  In many geoscientific applications, multiple noisy observations of different
origin need to be combined to improve the reconstruction of a common underlying
quantity. This naturally leads to multi-parameter models for which adequate
strategies are required to choose a set of 'good' parameters. In this study, we
present a fairly general method for choosing such a set of parameters, provided
that discrete direct, but maybe noisy, measurements of the underlying quantity
are included in the observation data, and the inner product of the
reconstruction space can be accurately estimated by the inner product of the
discretization space. Then the proposed parameter choice method gives an
accuracy that only by an absolute constant multiplier differs from the noise
level and the accuracy of the best approximant in the reconstruction and in the
discretization spaces.
