A combined Wigner-Ville and maximum entropy method for high-resolution time-frequency analysis of seismic data

Abstract

The variation of frequency content of a seismic trace with time carries information about the properties of the subsurface reflectivity sequence. As a result, analysis of the data in terms of the local frequency content can provide a worthwhile addition to the standard procedures that are used in seismic processing and seismostratigraphic interpretation. The theory of quadratic time-frequency (TF) representations, such as the Wigner-Ville distribution (WVD), provides a solid foundation for local frequency analysis of seismic data and seismic attribute extraction. However, because of its quadratic nature, the WVD processes cross terms, which can limit the readability of the decomposition. To overcome this problem, we have used the key idea of the maximum entropy method of Burg, to compute a prediction error operator associated with the power spectrum of a given signal. The operator was then used to extend the kernel of Wigner-Ville of the signal, given by the elements of its covariance matrix. The Fourier transform of the extended kernel provided a high-resolution maximum entropy power spectrum of Wigner-Ville. We found, from the framework of the proposed method, how the common seismic attributes can be extracted as characteristics of the local spectrum. Furthermore, we devised a formula to estimate a robust and stable average instantaneous frequency (AIF) in the time domain. The high resolution achieved in the TF domain has been a key aspect for applying the proposed method to the Gulf of Mexico data set. Mapping of the channels and infill lithology is made possible by analyzing the spectral variation of the AIF cube, and the spectral decomposition based on the proposed method allows reliable information on the probable location and extension of a gas reservoir.