ABSTRACT

The seismic quality factors Q used in many applications of exploration seismology are not automatically equivalent. We identified three groups of usage of the concept of a Q: (1) a measure of internal mechanical friction within rocks, as implied in petrophysical interpretations, (2) several types of apparent Q arising from attenuation measurements, and (3) axiomatic Q defined in the viscoelastic theory. These groups differ by their roles in the interpretation, sensitivity to model assumptions, frequency dependences, and particularly by the temporal and spatial resolution. Among all types of Q, those that are most robust and useful for characterizing the material are also strongly limited in resolution and accuracy. For example, from spectral coherency studies, it is known that to measure a Q of approximately 100 with modest accuracy of 30%, measurement time intervals of about 500 ms are required. Although several inversion techniques offer models of Q at much higher resolution, such detailed Q models are usually dominated by the effects of localized structures, such as “colored” transmission across boundaries, reflectivity, or scattering. Such types of Q can be called “structural,” and they differ from the Q-factor of the medium. Detailed Q images are also sensitive to theoretical models such as background geometric spreading and assumptions about the frequency dependence of the Q. Direct association of such Qs with material properties may be inaccurate and unreliable. Measurement of geometric spreading and averaging of the structural Q produce estimates of “geometric” and scattering attenuation; however, these estimates are also strongly limited in accuracy and resolution. The viscoelastic Q (group 3 above) heavily relies on a specific mathematical model. Despite producing detailed images, the spatial resolution of viscoelastic Q is inherently limited by the nature of its relation to the frequency-dependent velocity. This resolution limit is difficult to assess quantitatively.

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