LOCAL SIGNAL REGULARITY AND LIPSCHITZ EXPONENTS AS A MEANS TO ESTIMATE Q

摘要

The sharp, transient nature of events in a seismic trace make them classifiable as "edges" in the signal processing sense, and make edge detection and analysis a suitable tool for the extraction of information from seismic data. A specific signal model, one of whose parameters is the Lipschitz exponent (a measure of regularity), is herein reviewed, and developed as the basis upon which to locally determine the regularity of seismic events. This determination requires the collection of wavelet transform modulus maxima information, which is used in a nonlinear estimation scheme (and has, of course, its own list of sensitivities and accuracy issues). Within its regime of accuracy lies the detection of changes in the local regularity of a trace due to nonstationarity in the response. I consider a popular model of nonstationarity, i.e., a model of attenuation and dispersion, and propose local regularity as a potential means for the estimation of Q. This involves (1) utilizing a time-domain approximation of the constant Q impulse response to make some broad comments on the limiting behaviour of the regularity (Lipschitz/Holder exponent) as a function of Q, and (2) numeric tests to confirm (1) and flesh out the behaviour of the regularity with changing Q. The simplicity of the relationship suggests the use of an empirical map based on a single parameter log regression. Such a map, contingent on some basic details of a specific seismic experiment (e.g. At) might be used to generate a distribution of local Q values from derived Lipschitz exponents. Bandlimitation may be fit into the framework such that it is an impediment only as a source of inaccuracy in the estimation.