Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

摘要

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