  In global seismology Earth's properties of fractal nature occur.
  Zygmund classes appear as the most appropriate and systematic way to measure
this local fractality. For the purpose of seismic wave propagation, we model
the Earth's properties as Colombeau generalized functions. In one spatial
dimension, we have a precise characterization of Zygmund regularity in
Colombeau algebras. This is made possible via a relation between mollifiers and
wavelets.
