Anelastic attenuation factor: Difference between revisions

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In [[reflection seismology]], the '''anelastic attenuation factor''' or the '''seismic quality factor''', oroften expressed as the '''Q factor''' quantifies(where thehigher effectsQ ofmeans anelasticless energy loss), measures how [[attenuationSeismic wave|seismic waves]] onweaken thedue to anelastic [[seismicattenuation]]—the loss of wave |energy seismicthat wavelet]]eventually ends up as heat, caused by fluid movement and grainfriction boundarywithin frictionthe Earth’s subsurface. As Ita iswave definedtravels asthrough <math>Qa =medium 2{\pi}\leftlike (rock, \frac{E}{{\delta}E}this \rightabsorption )</math>;gradually wherereduces <math>\frac{E}{{\delta}E}</math>its isstrength theand fractioncan ofeventually energymake lostit perdisappear cyclecompletely.<ref> SheriffToksoz, RW. EM., Geldart& Johnston, LD. PH., (1995),1981. 2ndSeismic Edition.Wave Exploration SeismologyAttenuation. Cambridge University PressSEG. </ref> The ItsQ behaviourfactor saidhelps togeophysicists beunderstand [[dispersive]]these becauseeffects theon rateseismic ofsignals, attentuationaiding increasesin the study of withunderground frequencystructures.

==Introduction==

As a seismic wave propagates through a medium, the [[elastic wave | elastic]] energy associated with the wave is gradually absorbed by the medium, eventually ending up as [[heat energy]]. This is known as [[absorption]] (or anelastic attenuation) and will eventually cause the total disappearance of the seismic wave.<ref>Toksoz, W.M., & Johnston, D.H. 1981. Seismic Wave Attenuation. SEG.</ref>

==Why Measure Q?==

Q 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 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>

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

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.

''Q'' is defined as

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

where <math>\frac{{\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>

QThe 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>===

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===

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:

===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:

:<math>\frac{A_{final}}{A_{initial}}=R.G.e^{{\frac{-{\pi}ft}{Q}}}</math>;

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:<math>Y = m X + C</math>

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>

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==

* [[Acoustic attenuation]]

* [[Attenuation]]

* [[Q models (seismology)]]

* [[Kolsky Q models]]

* [[Azimi Q models]]

==References==