In this thesis, I have introduced and presented a new time-frequency distribution, termed the Signal-Dependent Distribution (SDD), which can by-pass the Gabor Uncertainty Principle, with a trade-off instead between joint time-frequency transform and suppression of transform artefacts. In two different synthetic seismic data sets, the SDD provided estimates of attenuation in closer agreement to the input attenuation than those from a fixed- (short-time-Fourier-transform) and a variable-window (Stockwell transform) time-frequency transform. The SDD also provided spectral ratio surfaces from a pre-stack gathers, using the pre-stack Q inversion (PSQI) method, more consistent with a frequency-independent attenuation model than the fixed- and variable-window transforms.
Frequency-dependent Q can be estimated in the PSQI method if the seismic attenuation quality factor, Q, is assumed to follow a powerlaw frequency-dependence, Q=af^b. Utilising the SDD to form spectra, the modified PSQI method found a frequency exponent, b, of only 0.074±0.001 (median 0.06) for the Kinnoull field in the North Sea, implying that an approximation of frequency-independent Q is valid for the Kinnoull dataset. Higher b values were found to coincide with sudden, localised, drops in centroid frequency beneath amplitude anomalies: they were inferred not to be due to a genuine frequencydependence of Q, but to interference on the spectral ratio surface.
The SDD was then used to estimate spectra in the PSQI method applied to: the Kinnoull pre-stack surface seismic dataset; a spectral ratio method applied to a stacked surface seismic survey;
and VSP data for well 16/23-7. The three sets of attenuation estimates were compared to each other, and also to average energy and average centroid frequency maps derived from the stacked seismic dataset. Only the attenuation values estimated from the stacked seismic data and the VSP data correlated well with each other (median 1000/Q of 9.2±0.1 and 10.4±2.0 respectively). 1/Q attenuation maps from stacked and pre-stack seismic data did not correlate coherently with the centroid frequency or energy maps, nor did the pre-stack attenuation values correlate with the VSP data. This inconsistency remains unexplained.
This method of estimating frequency-dependent seismic attenuation quality factor was then applied to 6 VSP datasets located in the Barents Sea. Although the formation-averaged frequency exponent b varied between -0.1 and 0.2, the median value was 0.02, again supporting an assumption of frequency-independent attenuation within the seismic bandwidth. Using coincident well logs, statistically significant correlations were found between intrinsic attenuation and bulk, shear, and Young’s moduli, and Poisson’s ratio. In contrast, no robust relationship was found between petrophysical parameters and attenuation in the seismic bandwidth. However, a squirt flow model fitted to the estimated power-law curves of frequency-dependent 1/Q implied crack aspect of between 1 and 6 x 10^−3, similar to the crack aspect ratio of 0.1-1.0 x 10^−3 expected to be responsible for the majority of squirt flow induced attenuation.
