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"Geomodeling" by Jean-Laurent Mallet

Applied Geostatistics Series

This book presents some of the more important methods that have constituted the backbone of the gOcad project from its early days to the present.

Author presents a new interpolation method for modeling natural objects that allows application of a wide range of complex data.

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TOC

1 Discrete Modeling for Natural Objects

1.1 Introduction

1.2 Discrete modeling

1.3 Interpolation

1.4 Examples of applications

1.5 Conclusions

2 Cellular Partitions

2.1 Introduction

2.2 Elements of topology

2.3 Cellular partition of an n-manifold object

2.4 Generalized Maps

2.5 Implementing GMap-based models

2.6 Conclusions

3 Tessellations

3.1 Introduction

3.2 Delaunay's tessellation

3.3 Non-Delaunay triangulated surfaces

3.4 Notion of a regular n-grid

3.5 Notion of an irregular n-grid

3.6 Implicit surfaces

3.7 Conclusions

4 Discrete Smooth Interpolation

4.1 Introduction

4.2 The DSI problem

4.3 Uniqueness of the DSI solution

4.4 The local DSI equation

4.5 Accounting for hard constraints

4.6 Accelerating the convergence

4.7 The fuzzy Control-Point paradigm

4.8 The fuzzy Control-Node paradigm

4.9 From a discrete to a continuous model

4.10 Conclusions

5 Elements of Differential Geometry

5.1 Parametric curves

5.2 Parametric surfaces

5.3 Curvature of curves drawn on a surface

5.4 Miscellaneous

5.5 Discrete modeling

5.6 Examples of applications to geology

5.7 Conclusions

6 Piecewise Linear Triangulated Surfaces

6.1 Introduction

6.2 Basic DSI constraints

6.3 Modeling a faulted surface

6.4 Continuity through faults

6.5 Global parameterization

6.6 Modifying the topology

6.7 Conclusions

7 Curvilinear Triangulated Surfaces

7.1 Introduction

7.2 Building a smooth curvilinear triangle

7.3 Gregory G1 patchwork

7.4 Recursive subdivisions

7.5 Conclusions

8 Elements of Structural Geology

8.1 Geometry of faults and horizons

8.2 Modeling stratified media

8.3 Merging seismic data with well data

8.4 Deformation analysis

8.5 Unfolding a horizon

8.6 Unfolding a stack of layers

8.7 Conclusions

9 Stochastic Modeling

9.1 Simulation versus interpolation

9.2 Probabilities in a nutshell

9.3 Random Functions

9.4 Random Fourier Series

9.5 Uniform Random Functions and P-fields

9.6 Stochastic simulators

9.7 Kriging-based methods

9.8 Blending-based method

9.9 Assessing geometric uncertainties

9.10 Conclusions

10 Discrete Smooth Partition

10.1 Introduction

10.2 The probabilistic approach

10.3 Structural constraints

10.4 Moving-Centers-based methods

10.5 A tutorial example

10.6 Conclusions

Index

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