Taxonomy of Q

Abstract

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.

Windowless Q‐factor tomography by the instantaneous frequency

“…2003; Prasad et al . 2005; Carcione and Picotti 2006; Carcione 2014; Morozov and Baharvand Ahmadi 2015, among many others). A possible cause for energy loss is the boundary friction of the grains composing the rocks: thus, a low Q factor may suggest a poorly consolidated formation.…”

Compensating elastic transmission losses for P‐wave attenuation estimation from sonic logs

“…The SA method yields the relative attenuation from the measurement of a single source–receiver pair leaving the combination of (a) source signature and coupling, (b) geometrical spreading and (c) receiver coupling and response to be an unknown constant. This relative attenuation is evaluated over the span from transmitter to receiver instead of array aperture because the random error could be notably suppressed with a longer measurement time interval to give a more stable estimate (White ; Morozov and Baharvand Ahmadi ). The averaging effect over the distances between transmitter and receivers makes the resolution of attenuation profile lower (for example, 3.65‐4.72 m for Baker Hughes XMAC‐F1 tool) than the receiver array aperture (1.07 m for XMAC‐F1; Tang and Cheng ).…”

“…Depending on different types of measurements (lab, vertical seismic profile or sonic logging) and attenuation estimation methods, various kinds of elastic transmission losses may be mixed into the estimated attenuation, making the relation between petrophysical properties and attenuation intricate and variable (White ; Morozov and Baharvand Ahmadi ). In order to measure the attenuation, an adequately accurate model of the underlying elastic structure is normally required (Deng and Morozov ).…”

Seismic attenuation attributes with applications on conventional and unconventional reservoirs

“…Conventionally, energy loss is represented by the quality (Q) factor. However, despite different authors having used the identical name, Q-value computation in different contexts is not the same (Morozov and Ahmadi, 2015). Attenuation estimation of a given type should imply a specific energy loss mechanism.…”