Abstract
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Seismograms are synthesized for models with arbitrary spatial variations in compressional- and shear-wave quality factors (Qusd\rm\sb{p}usd and Qusd\rm\sb{s}usd), as well as in density (usd\rhousd) and compressional- and shear-wave velocities (Vusd\rm\sb{p}usd and Vusd\rm\sb{s}usd). Q effects, including their interaction with Vusd\rm\sb{p}usd, Vusd\rm\sb{s}usd, and usd\rhousd, contribute significantly to the seismic response of reservoirs. Comparisons of elastic and viscoelastic responses for both surface and borehole recordings for a sequence of viscoelastic models of increasing complexity from a homogeneous medium, to a fault zone, a near-surface attenuating zone, inclusions and hydrocarbon reservoirs show pronounced Q-dependent attenuation; analysis of data from viscoelastic media using elastic, rather than a viscoelastic, model may result in misleading or erroneous interpretations. Q estimates are made by direct measurements of energy loss per cycle from primary P and S waves, as a function of frequency. Assuming that intrinsic Q is frequency-independent and scattering Q is frequency-dependent over the frequencies of interest, the relative contributions of each, to a total observed Q, may be estimated. Test examples are produced by computing viscoelastic synthetic seismograms using a pseudospectral solution with inclusion of relaxation mechanisms (for intrinsic Q) and a fractal distribution of scatterers (for scattering Q). In the inverse problem, performed by a global least squares search, intrinsic Qp and Qs estimates are reliable and unique when their absolute values are sufficiently low that their effects are measurable in the data. Large Qp and Qs have no measurable effect and hence are not resolvable. and A are less unique as they exhibit a tradeoff as predicted by Blair's equation. In-situ measurements are made from data from the North Sea, the New Madrid seismic zone, Turkey, and north Texas. All provide internally consistent, and geologically reasonable, results. For the P-waves in all four data sets, intrinsic and scattering contributions are of approximately the same importance; for S-waves, the intrinsic contributions dominate.
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