Local signal regularity and smoothness as a means for seismic Q estimation

Abstract

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, such as Q estimation. 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 MHZ parameters 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, analysing the smoothness parameter provides an invertible power law relation between the aforementioned parameter and Q. Applying the non-linear MHZ model to the Ross Lake VSP field, provides reasonable Q values comparable to traditional methods. 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.