An examination of the exponential decay method of mixed‐phase wavelet estimation

Signal processing theory states that an isolated wavelet which is causal and mixed phase may be converted to minimum phase by applying an exponential decay of amplitude with time. The exponential decay might therefore be a useful preprocessing step for seismic wavelet estimation since many estimation methods require that the wavelet in the data be minimum phase. This is the basis of a method proposed by Taner and Coburn (1980). The wavelets in a seismic trace, however, are generally not isolated, but instead are convolved with a densely populated reflection coefficient series causing severe wavelet overlap. Wavelet estimation is generally done using a window of data from the seismic trace which excludes refractions, surface waves, and data with poor signal‐to‐noise ratios. Due to the wavelet overlap, the window generally truncates wavelets at the window edges. When exponential decay is applied to the window, these truncated wavelets dominate the wavelet estimation methods. When no wavelet truncation occurs, the exponential decay converts each wavelet to minimum phase, and complete wavelets dominate the data window. If the reflection series is uncorrelated, then the autocorrelations of these data windows, when averaged over many traces, give an average autocorrelation which equals that of the decayed wavelet. This autocorrelation gives the correct minimum‐phase estimated wavelet. When truncation of wavelets does occur, the autocorrelation of the decayed data window does not equal that of the decayed wavelet, and an erroneous wavelet is estimated. Therefore, the exponential decay method is only useful for seismic wavelet estimation when data windows may be chosen such that no wavelets are truncated at the window onset.