ABSTRACT

The intrinsic seismic quality factor Q 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 Q. Thus, measuring frequency-dependent Q 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 Q from pairs of reflections in prestack τ-p 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 Q is modeled as a power law, Q(f)=afb. Inversion is done with a simple grid search over coefficient (1/a) and exponent b, seeking a minimum L1-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, Q is estimated for some 955 250×250  m 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-Q results. The median coefficient (1/a) and exponent b were 0.0074 and 0.06, respectively, with sharply peaked distributions (excess kurtosis >10). Outlier, strongly frequency-dependent results, given by |b|>0.2, coincide with low-frequency “shadows” under amplitude anomalies, adversely affecting the spectra of reflections. The inferred frequency-dependent Q at 32.5 Hz, the center of the available bandwidth, is not statistically different from the frequency-independent Q, 181 with a standard error from the distribution of one, derived from the same data. Hence for this data set, a constant-Q assumption would in fact be adequate. However, our method has the ability to measure stable estimates of Q(f).

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