  In geophysics, inverse modelling can be applied to a wide range of goals,
including, for instance, mapping the distribution of rock physical parameters
in applied geophysics and calibrating models to forecast the behaviour of
natural systems in hydrology, meteorology and climatology. A common, thorough
conceptual framework to define inverse problems and to discuss their basic
properties in a complete way is still lacking. The main goal of this paper is
to propose a step forward toward such a framework, focussing on the discrete
inverse problems, that are used in practical applications. The relevance of
information and measurements (real world data) for the definition of the
calibration target and of the objective function is discussed, in particular
with reference to the Bayesian approach. Identifiability of model parameters,
posedness (uniqueness and stability) and conditioning of the inverse problems
are formally defined. The proposed framework is so general as to permit
rigorous definitions and treatment of sensitivity analysis, adjoint-state
approach, multi-objective optimization.
