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