  Geo-neutrinos emitted by heat-producing elements (U, Th and K) represent a
unique probe of the Earth interior. The characterization of their fluxes is
subject, however, to rather large and highly correlated uncertainties. The
geochemical covariance of the U, Th and K abundances in various Earth
reservoirs induces positive correlations among the associated geo-neutrino
fluxes, and between these and the radiogenic heat. Mass-balance constraints in
the Bulk Silicate Earth (BSE) tend instead to anti-correlate the radiogenic
element abundances in complementary reservoirs. Experimental geo-neutrino
observables may be further (anti)correlated by instrumental effects. In this
context, we propose a systematic approach to covariance matrices, based on the
fact that all the relevant geo-neutrino observables and constraints can be
expressed as linear functions of the U, Th and K abundances in the Earth's
reservoirs (with relatively well-known coefficients). We briefly discuss here
the construction of a tentative "geo-neutrino source model" (GNSM) for the U,
Th, and K abundances in the main Earth reservoirs, based on selected
geophysical and geochemical data and models (when available), on plausible
hypotheses (when possible), and admittedly on arbitrary assumptions (when
unavoidable). We use then the GNSM to make predictions about several
experiments ("forward approach"), and to show how future data can constrain - a
posteriori - the error matrix of the model itself ("backward approach"). The
method may provide a useful statistical framework for evaluating the impact and
the global consistency of prospective geo-neutrino measurements and Earth
models.
