Wavelet transforms appear to hold much promise for seismic processing. One important advantage is that while the familiar Fourier transforms are constrained to work globally, or on an entire time sequence, wavelet transformations allow localization of the transform in time.
The basic features of the application of wavelet transforms are translation and dilation of a basic wavelet. Daubechies (1992) reviews these features, including orthonormal bases and frames. Strang (1989) introduces these features in a shorter presentation.
We examined wavelet transforms for applications to seismic processing and found that these transforms now appear to have limited application because of the lack of useful properties within the transformed domain. There are some data compression applications, but seismic data are not well suited to these.
The sliding Fourier transform, the Haar transform, and Daubechies D4 wavelet are examined and applied. Examples of these transforms are shown to allow a better understanding of the limits of each technique.