Geostatistics on stratigraphic grids.

@inproceedings{224_bertoncello,
 abstract = { For computational reasons, practical implementations of many geostatistical algorithms are
designed for Cartesian grids. However, many applications in folded or faulted geological structures
with complex stratigraphy, require unstructured grids containing blocks with varying support. The
current practice deals with these grids by defining a physical space, where all structural geological
features are incorporated (stratigraphic grid) and an original depositional space, where geostatistical
algorithms are applied (typically a Cartesian grid). Therefore, these two spaces need to be linked,
which is not straightforward. The traditional method consists of a direct mapping between the
two spaces, fast and easy to complete. However, this method does not ensure the respect of the
target statistics in the real space. In addition, it assumes that all the cells of the stratigraphic
grid have the same volume. Hence, important global measures such as NTG or OOIP can become
biased. The method introduced in this paper aims at overcoming these problems. It consists
first, of sampling the stratigraphic grid with a regular lattice of points. These points are then
mapped in the depositional space into a set of irregularly spaced points (due to the unfolding
and unfaulting affecting the grid-geometry). Thus, the repartition of the points in the depositional
space reflects implicitly the model geometry. Performing estimation/simulation on this set of points
and then mapping back the result ensures reproduction of target statistics in the real space and
properly accounts for the support effect. As a consequence, variances are correctly modeled, the
estimated/simulated values are smoothed according to the volume of the cells and statistics are
respected. },
 author = { Bertoncello, Antoine AND Caers, Jef AND Biver, Pierre AND Caumon, Guillaume },
 booktitle = { Proc. 28th Gocad Meeting, Nancy },
 title = { Geostatistics on stratigraphic grids. },
 year = { 2008 }
}