Multi-scale geophysical data analysis using the eigenimage discrete wavelet transform

Discrete wavelet transforms are useful in a number of signal-processing applications. When non-stationary noise spans most wavelet scales, simple rejection of certain scales in the wavelet domain often fails to achieve the desired effect because of strong intra-scale coupling effects. 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 and the feasibility of combining these transforms with eigenstructure seismic interference cancelling techniques. 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. The method also gives excellent results in coherent or random noise attenuation, wavefield separation, low-frequency processing, optimal velocity smoothing, data upscaling, and integration of well logs and seismic data. Particular benefits are due to trace matching for multiple subtraction and 4D cross-equalization that extracts subtle variations due to changes in reservoir properties from a signal whose spectral density is not stationary.