41b
Ryzhikov G.A. and Troyan V.N., 1993,
Diffraction tomography and back-projection,
in Geophysical Data Interpretation
by Inverse Modelling.
Proc. of the 9-th International Seminar on
Model
Optimization in Exploration Geophysics.
Berlin 1991. Ed. by A.Vogel et al,
Vieweg. Wiesbaden, 47-52.
Ryzhikov G.A. and Troyan V.N., 1993,
On regularization methods in 3-D ray tomography
in Geophysical Data Interpretation by
Inverse Modelling.
Proc. of the 9-th International Seminar
on Model Optimization in Exploration Geophysics.
Berlin 1991. Edited by A.Vogel, Vieweg. Wiesbaden,
37-46.
Also: V.Troyan's lectures "Inverse
seismic problems"
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Yet in Russian