Anelastic attenuation factor: Difference between revisions

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In [[reflection seismology]], the '''anelastic attenuation factor''', often expressed asor '''seismic quality factor''', oroften expressed as the '''Q factor''' (whichwhere ishigher inverselyQ proportionalmeans toless attenuationenergy factorloss), quantifiesmeasures thehow effects[[Seismic ofwave|seismic waves]] weaken due to anelastic [[attenuation]]—the onloss the [[seismicof wave |energy seismicthat wavelet]]eventually ends up as heat, caused by fluid movement and grainfriction boundarywithin frictionthe Earth’s subsurface. As a seismic wave propagatestravels through a medium, thelike [[elasticrock, wavethis | elastic]] energy associated with the wave isabsorption gradually absorbedreduces byits the medium, eventually ending up as [[heat energy]]. This is known as [[Absorption_(electromagnetic_radiation)|absorption]] (or anelastic attenuation)strength and willcan eventually causemake theit totaldisappear disappearance of the seismic wavecompletely.<ref>Toksoz, W.M., & Johnston, D.H. 1981. Seismic Wave Attenuation. SEG.</ref> The Q factor helps geophysicists understand these effects on seismic signals, aiding in the study of underground structures.

==Quality factor, ''Q''==

''Q'' is defined as

:<math>Q = 2{\pi}\left ( \frac{E}{{\delta}E} \right )</math>

where <math>\frac{E}{{\delta}E}{E}</math> is the fraction of energy lost per cycle.<ref> Sheriff, R. E., Geldart, L. P., (1995), 2nd Edition. ''Exploration Seismology''. Cambridge University Press. </ref> Its behaviour said to be [[dispersive]] because the rate of attenuation increases with frequency.

The earth preferentially attenuates higher frequencies, resulting in the loss of signal resolution as the seismic wave propagates. Quantitative [[seismic attribute]] analysis of [[amplitude versus offset]] effects is complicated by anelastic attenuation because it is superimposed upon the [[Amplitude versus offset|AVO effects]].<ref> Dasgupta, R., & Clark, R.A. (1998) Estimation of Q from surface seismic reflection data. ''Geophysics'' '''63''', 2120-2128 </ref> The rate of anelastic attenuation itself also contains additional information about the lithology and reservoir conditions such as [[porosity]], saturation and [[pore pressure]] so it can be used as a useful reservoir characterization tool.<ref> Enhanced seismic Q compensation, Raji, W.O., Rietbrock, A. 2011. ''SEG Expanded Abstracts'' '''30''', 2737</ref>

where <math>\frac{E}{{\delta}E}</math> is the fraction of energy lost per cycle.<ref> Sheriff, R. E., Geldart, L. P., (1995), 2nd Edition. ''Exploration Seismology''. Cambridge University Press. </ref> Its behaviour said to be [[dispersive]] because the rate of attenuation increases with frequency.

Therefore, if ''Q'' can be accurately measured then it can be used for both compensation for the loss of information in the data and for seismic attribute analysis.

The earth preferentially attenuates higher frequencies, resulting in the loss of signal resolution as the seismic wave propagates. Quantitative [[seismic attribute]] analysis of [[amplitude versus offset]] effects is complicated by anelastic attenuation because it is superimposed upon the [[Amplitude versus offset|AVO effects]].<ref> Dasgupta, R., & Clark, R.A. (1998) Estimation of Q from surface seismic reflection data. ''Geophysics'' '''63''', 2120-2128 </ref> The rate of anelastic attenuation itself also contains additional information about the lithology and reservoir conditions such as [[porosity]], saturation and [[pore pressure]] so it can be used as a useful reservoir characterization tool.<ref> Enhanced seismic Q compensation, Raji, W.O., Rietbrock, A. 2011. ''SEG Expanded Abstracts'' '''30''', 2737</ref>

Therefore if ''Q'' can be accurately measured then it can be used for both compensation for the loss of information in the data and for seismic attribute analysis.

==Measurement of Q==

===Spectral ratio method<ref> Tonn, R. 1991. The determination of seismic quality factors Q from VSP data: A comparison of different computational methods. ''Geophys. Prosp.'' '''39''', 1-27.</ref>===

===Spectral ratio method===

The geometry of a zero-offset vertical seismic profile (VSP) makes it an ideal survey to use for the calculation of Q using the spectral ratio method. This is because of the coincident raypaths that traverse a given rock layer, ensuring that the only path difference between two reflected waves (one from the top of the interval and one from the bottom) is the interval of interest. Stacked surface [[seismic reflection]] traces would offer similar signal-to-noise ratio over a much larger area but cannot be used with this method because every sample represents a different raypath and therefore will have experienced different attenuation effects.<ref>Dasgupta, R., & Clark, R.A. (1998) Estimation of Q from surface seismic reflection data. ''Geophysics'' '''63''', 2120-2128</ref>

===Spectral ratio method<ref> Tonn, R. 1991. The determination of seismic quality factors Q from VSP data: A comparison of different computational methods. ''Geophys. Prosp.'' '''39''', 1-27.</ref>===

The geometry of a zero-offset vertical seismic profile (VSP) makes it an ideal survey to use for the calculation of Q using the spectral ratio method. This is because of the coincident raypaths that traverse a given rock layer, ensuring that the only path difference between two reflected waves (one from the top of the interval and one from the bottom) is the interval of interest. Stacked surface [[seismic reflection]] traces would offer similar signal-to-noise ratio over a much larger area but cannot be used with this method because every sample represents a different raypath and therefore will have experienced different attenuation effects.<ref>Dasgupta, R., & Clark, R.A. (1998) Estimation of Q from surface seismic reflection data. ''Geophysics'', '''63''', 2120-2128</ref>

Seismic wavelets captured before and after traversing a medium with seismic quality factor, ''Q'', on coincident raypaths will have amplitudes that are related as follows:

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This equation shows that if the logarithm of the spectral ratio of the amplitudes before and after traversing the medium is plotted as a function of frequency, it should yield a [[linear relationship]] with an [[Y-intercept|intercept]] measuring the elastic losses (R and G) and the [[gradient]] measuring the inelastic losses, which can be used to find ''Q''.

The above formulation implies that Q is independent of frequency. If Q is frequency-dependent, the spectral ratio method can produce systematic bias in Q estimates <ref>Gurevich, B., and Pevzner, R., 2015, How frequency dependency of Q affects spectral ratio estimates, ''Geophysics'' '''80''', A39-A44.</ref>

==References==

{{reflist}}

In practice prominent phases seen on seismograms are used for estimating the Q. Lg is often the strongest phase on the seismogram at regional distances from 2° to 25°, because of its small-energy leakage into the mantle and used frequently for estimation of crustal Q. However, attenuation of this phase has different characteristics at oceanic crust. Lg may be suddenly disappeared along a particular propagation path which is commonly seen at continental-oceanic transition zones. This phenomenon refers as "Lg-Blockage" and its exact mechanism is still a puzzle.<ref>Mousavi, S. M., C. H. Cramer, and C. A. Langston (2014), Average QLg, QSn, and observation of Lg blockage in the continental, J. Geophys. Res. Solid Earth, 119, doi:10.1002/2014JB011237.</ref>

==See also==

* [[Attenuation]]

* [[Acoustic attenuation]]

* [[Attenuation]]

* [[Q models (seismology)]]

* [[Kolsky Q models]]

* [[Azimi Q models]]

==References==

{{reflist}}

[[Category:Seismology measurement]]