High-resolution seismic signals from band-limited data using scaling laws of wavelet transforms

Time-scale spectra, obtained from seismic data wavelet transforms, are useful in analyzing local scaling properties of seismic signals. In particular, the wavelet transform modulus maxima (WTMM) spectra, obtained by following the local extrema of wavelet transforms along a constant phase line, describe characteristics of discontinuities such as interfaces. They also show a smooth behavior as a function of scale and thus allow us to derive local scaling laws. We use scaling behavior of WTMM spectra to enhance the bandwidth of seismic data. An analysis of well-log scaling behaviors and the seismic data shows that, whereas the WTMM spectrum of well logs at each interface exhibits a power-law behavior as a function of scale, the corresponding seismic signal spectrum shows a more complicated behavior, arising from seismic wavelet effects. Under the assumption that local well-log power-law behavior holds in general, a scaling law for seismic signals can be derived in terms of parameters that describe subsurface scaling effects and the seismic wavelet. A stable estimation of these parameters can be carried out simultaneously, as a function of time and over the seismic bandwidth, using the modified scaling law. No well-log information is needed to derive the seismic wavelet. Then wavelet transforms can be corrected for seismic wavelet effects and a high-resolution signal reconstructed. This reconstructed high-resolution signal can be used to map features that might not be obvious in the original seismic data, such as small faults, fractures, and fine-scale variations within channel margins.