Theory and seismic applications of the eigenimage discrete wavelet transform

Discrete wavelet transforms are useful in a number of signal processing applications. To improve the scale resolution, a joint function of time, scale and eigenvalue that describes the energy density or intensity of a signal simultaneously in the wavelet and eigenimage domains is constructed. A hybrid method, which decomposes eigenimages in the wavelet domain, is developed and tested on field data with a variety of noise types. Several illustrative examples examine the ability of wavelet transforms to resolve features at several scales. Successful applications to time‐lapse seismic reservoir monitoring are presented. In reservoir monitoring, the scale‐dependent properties of the eigenstructure of the 4D data covariance matrix enable us to extract the low‐frequency time‐lapse signal that is the result of internal diffusive losses caused by fluid flow.