Measures of scale based on the wavelet scalogram with applications to seismic attenuation

摘要

The attenuation of seismic signal is usually characterized in the frequency domain using Fourier power spectra and is often usefully characterized by average measures, such as the center frequency or spectral mean. Fourier analysis, however, suffers from time-frequency resolution problems. Wavelet analysis has better time-frequency localization and offers superior spectral decomposition. In this paper, we show that seismic attenuation can be characterized by the scalogram (also called energy density) in the wavelet domain. A single scale encompasses a frequency band. The scalogram relates absorption to peak-scale variations. The peak scale is the scale of maximum amplitude in the scalogram. Seismic attenuation can be estimated directly from the scalogram according to the scale shift of the data and can also be described indirectly by the centroid of scale (the mean of a scalogram). In absorbing media, seismic attenuation increases with frequency, i.e., decreases with scale. In the wavelet domain, small-scale energies of the seismic signal are attenuated more rapidly than are large-scale energies as waves propagate. As a result, both the peak scale and the centroid of the signal's scalogram increase during propagation. Under the assumption of a frequency-independent Q model, these increases of the peak scale and the centroid of scale are inversely proportional to the quality factor, i.e., a lower quality factor results in an upshift of the peak scale in the scalogram and an increase of the centroid of scale. The peak-scale-shift method can be applied to seismic data with sufficiently broad signal bandwidth. The centroid of scale can be used as an attribute to qualitatively characterize seismic attenuation. Examples of gas detection in both synthetic and field data show the value of this technique.