Abstract. Multiple-point statistics (MPS) has shown promise in
representing complicated subsurface structures. For a practical
three-dimensional (3-D) application, however, one of the critical issues is
the difficulty in obtaining a credible 3-D training image. However,
bidimensional (2-D) training images are often available because established
workflows exist to derive 2-D sections from scattered boreholes and/or other
samples. In this work, we propose a locality-based MPS approach to
reconstruct 3-D geological models on the basis of such 2-D cross sections (3DRCS),
making 3-D training images unnecessary. Only several local
training subsections closer to the central uninformed node are used in the
MPS simulation. The main advantages of this partitioned search strategy are
the high computational efficiency and a relaxation of the stationarity
assumption. We embed this strategy into a standard MPS framework. Two
probability aggregation formulas and their combinations are used to assemble
the probability density functions (PDFs) from different subsections.
Moreover, a novel strategy is adopted to capture more stable PDFs, where the
distances between patterns and flexible neighborhoods are integrated on
multiple grids. A series of sensitivity analyses demonstrate the
stability of the proposed approach. Several hydrogeological 3-D application
examples illustrate the applicability of the 3DRCS approach in reproducing
complex geological features. The results, in comparison with previous MPS
methods, show better performance in portraying anisotropy characteristics
and in CPU cost.
Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross sections
