Support Vector Machines for delineation of geologic facies from poorly differentiated sedimentological data.
Creators: name: Guadagnini, Alberto
name: Tartakovsky, Daniel M.
name: Wohlberg, Brendt E.
name: Tartakovsky, Daniel M.
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: Our knowledge of the spatial distribution of the physical properties of geologic 
formations is often uncertain because of ubiquitous heterogeneity and the sparsity 
of data. While many studies consider the effects of incorporating various types of 
data (including transmissivity, electrical resistivity, hydraulic heads and/or 
travel times) on predicting flow and transport processes in heterogeneous systems, 
the uncertainty associated with the delineation of lithofacies and associated 
hydraulic conductivity and porosity from limited geological and geophysical data are 
only marginally analyzed.  Such data, which include grain size distribution curves, 
are typically derived from core samples and are often poorly differentiated thus 
further compounding predictive uncertainty. 
Within statistical and stochastic frameworks, this uncertainty is quantified by 
treating a formation's properties (e.g., hydraulic conductivity) as random fields 
that are characterized by multivariate probability density functions or, 
equivalently, by their joint ensemble moments. Since in reality only a single 
realization of a geologic site exists, it is necessary to invoke the ergodicity 
assumption in order to substitute the sample spatial statistics, which can be 
calculated, for the ensemble statistics, which are actually required.  This and 
other related assumptions are often impossible to validate.
Recently we (Wohlberg et al., 2006) demonstrated that Support Vector Machine (SVM) 
techniques provide a viable alternative to geostatistical frameworks by allowing one 
to delineate lithofacies in the absence of sufficient data parameterization, without 
treating geologic parameters as random and, hence, without the need for the 
ergodicity assumptions.  This has been done by using well differentiated data.  
Here, we extend our approach to account for poorly differentiated grain size 
distribution data.  The procedure starts with the inference of hydraulic 
conductivity from the grain size distribution curves, which relies upon empirical 
relationships of, e.g., Beyer, 1964.  The heterogeneous aquifer structure can then 
be assessed by analyzing the whole ensemble of grain size distribution curves with 
the aim of identifying distinct clusters. These are then taken as representative of 
different types of materials and identify different sedimentological data. The data 
can then be analyzed by means of geostatistical or machine learning-based methods in 
order to provide an estimate of the spatial arrangement of the identified 
lithofacies. The step involving the classification of geologic information is based 
on the possibility of differentiating the available data in order to clearly 
identify distinct geologic facies. This is a crucial point, since very often grain 
size distribution curves (and geologic data in general) are poorly differentiated, 
forcing the introduction of modeling approximations.

References
Beyer, W., Zur Bestimmung der Wasserdurchlässigkeit von Kiesen und Sanden aus der 
Kornverteilung. Wasserwirtschaft-Wassertechnik (WWT) 14, 165-168, Berlin (Verlag für 
Bauwesen), 1964.
Wohlberg, B., D. M. Tartakovsky, and A. Guadagnini, Subsurface Characterization with 
Support Vector Machines, IEEE Transactions on Geoscience and Remote Sensing, in 
press, 2006.