Estimating frequency-dependent attenuation quality factor values from prestack surface seismic data

Abstract

The intrinsic seismic quality factor [Formula: see text] is known from poroelastic rock-physics theory to be frequency dependent, even within typical bandwidths of individual surface- and borehole-based surveys in which measurement methods usually deliver frequency-independent [Formula: see text]. Thus, measuring frequency-dependent [Formula: see text] instead offers better characterization of seismic properties and moreover a potential step toward estimating permeability directly from seismic data. Therefore, we have introduced a method to measure frequency-dependent [Formula: see text] from pairs of reflections in prestack [Formula: see text]-[Formula: see text] domain surface seismic data — a data type that, unlike a vertical seismic profile, offers useful areal coverage. Although, in principle, any analytic form with a manageable number of parameters could be prescribed, the frequency dependence of [Formula: see text] is modeled as a power law, [Formula: see text]. Inversion is done with a simple grid search over coefficient ([Formula: see text]) and exponent [Formula: see text], seeking a minimum [Formula: see text]-norm. We have found, using a numerical experiment and a synthetic data set, that it is robust and also accurate down to a signal-to-noise ratio of approximately 0.65. Then, [Formula: see text] is estimated for some 955 [Formula: see text] superbins of a 3D prestack ocean bottom cable data set over the Kinnoull field, central North Sea. All combinations of eight prominent reflections between Top Miocene and Base Cretaceous were treated together to give some 21,000 frequency-dependent and (for comparison) constant-[Formula: see text] results. The median coefficient ([Formula: see text]) and exponent [Formula: see text] were 0.0074 and 0.06, respectively, with sharply peaked distributions (excess kurtosis [Formula: see text]). Outlier, strongly frequency-dependent results, given by [Formula: see text], coincide with low-frequency “shadows” under amplitude anomalies, adversely affecting the spectra of reflections. The inferred frequency-dependent [Formula: see text] at 32.5 Hz, the center of the available bandwidth, is not statistically different from the frequency-independent [Formula: see text], 181 with a standard error from the distribution of one, derived from the same data. Hence for this data set, a constant-[Formula: see text] assumption would in fact be adequate. However, our method has the ability to measure stable estimates of [Formula: see text].