Wednesday, October 22, 2008

Letter: Albin Kerekes

date: Mon, Oct 20, 2008 at 9:23 PM
subject: TLE Article October 2008


With regard to vibroseis energy source: If one would re-plot Figure 1 not as particle displacement but rather as energy, would one get a more linear response?

I was often criticized for using surface dynamite where “most of the energy goes up in the air.” The truth is that only the particle motion is small to the ground and large to the air, but (seismic) energy which is particle motion times force, is the same in both direction.

Would the same be true for down stroke and up stroke in vibroseis?

My field experience points towards saturation of the elastic limits of the ground below the base plate as the source of harmonics. The greater such “decoupling” the more the harmonics. To reduce harmonics, I have always advocated reducing drive levels and using more units to get the same level of source energy.

Your thoughts?

Best regards,



date: Wed, Oct 22, 2008 at 11:37 AM
subject: Re: TLE Article October 2008


I can't really say much about the physics that leads to the compressed
wave and harmonics. In the hearing case, the wave propagation is
linear outside and inside the ear. it is just the interaction of
sound with the eardrum that is nonlinear. By analogy, I suspect (but
cannot prove) that elastic waves in the earth from a vibroseis source
are linear, even in the near field. That would mean the harmonics
arise from nonlinear interaction at the source point, rather than
nonlinear propagation.

I am thinking about rigging up a lab experiment here at UH to study this.

Thanks for the question and comments,


Letter: Marlan Downey

date:      Tue, Oct 14, 2008 at 4:04 PM
subject: James Jeans

May I say that your own article in the Leading Edge is in the same high 'Jeans' tradition of simply phrased, erudite explanations. I was delighted with your note and would make it a model for what Leading Edge articles should be. Thank you!

Marlan W Downey

Monday, October 13, 2008

Walt Whitman and Seb's qualifying exam

I just got a very pleasant email from Enders Robinson, an old friend, who had cc'd it to Dr. Walt Whitman.  Just Saturday night I was telling a story involving Walt, and this email made me think to repeat the story here.

Back in the mid-1980s I was a PhD candidate at the Colorado School of Mines working with Norm Bleistein and Jack Cohen at the Center for Wave Phenomena.  Walt was a professor at CSM.  Each PhD candidate had to go through a qualifying exam that involved a committee and, in those days (still?), one member of the committee had to be a student.  I was assigned the committee for my good friend Sebastian Geoltrane, a tall, lanky Frenchman who was fearless and fiercely talented at many things.  I once saw his long legs poking out from under his small euro sedan near the CSM campus and heard the familiar voice ranting in French.  He was casually taking on the job of pulling and repairing the transmission.   Another time we went skiing at A-basin during an ice storm that he left the mountain a glazed death trap.  Seb swooshed and zagged like it was powder while I tumbled, skidded, and crawled seemingly miles behind him.

Anyway, Seb's qualifier came along and Walt was on the committee along with an all-star cast of professors.   In the usual fashion, there had been a written exam that was now further discussed along with anything else in the universe the committee felt like asking.  Seb was a wonder.  A whirling dervish of activity deriving equations, sketching solutions to fantastic problems, plumbing tensors to any depth, and waving those long arms in dismay that such childish questions should even arise.  I think I asked him something about a cosine, just to say something.  Finally, the session was over and Sebastian was asked to leave while we deliberated.  The room was quiet for what seemed like a long time.  

Then Walt said, "I think we should flunk him."  The room rumbled with objection till someone actually asked, "Why?".  Walt responded cool and calm, "We'd be doing him a favor.  He should be at MIT."  The joke passed and so did Sebastian.

Tuesday, October 7, 2008

Phase and time

The issue came up the other day about phase and apparent time shift.  A certain reflection coefficient was found to be complex and have a phase that is a linear function of frequency.  Numerical experiments showed a curious behavior; each frequency component was time shifted equally.  When all the frequencies were added up the resulting waveform was zero phase, even though the phase was linear with frequency.  

This goes back to a Seismos column from May 2002 about the various interpretations of the word 'phase'.  The meaning at issue here is the apparent time shift associated with a particular phase at a given frequency.  Think about a cosine with zero phase.  Now let the phase be pi/2 and the cosine becomes a sine, whose peak coincides with the zero crossing of the original cosine.  By definition this zero crossing occurs at 1/4 of the period of the cosine.  If the phase is pi then the first peak lines up with the first trough of the original cosine, for an apparent time shift of 1/2 of the period.  Letting the period of the wave be T=1/f, where f is the frequency in Hz, we can summarize this as follows:
  • phase=0              t-shift=0
  • phase=pi/2          t-shift=T/4
  • phase=pi              t-shift=T/2
Or as an equation:  t-shift = phase * T / (2 pi) = phase / (2 pi f)

In other words, if the phase is a linear function of frequency then the apparent time shift will be the same for all frequencies (because the f cancels out).  This is in agreement with the numerical tests that showed the summation over all frequencies generated a zero phase, t-shifted waveform.  

The figure below is a Mathematica plot that illustrates the connection between phase and apparent time shift for a single frequency.  The solid curve is zero phase and the dashed curve is phase shifted.  In this case the frequency is 1 Hz, the period is 1 second, and we see that a phase shift of pi/2 moves the peak 0.25 s or one-quarter of the period in accord with our formula.

Monday, October 6, 2008


I'm always on the hunt for free software that might do something interesting with seismic data. On the Apple site (under Downloads, Math&Science) I found MeVisCalc last week. This is a medical imaging system with a twist. It is a bit like LabView, a commercial software for driving experimental acquisition systems, that avoids programming by using a graphic interface to lay out and connect modules. So in MeVisCalc there is a Modules menu with maybe 100 items in nested levels. For example, selecting Modules>File>ImgLoad creates an object in the project space that reads many kinds of multidimensional data.

I got some seismic data into MeVisCalc by starting with a 3D migrated data volume, running the seismicunix (SU) program sustrip to create raw 32-bit binary data. By double clicking on the ImgLoad icon a parameter window pops up and you can enter the dimensions and type of your data. Some experimentation is needed since seismic data is column-major and medical software expects row-major data that comes naturally from medical scanning devices. In other words, your data is likely to end up sideways in MeVisCalc, but that is no problem since the 3D viewer (Modules>Visualization>3DVeiwers>View3D) is an openGL type of interactive display and you can easily spin the data around to the orientation you want.

At first it seems a lot of trouble to plot some data. But after playing with it a bit, I can see it is a middle ground between writing code and a menu based application like, say, ImageJ.  Once you have set up the flow and parameters in MeVisCalc, it is very easy to duplicate the process on new data as opposed to large number of menu operations.  But ImageJ has a macro recorder that may play a similar role.

The medical imaging demos in MeVisCalc are impressive (VTK and other graphics engines are build in).  Here is a shot of a little program I built to display some 3D GoM data....


Saturday, October 4, 2008

iPhone photo test (nope)

iPhone test

Turns out that you have to 'edit HTML' for the iphone keyboard to pop up.
It is not much yet, but the seismos blog has begun...