Abstract
This paper presents a new copula-based methodology for Gaussian and
non-Gaussian inverse modeling of groundwater flow. The presented
approach is embedded in a Monte Carlo framework and it is based on the
concept of mixing spatial random fields where a spatial copula serves as
spatial dependence function. The target conditional spatial distribution
of hydraulic transmissivities is obtained as a linear combination of
unconditional spatial fields. The corresponding weights of this linear
combination are chosen such that the combined field has the prescribed
spatial variability, and honors all the observations of hydraulic
transmissivities. The constraints related to hydraulic head observations
are nonlinear. In order to fulfill these constraints, a connected domain
in the weight space, inside which all linear constraints are fulfilled,
is identified. This domain is defined analytically and includes an
infinite number of conditional fields (i.e., conditioned on the observed
hydraulic transmissivities), and the nonlinear constraints can be
fulfilled via minimization of the deviation of the modeled and the
observed hydraulic heads. This procedure enables the simulation of a
great number of solutions for the inverse problem, allowing a reasonable
quantification of the associated uncertainties. The methodology can be
used for fields with Gaussian copula dependence, and fields with
specific non-Gaussian copula dependence. Further, arbitrary marginal
distributions can be considered.
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