10.4122/1.1000000209
Guadagnini, Alberto
Alberto
Guadagnini
alberto.guadagnini@polimi.it
Tartakovsky, Daniel M.
Daniel M.
Tartakovsky
dmt@ucsd.edu
Wohlberg, Brendt E.
Brendt E.
Wohlberg
brendt@t7.lanl.gov
Tartakovsky, Daniel M.
Daniel M.
Tartakovsky
dmt@ucsd.edu
Support Vector Machines for delineation of geologic facies from poorly differentiated sedimentological data.
XVI International Conference on Computational Methods in Water Resources
2006
2006
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.