Monday, October 29, 2012

DISC Questions

How many have you given and how many will be left after Las Vegas? 

 Las Vegas will be DISC number 25 of 30. A full list and annotated calendar can be found here:

 Do you have any idea how far you’ve traveled…to how many continents, etc, and how does the “wear and tear” of travel impact the presentation? 

 By the time I finish in December, the DISC will have been presented in 5 of the 7 continents (no Africa or Antarctica) and 22 countries. A careful record has been kept of DISC attendance. Going into Las Vegas the number of people who have attended the 2012 DISC stands at 1058.

Mileage is a bit more fuzzy. My preferred carrier has been United Air Lines (no endorsement intended), but several of the more remote locations involved travel on carriers not associated with UA. At any rate, we can get an idea about the magnitude of DISC travel from the fact that I have booked 113000 miles on UA in 2012. How far is this? It is 4.5 times the equatorial circumference of the Earth or, if you prefer, a bit more than the diameter of Jupiter.

Earth and Jupiter size comparison.

And India, Oman, Abu Dhabi, Saudi Arabia, and Turkey are still ahead. Yikes, no wonder my lovely wife Dolores is tired of seeing me head out the door.

Do you see people you know at all, or most, tour stops? 

It has been amazing to see so many friends and colleagues around the world. I would guess that only 5 or 6 of the DISCS have found me without someone in the room I have met before. But many more seem to know me. Perhaps because of my serving as Editor of Geophysics (1999-2001) or, more likely, through the Seismos column in The Leading Edge (now perpetuated in the Seismos Blog it seems my reputation precedes me into the remotest parts of the world. Add to that generations of students from the Universities of Tulsa and Houston, and it seems that I always walk into a room of friends.

Has your tour caused you to “re-think” the subject and changed your opinions about things? 

The thorniest subject in my DISC is seismic attenuation, a topic intensely studied for nearly a century and the subject of many hundreds of scientific papers, dozens of books, and endless discussion. Making enough sense of this to present a coherent meaningful overview was the greatest challenge of writing the DISC book. My approach was to focus on fundamentals and find the foundation publications that best make the case for each attenuation theory.

It slowly became clear that the vast amount of scientific data supported a dual attenuation model. At the small scale intrinsic viscous attenuation is in accord with laboratory experiments and the best poro-elastic theory we have (Biot). But field data clearly supports the existence of an apparent attenuation mechanism that is Constant-Q in nature, this is due to layer scattering effects.

Elsewhere in the DISC, there is much discussion of interference effects due to time-domain spikes (e.g., reflection coefficients). In particular, the amplitude spectrum of a spike series was shown to contain notches representing hidden frequencies locally phased out by interference.

Back to the question asked, I had developed some evidence in the early DISC work to support the argument of Constant-Q behavior due to layering. But the evidence was complicated, rather ambiguous, and hardly convincing. As I presented this evidence around the world, I became increasingly dissatisfied with it. Then it occurred to me that a simple argument was possible: the mathematics of Constant-Q implies that an initially flat amplitude spectrum with change as the wave passes through a Constant-Q earth. Specifically, it will change in such a way as to be linear in a plot of log-amplitude versus linear frequency. But we cannot really expect a straight line on the amplitude spectrum of real data because of three factors: (1) low frequencies are absent due to instrumentation limits, (2) high frequencies are absent because we have a finite-bandwidth source, and (3) in the observed frequency band there are interference notches complicating the picture. Anyway, all this leads to the figure below.

Raw spectrum plotted in linear-linear space (upper). 
The same spectrum in log-linear space with annotations (lower).

Anything else you want to say? 

It has been an exhausting, exhilarating, rewarding honor to serve as the 2012 DISC. I plan to spend a lot of time in my new home at the University of Arkansas during 2013, someone else can book those miles back and forth through Jupiter next year.

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