  Recently there has been a renewed activity in the physics of violations of
Lorentz invariance in the neutrino sector. Flavor dependent Lorentz violation,
which generically changes the pattern of neutrino oscillations, is extremely
tightly constrained by oscillation experiments. Flavor independent Lorentz
violation, which does not introduce new oscillation phenomena, is much more
weakly constrained with constraints coming from time of flight and anomalous
threshold analyses. We use a simplified rotationally invariant model to
investigate the effects of finite baselines and energy dependent dispersion on
anomalous reaction rates in long baseline experiments and show numerically that
anomalous reactions do not necessarily cut off the spectrum quite as sharply as
currently assumed. We also present a revised analysis of how anomalous
reactions can be used to cast constraints from the observed atmospheric high
energy neutrinos and the expected cosmogenic ones.
