A time-varying wavelet phase extraction method using the wavelet amplitude spectra

Abstract

The vertical resolution of seismic data is greatly affected by time-varying seismic wavelets, and the phase extraction is the key topic for the accurate wavelet extraction. The traditional methods are limited to the piecewise stationary and constant-phase assumptions, so that the extracted results are not satisfactory. In this paper, we try to explore a new time-varying wavelet phase extraction method using the wavelet amplitude information. The propagation and attenuation law of seismic wavelets is analyzed, and the relationship between the amplitude and phase spectra of time-varying wavelets is obtained by deriving the wave equation for a viscoelastic medium. We find that accurately estimating the amplitude spectra at different time points and the initial phase spectrum is necessary to extract accurate time-varying wavelet phase spectra. Based on this conclusion, the wavelet amplitude spectra and initial phase spectrum are estimated based on time–frequency spectral modelling and higher-order cumulants, respectively, so that the phase spectra of time-varying wavelets are estimated by applying the obtained relationship. The numerical simulation and real seismic data processing results demonstrate that the proposed method can improve the accuracy of time-varying wavelet phase extraction compared to the traditional method.

Keywords

• Time-varying seismic wavelet
• phase extraction
• amplitude spectra
• seismic wave equation