  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.
