Characterizing seismic time series using the discrete wavelet transform

The discrete wavelet transform (DWT) has potential as a tool for supplying discriminatory attributes with which to characterize or cluster groups of seismic traces in reservoir studies. The wavelet transform has the great advantage over the Fourier transform in being able to better localize changes. The multiscale nature and structure of the DWT leads to a method of display which highlights this and allows comparison of changes in the transform with changing data. Many different sorts of wavelet exist and it is found that the quality of reconstruction of a seismic trace wavelet exist and it is found that the quality of reconstruction of a seismic trace segment, using some of the coefficients, is dependent on the choice of wavelet, which leads us to consider choosing a wavelet under a best reconstruction criterion. Location shifts, time zero uncertainties, are also shown to affect the transform, as do truncations, resampling, etc. Using real data, examples of utilizing the DWT coefficients as attributes for whole trace segments or fractional trace segments are given. Provided the DWT is applied consistently, for example with a fixed wavelet, and non-truncated data, the transform produces useful results. Care must be exercised if it is applied tomore » data of different lengths. However, as the algorithm is refined and improved in the future, the DWT should prove increasingly useful.« less