Wednesday, June 4, 2014

Backus averaging and (negative) Q

----- 10 June 2014 -----

Got this from Sven Treitel:

      I thoroughly enjoyed your article in the June issue of TLE. You do offer an intriguing way to compute scattering Q values from velocity logs (what some folks call "extrinsic" attenuation). 
      A question: you obtained your curves by assuming a Backus averaging distance of 46 meters. Would your results and conclusions differ were you to repeat these calculations with a set of additional Backus averaging distances, some larger, some smaller than 46 meters? 
      A remark: what you call "reverse dispersion",. Sheriff's dictionary calls "normal dispersion" (see p. 247 of his dictionary, 4. edition). 
      And another remark: The fact that T(0) can be as large as 2 can be justified on an energy conservation basis, as Larry Lines et al showed in their recent paper---an argument which could be carried over, it seems to me, to the case you make for negative Q. 

My response:

       Glad you enjoyed the article. I chose 46 meter averaging length (L) for this particular well because it calculated out to max P wave frequency of 120 Hz. A bit longer L would be appropriate for a bit lower frequency and the 1/Q values would increase. Using L of the original layer thickness would give no change to vp or vs from sonic readings, thus 1/Q would be zero. Of course this is layer-induced 1/Q, there could also be some intrinsic 1/Q below 100 Hz due to things like patchy saturation or high viscosity pore fluid.
      All of this is, to my mind, a direct parallel with anisotropy. Backus calculates layer-induced anisotropy that combines with intrinsic anisotropy of shale intervals to yield total anisotropy.
      I missed the 'normal dispersion' definition in Sheriff, thank you.
     The philosophical connection between negative Q and T(0)>1 is made in the paper, but perhaps not too clearly.

Sven again:

     You could try to use the 1/Q estimates from your method to correct total 1/Q measurements from the seismic data for "elastic" absorption, thus perhaps leading to better non-elastic, intrinsic 1/Q estimates. As far as i know, the industry has yet to find a good way to separate the two effects, and yours could be an answer.

----- 4 June 2014 -----

Figures from Long-wave elastic attenuation produced by horizontal layering (Liner, 2014, June The Leading Edge).  These are a bit higher resolution than figures that made it into print. 

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Here is my original form of Figure 2.

Figure 2 (original form)
Some readers may want to know how to make such a thing. It can be generated from Ashanti's Ajax/Graphviz site by pasting in this code (and hitting the Return/Enter key):

"Sonic [P,S] and Density"->"Backus Theory"
"Avgeraging Length"->"Backus Theory"
"Backus Theory"->Anisotropy
"Backus Theory"->Dispersion
Dispersion->"Constant Q Theory"
"Field Observations"->"Constant Q Assumption"
"Constant Q Assumption"->"Constant Q Theory"
"Constant Q Theory"->"Layer-Induced Attenuation"

Very useful for building  directed graphs using GraphViz originally developed by AT&T Labs


joy said...

The real necklace of a woman is not her looks but her heart. Visit my site for more interesting offer. Thank you and God bless!

Silvia Jacinto said...

We all need challenges in our life to keep motivated. I really had a great time scanning and reading your blog site and i was so amazed with your great artwork. I do hope you could inspire more readers. You can also visit my site for some interesting stuff.