| In seismic signal analysis, irregular structures and points of sharp variation contain critical information, thus making the study of a signal's local properties an appropriate mechanism for obtaining information from seismic data. 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, the linear and non-linear Mallat-Hwang-Zhong (MHZ) signal model based on the wavelet theory is reviewed and developed.;For isolated seismic events, resembling a delta function or a Heaviside function, the linear MHZ model is used to estimate the associated Lipschitz exponent and subsequently verify the theoretical properties of the exponent. However for practical settings, in particular, band-limited signal events, the more complex non-linear MHZ signal model must be applied in order to estimate the local regularity and the additional smoothness parameter.;Based on the synthetic vertical seismic profile (VSP) modelling, a relatively complicated mathematical mapping between the Lipschitz exponent and seismic quality factor Q is obtained. However, analysing the smoothness parameter results in an invertible power law relation between the aforementioned parameter and Q. Applying the non-linear MHZ model to the Ross Lake VSP field data captures the general absorption trend estimated by Zhang and Stewart (2006). Furthermore, the power law relation provides geophysically reasonable Q values comparable to the estimated values using traditional methods, such as the steepest descent. However, for a more robust mathematical relation between the Lipschitz exponent, smoothness parameter and seismic quality factor Q, additional theoretical and field data analysis is required. |
