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In geosciences, Geomodeling (or Geomodelling) concerns the methods to create a three-dimensional numerical model of a geological domain based on geophysical and geological observations made on and below the Earth surface. A Geomodel is the numerical equivalent of a three-dimensional geological map complemented by a description of physical quantities in the domain of interest .
Geomodeling is related to the concept of Shared Earth Model  which is a pluridisciplinary, interoperable and updatable knowledge base about the subsurface. Geomodeling is routinely used for exploration and management of hydrocarbon reservoirs. More generally, geomodeling can be involved in the management of natural resources and natural hazards.
Geomodeling generally involves the following steps:
- Preliminary analysis of geological context of the domain of study.
- Interpretation of available data and observations as point sets or polygonal lines (e.g. "fault sticks" corresponding to faults on a vertical seismic section).
- Construction of a structural model describing the main rock boundaries (horizons, unconformities, intrusions, faults) 
- Definition of a three-dimensional mesh honoring the structural model to support volumetric representation of heterogeneity (see Geostatistics) and solving the Partial Differential Equations which govern physical processes in the subsurface (e.g. seismic wave propagation, fluid transport in porous media).
- Defining an appropriate Ontology to describe geological objects at various scales of interest
- Integrating diverse types of observations into 3D geomodels: geological mapping data, borehole data and interpretations, seismic images and interpretations, potential field data, well test data, etc.
- Characterizing uncertainty about the geomodels to help assess risk. Therefore, Geomodeling has a close connection to Geostatistics and Inverse problem theory.
Geomodeling and CAD share a lot of common technologies. Software is usually implemented using object-oriented programming technologies in C++, Java or C# on one or multiple computer platforms. The graphical user interface generally consists of one or several 3D and 2D graphics windows to visualize spatial data, interpretations and modeling output. Such visualization is generally achieved by exploiting graphics hardware. User interaction is mostly performed through mouse and keyboard, altough 3D pointing devices and immersive environments may be used in some specific cases.
In the 70's, geomodeling mainly consisted of automatic 2D cartographic techniques such as contouring, implemented as FORTRAN routines communicating directly with plotting hardware. The advent of workstations with 3D graphics capabilities during the 80's gave birth to a new generation of geomodeling software with graphical user interface which became mature during the 90's  
Geomodeling is implemented through software applications. Current software is mainly developed and commercialized by oil and gas or mining industry software vendors:
- 3D Geomodeller (Intrepid Geophysics)
- DecisionSpace Earth Modeling (Haliburton)
- Earthvision (Dynamic Graphics)
- Geomodelling Corp.
- Gocad-SKUA (Paradigm)
- Jewel Suite (JOA)
- Kingdom Suite (SMT)
- Leapfrog (Aranz Geo Ltd)
- Petrel (Schlumberger)
- RMS (Roxar)
Moreover, industry Consortia or companies are specifically working at improving standardization and interoperability of earth science databases and geomodeling software:
- Standardization: GeoSciML by the Commission for the Management and Application of Geoscience Information, of the International Union of Geological Sciences.
- Standardization: RESQML(tm) by Energistics
- Interoperability: OpenSpirit, by TIBCO(r)
- Mallet, J.-L. (2008). Numerical Earth Models, EAGE, ISBN 978-90-73781-63-4
- Franchi, J. R. (2002). Shared Earth Modeling, Gulf Professional Publishing, ISBN 0750675225
- Caumon, G., Collon-Drouaillet, P., Le Carlier de Veslud, C., Sausse, J. and Viseur, S. (2009), Surface-based 3D modeling of geological structures, Mathematical Geosciences, 41(9):927-945
- Caumon, G., Towards stochastic time-varying geological modeling (2010), Mathematical Geosciences, 42(5):(555-569)
- Perrin, M., Zhu, B., Rainaud, J.F. and Schneider, S. (2005), Knowledge-driven applications for geological modeling, "Journal of Petroleum Science and Engineering", 47(1-2):89-104
- Mallet, J.-L., Geomodeling, Applied Geostatistics Series. Oxford University Press. ISBN 978-0195144604
- | Dynamic Graphics History
- Origin of the Gocad software
- J. L. Mallet, P. Jacquemin, and N. Cheimanoff (1989). GOCAD project: Geometric modeling of complex geological surfaces, SEG Expanded Abstracts 8, 126, DOI:10.1190/1.1889515
Further resources and information about geomodeling may be obtained from:
- American Association of Petroleum Geologists
- Geomodeling Division of the Canadian Society of Petroleum Geologists
- International Association of Mathematical Geosciences
- Gocad Consortium
- Society of Exploration Geophysicists
- Society of Petroleum Engineers
- Geomodeling Network on LinkedIn