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 practical settings, in particular band-limited signal events, the more complex non- linear MHZ signal model must minimised in order to estimate the local regularity and the additional smoothness parameter. Based on 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 Ross Lake VSP ﬁeld data captures the general absorption trend estimated by Zhang and stewart (2006). Furthermore, the power law relation provides relatively 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.
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