arXiv subjects

G. Hoermann

Publications and source records attributed to G. Hoermann.

2 recordsLinked to original sources

arXiv2001

Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

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.

math.AP↗

arXiv2001

Detection of wave front set perturbations via correlation: Foundation for wave-equation tomography

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals.

math-ph↗