The relationship between Lipschitz exponents and Q: synthetic data tests
Hormoz Izadi, Kristopher A. H. Innanen, Michael P. Lamoureux
In seismic signal analysis, points of sharp variation classified as "edges" contain a considerable amount of a signal's information, thus making edge detection and the study of a signal's local properties an appropriate mechanism for obtaining information from seismic data. Several important physical processes can in principle affect the local regularity of a reflected event in a seismic trace: processes of absorption and wave attenuation. The local regularity of a given signal is characterised by the continuous wavelet transform and subsequently measured by its corresponding Lipschitz exponent(s). For a single seismic event resembling a delta type function, a linear model can be used in order to estimate the associated Lipschitz regularity, however for practical settings a non-linear objective function would have to be minimised in order to estimate the associated regularity. A robust estimation of a functions local properties and differentiability from seismic data, alongside prior geological information, could potentially lead to processing and inversion algorithms able to discern and characterise such targets.