Seismos: DISC 16 Paris (14 June)

The Paris DISC was sponsored by CGGVeritas (thank you) and held in thier excellent conference room at the office in Massy. The head count was 50, including friends and dignitaries Julien Meunier (the 2011 DISC), Shuki Ronen and Kamal Al-Yahya (who could only drop by for a while and did not get in the photo). After the class I had a very nice chat with all of these luminaries over a glass of Bordeaux.

Front row far left is Shuki Ronen next to Julien Meunier.

An action photo from the audience.

Feed back and Q thoughts

One interesting thing was a very bright guy (Patrick Rasolofosaon of IFP) who pointed out that attenuation curves for the standard linear solid (SLS) and Biot theory are not quite the same; SLS has a symmetric attenuation curve in log-frequency, while Biot is a bit asymmetric. Since I have both Biot and SLS coded up in mathematica, I ran a test using gas sand parameters from Dutta and Ode (1983) to compute the Biot attenuation in dB/wavelength and then tried to fit this with SLS attenuation as b/Q where b is a fitting parameter. The result (below) shows that Biot attenuation in these units can be very well fit by SLS attenuation. I suppose one could argue that having Biot attenuation in dB/wavelength means it is an apples and oranges comparison. Still thinking about that.

I am increasingly unhappy with one aspect of my DISC, namely the nature of my evidence that apparent and total attenuation are constant Q in nature. Of course, there is Attewell and Ramana (1966) who clearly indicate that in situ attenuation estimates across a broad frequency range is linear with frequency (implying constant Q). But my demonstration of constant Q from log data and broadband amplitude decay is weak. In searching for more direct and clear evidence, I have come up with a couple of ideas. First, if constant Q attenuation behavior is present in real data then we should be able to show it from the following simple argument. The constant Q amplitude model is

Ax = Ao exp[ - (pi f x) / (v Q) ]

where Ax is the peak amplitude of a wave with frequency f after traveling a distance x with velocity v through an earth with a quality factor of Q (independent of frequency). If we are thinking about a zero offset reflection event at depth z, the distance traveled is x=2z which can be related to the reflection time by z=vt/2 or x=vt. With this association, our decay equation becomes

Ax = Ao exp[ - (pi f t) / Q ]

Taking the log of both sides, we find

log(Ax) = C + Bf

where

C = log(Ao)

B = - (pi t) / Q .

This says that if we pull out a window of data centered at time t, take its Fourier transform and plot the amplitude spectrum in log(amp)-linear(f) space... it should be a straight line. A quick test on some off-the-shelf migrated seismic data (window = 4.5-5.5 s) gave the plot below.

Interference effects (notches) can locally drag the spectrum down but there is no mechanism that can boost the spectrum above it's true value, so I have connected the peaks with a dashed red line. The linear trend is good in the signal band of 8-72 Hz. It might be possible to do a quantitative Q estimate from the line slope, which would be total Q (intrinsic and apparent) for the overlying rock column. Anyway, I think this is a compelling argument that attenuation in real data is well-modeled by constant Q. In the DISC book I argue this observed attenuation below 100 Hz is a combination of weak intrinsic viscous attenuation and strong layer scattering attenuation of O'Doherty-Anstey type that behaves like constant Q. My other idea about constant Q evidence involves Backus averaging, but that will have to wait for a later post.

About town

I had about about a day and a half in Paris before the DISC, so I took the train to Notre Dame a couple of times. The first trip was recon and find out what time things opened. The next day I went in early and walked through Notre Dame at about 8am, it is a lovely place when you have it to yourself. Also, the morning light made for some great photo opportunities.