  We provide a comprehensive analytic study (rigorous and qualitative) of the
conditions for the existence of a a positive kinematic back reaction term
$\QQ>0$, in the context of Buchert's scalar averaging formalism applied to
spherically symmetric Lema\^itre-Tolman-Bondi (LTB) dust solutions in which
averaging domains are given as spherical comoving regions containing a symmetry
center. We introduce proper volume and quasi-local average functionals and
functions in order to examine the conditions for $\QQ\geq 0$, and in the
process we also explore the relation between back reaction, spatial curvature
and binding energy for a wide variety of LTB configurations. The back reaction
term is positive for all "hyperbolic" regular domains with negative spatial
curvature, either in the full radial range or in the radial asymptotic range.
This result is also valid if these domains contain an inner "elliptic" region
with positive curvature undergoing local collapse. For some cases in which
positive spatial curvature decreases asymptotically, the conditions for a
positive back reaction can still be met but seem to be more restrictive. Since
$\QQ>0$ is a necessary condition for a positive "effective" acceleration that
would mimic the effect of dark energy (in the context of Buchert's formalism),
we examine this issue in LTB models in a follow up paper (part II).
