Statistic inversion of multi-zone transition probability models
for aquifer characterization in alluvial fans
L. Zhu, H. Gong
College of Resource Environment and Tourism, Capital Normal University,
Beijing Key Laboratory of Resource Environment and Geographic Information System, Beijing, China
Z. Dai, C. Gable
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA
P. Teatini
Dept. of Civil, Environmental and Architectural Engineering,
University of Padova, Padova, Italy
Understanding the heterogeneity arising from
the complex architecture of sedimentary sequences in alluvial
fans is challenging. This paper develops a statistical
inverse framework in a multi-zone transition probability
approach for characterizing the heterogeneity in alluvial
fans. An analytical solution of the transition probability
matrix is used to define the statistical relationships among
different hydrofacies and their mean lengths, integral scales,
and volumetric proportions. A statistical inversion is conducted
to identify the multi-zone transition probability
models and estimate the optimal statistical parameters using
the modified Gauss–Newton–Levenberg–Marquardt
method. The Jacobian matrix is computed by the sensitivity
equation method, which results in an accurate inverse solution
with quantification of parameter uncertainty. We use the
Chaobai River alluvial fan in the Beijing Plain, China, as an
example for elucidating the methodology of alluvial fan
characterization. The alluvial fan is divided into three sediment
zones. In each zone, the explicit mathematical formulations
of the transition probability models are constructed
with optimized different integral scales and volumetric
proportions. The hydrofacies distributions in the three zones
are simulated sequentially by the multi-zone transition
probability-based indicator simulations. The result of this
study provides the heterogeneous structure of the alluvial fan
for further study of flow and transport simulations.
