  We here analyze the propagation of transients of fluid-rock temperature and
pressure through a thin boundary layer, where a steady trend is present,
between two adjacent homogeneous rocks. We focus on the effect of convection on
transients crossing such thin layer. In comparison with early models where this
boundary was assumed a sharp mathematical plane separating the two rocks, here
we show a realistic analysis of such boundary layer that implies a novel
nonlinear model. Its solutions describe large amplitude, quick and sharp
transients characterized by a novel drift and variations of the signal
amplitude, leading to a nonlinear wave propagation. Possible applications are
in volcanic, hydrologic, hydrothermal systems as well as for deep oil drilling.
In addition, this formalism could easily be generalized for the case of a
signal arriving in a rock characterized by a steady trend of pressure and/or
temperature. These effects, being proportional to the initial conditions, can
also give velocity variations not particularly important. A further heuristic
model has therefore been analyzed, i.e. assuming a pressure dependent rock
permeability. In this way, a remarkable increase of the system velocities is
obtained.
