Continuous wavelet transforms and Lipschitz exponents as a means for analyzing seismic data

Hormoz Izadi, Kris Innanen and Michael P. Lamoureux


Irregular structures and regions of abrupt change contain important information in a signal. In seismic signal analysis, the study of singularities within a trace provides a potential for extraction of critical information. The local regularity of a seismic event is determined by the wavelet transform modulus maxima and the associated Lipschitz exponent. As a means of classifying regularities of a signal and estimating the associated Lipschitz exponent, a linear and non-linear model based on the wavelet theory is reviewed and developed. For certain kind of signal events, a simple linear model can be applied in order to determine the associated Lipschitz regularity. However, in particular for band-limited signal events with some degree of smoothness a more complex non-linear model has to be applied which can be computationally expensive and difficult to analyse. Our purpose is to try to understand the key features of this more complex model of Lipschitz regularity, and develop simple and robust methods for estimation based on this understanding.

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