Many thanks to Jeff Shragge of UWA for touring us around the Perth area after the DISC. A lovely day indeed.
********** FAQ **************
Q1. Is the attenuation you describe appropriate for displacement measurements, particle velocity, acceleration, or all three?
A1. I would say the mathematical models of constant Q or viscous attenuation are valid for all 3 so long as the data type is consistent. By that I mean if we compare Q from VSP and surface seismic, we should use the same data type for each.
Q2. In data processing, we typically use Q>100 for Q-compensation and modeling, yet you say that Q=20-25 is consistent with published data. How do you explain this? (same question was asked in Brisbane)
A1. I think the Q specified in processing and layer properties in, say, reflectivity modeling represent intrinsic attenuation and, therefore, I agree with a value of 100 or more. When I say Q=20-25 in field data, I am referring to total Q with includes intrinsic and apparent attenuation. For example, if you have a layered model from well logs and do reflectivity modeling with Q=5000 in each layer, the modeled wave field will still include layer scattering effects of O'Doherty-Anstey type leading to an effective Q in the 20-25 range.
Q3. Do you know how to derive the equation for constant-Q addition? (this came from side conversation with Tobias Muller)
A3. I have not seen a derivation in the literature, but here is one. Total attenuation Q is composed of intrinsic Qi and apparent Qa. The exponential decay relationship is
Exp(-(Pi f x)/(V Q)) = Exp(-(Pi f x)/(V Qi)) * Exp(-(Pi f x)/(V Qa))
Combining exponents on the righthand side and taking the log of both sides gives
-(Pi f x)/(V Q) = -(Pi f x)/(V Qi) - (Pi f x)/(V Qa)
Canceling common factors we get the constant-Q addition relationship
1/Q = 1/Qi + 1/Qa
********** Feedback ************** updated 10 June 2012
1. Tobias Müller
2. Mick Micenko
Tobias.Mueller@csiro.au Sun, Mar 4, 2012
I enjoyed very much the DISC lecture you gave the other day in Perth.
The way you promote the many aspects of seismic dispersion to
the oil/seismic industry is great.
It is interesting that we (my CSIRO colleagues and Boris Gurevich’s group at Curtin Uni)
noticed a recent spike of interest from the industry in seismic attenuation/dispersion studies.
For example, we have an ongoing project with Chevron to estimate apparent and intrinsic attenuation from VSP’s and well logs (all data coming from NW shelf Australia).
Something on the slow S wave you mentioned in one of your slides:
Q1) Why hasn’t it been predicted by Biot?
Biot decided to neglect shear stresses in the viscous fluid from the outset of his derivation. To fix that problem he introduced the viscous correction discussed in the 2nd JASA paper in 1956 (...’higher frequency range’). In the de la Cruz and Spanos (1985) theory this fluid shear stresses have been properly upscaled and give rise to a second shear wave Pratap Sahay summarized the whole story in his 2008 GEOPHYSICS paper ‘On the Biot slow S wave’).
Q2) Can it be experimentally observed?
In our analysis there are two regimes. Below the Biot critical frequency it is a damped diffusion process (that is, it not only diffusive but also damped). Above the Biot critical frequency it is a pure diffusion process. I thought Figure 1 in the attached paper is instructive: slow S behaves somewhat ‘inversely’ to the slow P (I plot imaginary over real part of the wavenumber instead of 1/Q, simply because there is some debate if one can attach a Q value to a diffusion wave). This means that there is no regime where slow S becomes a propagating wave. However, this does not imply that it is a negligible process because at each interface the conversion into the slow S wave takes a little bit of energy from the propagating wave (as does the conversion scattering process into the slow P wave).
In this sense it can be only observed indirectly. Nevertheless, I think we have some evidence that this happens. For example, as you presented in your lecture, a couple of experimental slow P wave observations have been made. Biot theory predicts that above the critical frequency slow P wave propagates without damping. Now, in some of these experiments we can clearly see that the slow P wave is attenuated (for example, a recent JGR paper from Doug Schmitt). But which mechanism is responsible for slow P wave attenuation? In my interpretation it is the conversion scattering mechanism from slow P into slow S.
This mechanism is most important in the presence of pore-scale heterogeneity (such as roughness of pore spaces etc), as for any scattering process to take place you need spatial heterogeneity. This could also explain the observation that slow P waves can be observed in (simple) porous media, like highly porous and clean sandstones, but not so easily in rocks with lots of complex microstructure (Grant Gist has a nice JASA paper summarizing such observations).
Please note that these statements represent just my current understanding. Some people to whom I talked to (including Jim Berryman) believe that there might be a frequency window in which slow S becomes a propagating wave. I can’t see that, but perhaps this is not yet the end of the story.
As per our discussion on the standard linear solid model (your Eq. 35) and its origin, I thought it all comes from the works of Clarence Zener in the 1940’s. You give the references Horton (1959) and Liu et al. (1976). Let me try to check if this generalized Hooke’s law really appears in this form in Zener’s book (for that I need to go to library ...).
Best regards and good luck for the upcoming DISC lectures,
Dr. Tobias M. Müller
CSIRO Earth Science & Resource Engineering
Australian Resources Research Centre
email@example.com Sun, Mar 4, 2012
Thanks for your enlightening DISC talk in Perth last week where you made most things understandable. I’ve been running through the book and my notes and I have a bit of trouble with the Slow P section so I’ve got the questions below.
Anyway, it looks like you had a good time in Brisbane and Perth and I hope you got in some time at Little Creatures or some equally interesting watering hole in Fremantle.
Slow P wave
Q1. Page 128 describes the slow P as travelling a tortuous path in the pore space/fluid. If the analogue is correct there are multiple possible tortuous paths as illustrated below. This would result in the slow P arrival being a “packet” of arrivals starting with the most direct route. However the experimental results on page 127 show the slow P is a single arrival (even the fast P is more spread over time). Can this be explained?
Is the slow P akin to the Feynman formulation of quantum theory? Are all possible routes taken but only the most probable prevails?
Because of the strong attenuation is the most direct route the only one that survives with the more tortuous routes being too long and fully attenuated?
Q2. Another question which was briefly touched on during the DISC. Is there a skin effect associated with P&S wave propogation (fast or slow). Is the propogation affected by drag from the side and how wide is this effect? Is it off the order of the particle motion or the actual wavelength?
Hi Mick, 8 March 2012
Sorry for the delayed response. I don't have an answer to either question, but I have pushed off the questions to a friend who has published widely on Biot theory. If I get anything back, I will let you know. I have posted your questions on my blog, so maybe someone out there in blog land will kick in a response.
Tobias.Mueller@csiro.au Sun, May 27, 2012
I hope your tour is going well.
There was one point with respect to the origin of Eq. 35 in your lecture notes I wanted to discuss with you. As you correctly state it is called the SLS model and you give credit to the Liu et al. (1976) paper.
I found the old book of Clarence Zener in our library. [Elasticity and anelasticity of metals, The University of Chicago Press, 1948]. In his chapter 7 “Physical Interpretation of Anelasticity” he derives a generalized Hook’s law (including the stress and strain rate terms, his Eq. 93) that is basically identical to your Eq. 35 (he wrote it in terms of relaxed and unrelaxed moduli M_r and M_u).
So, at least in the material science disciplines they knew about the importance of including both rate terms. Probably it took some time until this knowledge propagated into the geophysics space ( I haven’t checked it but I would presume that Horton (1959) refered to Zener’s work). [Horton does not give Zener as a reference. CLL]
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