1-D seismic signal decomposition and reconstruction

Figure 1a shows the basis wavelets for a 1-D signal. There are as many wavelets as signal elements. Wavelets of the same wavelength are grouped together in rows. There are log₂ n scale lengths or rows.

Figure 1b is the seismic signal decomposed into wavelets of Figure 1a. Of interest is the plot of transform coefficients ranging from DC on the left to Nyquist on the right. Figure 1c is the iterative reconstruction by successively adding rougher wavelets (from bottom to top). Figure 1d is the converse reconstruction by successively adding smoother components. Selective reconstructions accomplish bandpass filtering.