Abstract
The optimization of criteria related to geophysical data (e.g. seismic waves travel times) is the most used method for the determination of geological structures in petroleum exploration. In this thesis, we propose to define geological criteria whose optimization, simultaneously with geophysical ones, will permit to obtain a better constrained underground model. To do that, we use the geometrical concept of foliations to describe sedimentary structures and we represent such a foliation by one of its parametric representations. The study of the unit normal vector field and its directional derivative leads us to define geometrical data (normal vector, convergence vector, total curvature, mean curvature, axial curvature) traducing structure`s geological properties (dip, parallelism, developability, smoothness of interfaces, folds axis directions). The extrapolation problem consists in the optimization of these criteria under equality constraints. This problem, considers a single foliation and only the geological criteria. This approach permits to show the effects of the different data. The canonical indetermination, due to the multiplicity of parameterization describing the same geometrical object, is locally solved by a theorem we demonstrate. This leads us to implement a general method which allows to obtain interesting numerical results. Finally, we study the C{sub 2}-parametrization space and we deduce
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Citation Formats
Rakotoarisoa, H.
Geometric modeling and optimization of three-dimensional geologic structures.
France: N. p.,
1992.
Web.
Rakotoarisoa, H.
Geometric modeling and optimization of three-dimensional geologic structures.
France.
Rakotoarisoa, H.
1992.
"Geometric modeling and optimization of three-dimensional geologic structures."
France.
@misc{etde_10136334,
title = {Geometric modeling and optimization of three-dimensional geologic structures}
author = {Rakotoarisoa, H}
abstractNote = {The optimization of criteria related to geophysical data (e.g. seismic waves travel times) is the most used method for the determination of geological structures in petroleum exploration. In this thesis, we propose to define geological criteria whose optimization, simultaneously with geophysical ones, will permit to obtain a better constrained underground model. To do that, we use the geometrical concept of foliations to describe sedimentary structures and we represent such a foliation by one of its parametric representations. The study of the unit normal vector field and its directional derivative leads us to define geometrical data (normal vector, convergence vector, total curvature, mean curvature, axial curvature) traducing structure`s geological properties (dip, parallelism, developability, smoothness of interfaces, folds axis directions). The extrapolation problem consists in the optimization of these criteria under equality constraints. This problem, considers a single foliation and only the geological criteria. This approach permits to show the effects of the different data. The canonical indetermination, due to the multiplicity of parameterization describing the same geometrical object, is locally solved by a theorem we demonstrate. This leads us to implement a general method which allows to obtain interesting numerical results. Finally, we study the C{sub 2}-parametrization space and we deduce some partial conclusions about the existence and the unicity of a continuous solution to the extrapolation problem. 39 refs., 49 figs, 4 appendices.}
place = {France}
year = {1992}
month = {Nov}
}
title = {Geometric modeling and optimization of three-dimensional geologic structures}
author = {Rakotoarisoa, H}
abstractNote = {The optimization of criteria related to geophysical data (e.g. seismic waves travel times) is the most used method for the determination of geological structures in petroleum exploration. In this thesis, we propose to define geological criteria whose optimization, simultaneously with geophysical ones, will permit to obtain a better constrained underground model. To do that, we use the geometrical concept of foliations to describe sedimentary structures and we represent such a foliation by one of its parametric representations. The study of the unit normal vector field and its directional derivative leads us to define geometrical data (normal vector, convergence vector, total curvature, mean curvature, axial curvature) traducing structure`s geological properties (dip, parallelism, developability, smoothness of interfaces, folds axis directions). The extrapolation problem consists in the optimization of these criteria under equality constraints. This problem, considers a single foliation and only the geological criteria. This approach permits to show the effects of the different data. The canonical indetermination, due to the multiplicity of parameterization describing the same geometrical object, is locally solved by a theorem we demonstrate. This leads us to implement a general method which allows to obtain interesting numerical results. Finally, we study the C{sub 2}-parametrization space and we deduce some partial conclusions about the existence and the unicity of a continuous solution to the extrapolation problem. 39 refs., 49 figs, 4 appendices.}
place = {France}
year = {1992}
month = {Nov}
}