One of the goal of our research group is to develop new software and technologies. Consortium sponsors can use and industrialize software, royalty-free. In addition to internal use of software by sponsors, several commercial software products have been based on RING technologies.


The Gocad software was initiated by Prof. Jean-Laurent Mallet and his research group in 1989 (Mallet, 1992b). The main goal of this academic project was to develop a geomodeling software using triangulated surfaces, which have the capability to manage overturned and highly faulted geological surfaces. From its inception, Gocad made the choice to use graphics workstation and work in three dimensions and not only with depth maps. One of the key technologies introduced in Gocad was Discrete Smooth Interpolation, DSI in short (Mallet, 1989; Mallet, 1992a; Mallet, 1997). This original method uses least-squares minimization to smooth triangulated surfaces under constraints representing geological information. The systematic approach to represent subsurface data and geological objects consistently with points, lines, surfaces and volumetric grids has been a distinctive feature of Gocad as compared to other software aimed at solving just one class of problems. This led to interesting uses of Gocad in geophysics, reservoir modeling, archeology, ore geology and even medicine!

During the 90's, the Gocad software, orgininally developped in C, was translated into C++ with the help of several sponsor companies. A spin-off company (T-Surf) was created in 1998 to take care of the software evolution, maintenance and support. The source code of the Gocad software was then fully transferred to T-Surf (acquired by Paradigm in 2006). Since then, RING has mostly been using the Gocad software development kit to do its research.


At the beginning of the 2000's, Jean-Laurent Mallet started developing the Geochron concept and the first software prototypes with the help of his graduate students. The main idea is described in his 2004 Mathematical Geosciences paper (Mallet, 2004) and on several conference papers at the same period (Mallet et al., 2004; Macé et al., 2004; Moyen et al., 2004; Caumon et al. 2005; Royer et al., 2006; Caumon & Mallet, 2006; Tertois & Mallet, 2006; Frank et al., 2007; Tertois & Mallet, 2007). It is to numerically compute a chronostratigraphic transform mapping any subsurface point into its image in a flattened depositional space. The first implementation of this model used implicit surfaces (also known as level sets) on a tetrahedral mesh (Moyen et al., 2004). Implicit surfaces are able to deal with a very large number of data and make modeling more automatic than classical surface-based modeling.

In 2008, what had started as a research project to make the application of geostatistics easier became a commercial product: Paradigm introduced SKUA, the first commercial implementation of the Geochron concept, which also provided new reservoir gridding algorithms (Jayr et al., 2008; Gringarten et al. 2008a,b).

More recently, the SKUA Structure Uncertainty product (Tertois et al., 2010) has also benefited from prior research by the Consortium on the stochastic perturbation of implicit structural models (Caumon & Mallet, 2006; Caumon et al., 2007; Tertois & Mallet, 2007).

Since Prof. Mallet retired from the university in 2006, he has been deeply involved in further developing the theoretical framework of Geochron, as attested by his two recent books (Mallet, 2008; Mallet, 2014).

Petrel Volume Based Modeling

In 2013, Schlumberger introduced a new structural modeling approach called volumetric based modeling (Souche et al., 2013). This method also builds on the concepts of implicit surfaces in tetrahedral meshes introduced by the Consortium during the 2000's.

What is next?

If your company is a member of the Consortium, you can readily use the software prototypes developed by RING to test, evaluate and steer the technology before it becomes available on the market...


Caumon, G., Grosse, O., & Mallet, J. L. (2005). High resolution geostatistics on coarse unstructured flow grids. In Geostatistics Banff 2004 (pp. 703-712). Springer, Netherlands.
Caumon, G., & Mallet, J. L. (2006). 3D Stratigraphic models: representation and stochastic modelling. In Int. Assoc. for Mathematical Geology–XIth International Congres. 4p.
Caumon, G., Tertois, A. L., & Zhang, L. (2007, September). Elements for stochastic structural perturbation of stratigraphic models. InPetroleum Geostatistics, EAGE.
Frank, T., Tertois, A. L., & Mallet, J. L. (2007). 3D-reconstruction of complex geological interfaces from irregularly distributed and noisy point data. Computers & Geosciences, 33(7), 932-943.
Gringarten, E., Arpat, B., Haouesse, A., Dutranois, A., Deny, L., Jayr, S., ... & Nghiem, L. (2008a). New grids for robust reservoir modeling. In SPE annual technical conference and exhibition (SPE 116649).
Gringarten, E., Arpat, B., Jayr, S., & Mallet, J. L. (2008b). New geologic grids for robust geostatistical modeling of hydrocarbon reservoir. In Proc eighth geostatistical geostatistics congress (Vol. 2, pp. 647-656).
Jayr, S., Gringarten, E., Tertois, A. L., Mallet, J. L., & Dulac, J. C. (2008). The need for a correct geological modelling support: the advent of the uvt-transform. First Break, 26(10)
Macé, L., Souche, L., & Mallet, J. L. (2004). 3D Fracture Modeling Integrating Geomechanics and Geologic Data. In 9th European Conference on the Mathematics of Oil Recovery, EAGE.
Mallet, J. L. (1989). Discrete smooth interpolation. ACM Transactions on Graphics, 8(2), 121-144.
Mallet, J. L. (1992a). Discrete smooth interpolation in geometric modelling. Computer-aided design, 24(4), 178-191.
Mallet, J. L. (1992b). GOCAD: a computer aided design program for geological applications. In K. Turner (Ed.),Three-dimensional modeling with geoscientific information systems (pp. 123-141). Springer Netherlands.
Mallet, J. L. (1997). Discrete modeling for natural objects. Mathematical Geology, 29(2), 199-219.
Mallet, J. L. (2004). Space-Time Mathematical Framework for Sedimentary Geology. Mathematical Geology, 36(1), 1-32.
Mallet, J. L., Moyen, R., Frank, T., Castanie, L., Leflon, B., & Royer, J. J. (2004). Getting Rid of Stratigraphic Grids. In 66th EAGE Conference & Exhibition.
Mallet, J. L. (2008). Numerical Earth Models. EAGE Publications BV.
Mallet, J. L. (2014).Elements of Mathematical Sedimentary Geology: the GeoChron Model. EAGE Publications BV.
Moyen, R., Mallet, J. L., Frank, T., Leflon, B., & Royer, J. J. (2004). 3{D}-Parameterization of the 3{D} geological space - The {G}eo{C}hron model. In 9th European Conference on the Mathematics of Oil Recovery, EAGE.
Royer, J. J., Mallet, J. L., Cognot, R., & Moyen, R. (2006). Geochron: a framework to estimate fracturation of deformed sedimentary layers. Proceedings of International Association of Mathematical Geology, S14-22.
Souche, L., Lepage, F., & Iskenova, G. (2013). Volume based modeling-automated construction of complex structural models. In 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013.
Tertois, A. L., & Mallet, J. L. (2006). Preserving geological information during real-time editing of faults in tetrahedral models. Proc. IAMG’2006.
Tertois, A. L., & Mallet, J. L. (2007). Editing faults within tetrahedral volume models in real time. Geological Society, London, Special Publications, 292(1), 89-101.
Tertois, A. L., Mallet, J. L., Gringarten, E., & Haouesse, A. (2010). Assessing Geometric Uncertainties in Solid Earth Models. In 72nd EAGE Conference & Exhibition.

The goal of RING is to invent, design and develop game changing technologies to reconcile earth processes and field observations within a stochastic and multiscale workflow. These technologies are implemented as software which not only serve as proofs of concept to support publications, but also can be used by others.

RING software take the form of stand-alone libraries or SKUA-GOCAD plugins (you can learn more about SKUA-Gocad on this page and on Paradigm's site). The software developed by RING may consist of:

  • Public-domain software and codes can be accessed freely (See terms of license for each particular project)
  • Closed source software is only accessible to consortium members. Sponsors can access both executable and source code of our technologies and are allowed to industrialize them, royalty free.


Concurrent Number Cruncher (CNC)

The Concurrent Number Cruncher (CNC) is a high-performance preconditioned conjugate gradient solver on the GPU using the GPGPU AMD-ATI CTM and NVIDIA CUDA APIs. The CNC was developed by Luc Buatois using a general optimized implementation of sparse matrices using Block Compressed Row Storage (BCRS) blocking strategies for various block sizes, and optimized BLAS operations through massive parallelization, vectorization of the processing and register blocking strategies.

Uncertainty Visualizer

Uncertainty Visualizer is a stand-alone application dedicated to uncertainty visualization, developped by Thomas Viard. It features two different methods, which respectively map uncertainty to the intensity of a 'fabric' texture pattern or to the blending ratio between a sharp and a blurred display of the model. Input data should be provided as grid slices given in the GSLIB format.
Uncertainty Visualizer reproduces the basic behavior of the UncertaintyViewer Gocad plugin. The Gocad plugin (accessible to sponsors) has much more features for the uncertainty displays on corner-point reservoir grids.


ParticleEngine is a visualization engine dedicated to vector fields developed by Thomas Viard and MSc student Gregoire Piquet. It is based on particles randomly sampled over the domain of interest and displaced according to the local orientation and intensity of the vectors. The vector fields are read from a file written in an extended GSLIB format. The package features two different modes of particle displacement, one on the CPU and the other on the GPU.

Magnetostratigraphic correlation (Cupydon)

Magnetostratigraphic correlation is generally a manual task. The Cupydon software allows you to automatically correlate your mag section to the reference scale. The main benefit is not so much the gain in time but the possibility to look at a large number of likely correlations depending on the length of your section and on the variations of the sedimentation rate.

Free 3D structural models

We provide 9 synthetic structural models. Their purpose is to test and benchmark geomodeling algorithms. You may reused and modify these models for research and educational purposes without limitations, provided that you cite our 2015 Computers&Geosciences paper.