Q Estimation via Continuous Wavelet Transform
Hormoz Izadi, Kristopher A. Innanen, Michael P. Lamoureux
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.