  It is common and convenient to treat distributed physical parameters as
Gaussian random fields and model them in an "inverse procedure" using
measurements of various properties of the fields. This article presents a
general method for this problem based on a flexible parameterization device
called "anchors", which captures local or global features of the fields. A
classification of all relevant data into two categories closely cooperates with
the anchor concept to enable systematic use of datasets of different sources
and disciplinary natures. In particular, nonlinearity in the "forward models"
is handled automatically. Treatment of measurement and model errors is
systematic and integral in the method; however the method is also suitable in
the usual setting where one does not have reliable information about these
errors. Compared to a state-space approach, the anchor parameterization renders
the task in a parameter space of radically reduced dimension; consequently,
easier and more rigorous statistical inference, interpretation, and sampling
are possible. A procedure for deriving the posterior distribution of model
parameters is presented. Based on Monte Carlo sampling and normal mixture
approximation to high-dimensional densities, the procedure has generality and
efficiency features that provide a basis for practical implementations of this
computationally demanding inverse procedure. We emphasize distinguishing
features of the method compared to state-space approaches and
optimization-based ideas. Connections with existing methods in stochastic
hydrogeology are discussed. The work is illustrated by a one-dimensional
synthetic problem.
  Key words: anchored inversion, Gaussian process, ill-posedness, model error,
state space, pilot point method, stochastic hydrogeology.
