Wavelet transform filtering of seismic data by semblance weighting
Victor Iliescu, Gary F. Margrave
The presence of noise in a nonstationary signal (i.e., whose frequency content varies with time) complicates the extraction of meaningful information from the signal. The classical Fourier domain of such a signal can only separate the noise from the useful signal energy if they have different frequency content. For nonstationary signals the windowed Fourier transform has been introduced to localize the signal in time. The windowing is accomplished by a weight function that places less emphasis near an interval's endpoints than in the middle. The short-time Fourier transform (STFT) thereby decomposes a signal into a time frequency plane. Nonstationary filtering can be done by prescribing weights that vary with time and frequency, which are applied to the decomposed data. An inverse STFT then reconstructs the filtered signal. Recently, the wavelet transform (WT) has been applied in diverse fields such as mathematics, quantum physics, engineering and geophysics. The WT decomposes a signal in a time-scale frame. The seismic data can be filtered using the WT in a form similar to time-frequency filtering techniques. This paper explores a method of filtering seismic data using the discrete wavelet transform (DWT) with filter weights in the wavelet domain using a time-domain semblance measure. The semblance coefficients, as a measure of multichannel coherence, serve to emphasise the signal in the wavelet coefficients of the decomposed trace. This method has been tested on a Blackfoot final stack where it appears to improve the resolution of the section.