Why Ricker Wavelets Are Successful in Processing Seismic Data: Towards a Theoretical Explanation

Authors

Afshin Gholamy, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2014

Comments

Technical Report: UTEP-CS-14-47b

Published in Proceedings of the IEEE Symposium on Computational Intelligence for Engineering Solutions CIES'2014, Orlando, Florida, December 9-12, 2014, pp. 11-16.

Abstract

In many engineering applications ranging from engineering seismology to petroleum engineering and civil engineering, it is important to process seismic data. In processing seismic data, it turns out to be very efficient to describe the signal's spectrum as a linear combination of Ricker wavelet spectra. In this paper, we provide a possible theoretical explanation for this empirical efficiency. Specifically, signal propagation through several layers is discussed, and it is shown that the Ricker wavelet is the simplest non-trivial solution for the corresponding data processing problem, under the condition that the described properties of the approximation family are satisfied.