Gocad implementation of a new space/time mathematical framework: The geochronological space

@inproceedings{Moyen02GM,
 abstract = { One of the most difficult and recurrent problem in petroleum geology is the modeling of subsurface petrophysical
properties, such as porosity or permeability. Part of the difficulty comes from the sometimes
complex structural geology underlying. This complexity forces the building of 3D meshes, and the use of
geostatistical method to compensate. Property modeling thus often has to mix structural and petrophysical
information. Since the geometry of the layers is generally much better known than the properties,
it could be wise to “simplify the geology” by removing the influence of the geometry of layers, keeping
then only the petrophysical data.
Removing the influence of geometry not only means reducing the effects of post-depositionnal deformation,
but also erasing the geometrical variation at time of deposition. The model used for geostatistics
is thus one where all layers are horizontal, the general aspect being similar to the one of the Wheeler
diagrams used in stratigraphy. In such a space, all the faults have disappeared, and the vertical axis is no
more a geometrical coordinate z , but a geological time of deposition f . The purpose of this article is to
describe a method to concretely build such a space, using a new 3D parameterization, in GOCAD.
This new approach of the parameterization of space can also be used in many more applications, such
as estimating the tensor of deformation applied in each point of the studied volume during its history, or
measuring the sedimentary deposition speed. These application will not be developed in this article, but
are some of the goals for future improvements. We will focus on the mathematical principles necessary
to build such a parameterization, then we will look at the way it is implemented in GOCAD. Finally,
some tests and functionalities allowing to concretely use the new parameterization will be shown. },
 author = { Moyen, Rémi AND Mallet, Jean-Laurent },
 booktitle = { Proc. $22^{nd}$ Gocad Meeting, Nancy },
 title = { Gocad implementation of a new space/time mathematical framework: The geochronological space },
 year = { 2002 }
}