Gravimetric multiscale approximation and mollifier decorrelation

The specific idea of the mollifier method in the theory of inverse problems is a “replacement (re)solution”, where one finds a too “strong ill-posedness” to bring one of the standard regularization methods (e. g. the computation of a pseudoinverse) into use. A heuristic motivation for a “mollification” is on the one hand the annoyance that high-frequency components in the solution have to be specifically damped by certain smoother structures in order to arrive at (re)solution statements at all. On the other hand, a certain amount of high-frequency components are needed to tease out transition structures in geologic signatures for decorrelation. So, at the end of a mollifier regularization, a compromise should be able to provide a wavelet decorrelation of geologic strata as much as possible in terms of geophysically relevant approximation structures close to reality, however, under (often disadvantageous) constraints of the data situation and the measurement accuracy.