| Prompted by the desire to find techniques that enable the removal of coherent noise from seismic data that is nonstationary and time-localized in nature, an investigation was initiated in pursuit of suitable time-dependent representations. Specifically, the techniques investigated are methods that have received much recent attention: time-dependent distributions, time-dependent ARMA models, and time-dependent signal decompositions. Furthermore, while investigating these techniques, attention was given to other nonstationary aspects of seismic data where these techniques may be useful. The nonstationarities of primary interest here are wavelet spreading, time-varying gain, and coherent noise.; It was determined that time-dependent distributions are of little use in the issues discussed here; however, time-dependent ARMA models and time-dependent decompositions do show promise. Time-dependent ARMA models with time-varying coefficients may be useful in cases where wavelet nonstationarity is such that pseudo-stationary assumptions are invalid. The most notable case for this is time-varying gain. Time-dependent signal decompositions that are comprised of functions that have time and frequency concentration show promise for the removal of coherent noise, even in cases where the signal and noise have overlapping spectra. Furthermore, it was determined that, for two-dimensional coherent noise removal, the Gabor representations are the most likely to be successful. However, the results show that the Gabor representations are no better than traditional filtering in the removal of coherent noise; in contrast, they are better than Singular Value Decomposition at the removal of localized incoherent noise. |
