Multi-Scale Analysis of Well-Logs and of Seismic Reflection Data

In well-logs we often encounter sharp outliers, or singularities, that are responsible for strong reflections. However, these reflectors are different from step-functions, in the sense that step-functions are scale-invariant whereas these singularities are not. In this paper a multi-scale analysis is performed on synthetic and real well-logs, as well as on their reflection responses, in order to test a method that can distinguish between scale-invariant and scale-variant reflectors. We will show that it is possible to extract a stable local singularity exponent exfrom a well-log, and that we can obtain the same exponent from seismic reflection data.