Great geophysicists #7: Leonhard Euler

Leonhard Euler (pronounced 'oiler') was born on 15 April 1707 in Basel, Switzerland, but spent most of his life in Berlin and St Petersburg, where he died on 18 September 1783. Has was blind from the age of 50, but took this handicap stoically—when he lost sight in his right eye at 28 he said, "Now I will have less distraction".

It's hard to list Euler's contributions to the toolbox we call seismic geophysics—he worked on so many problems in maths and physics. For example, much of the notation we use today was invented or at least popularized by him: f (x), e, i, π. He reconciled Newton's and Liebnitz's versions of calculus, making huge advances in solving difficult real-world equations. But he made some particularly relevant advances that resonate still:

• Leonardo and Galileo both worked on mechanical stress distribution in beams, but didn't have the luxuries of calculus or Hooke's law. Daniel Bernoulli and Euler developed an isotropic elastic beam theory, and eventually convinced people you could actually build things using their insights. 
• Euler's equations of fluid dynamics pre-date the more complicated (i.e. realistic) Navier–Stokes equations. Nonetheless, this work continued into vibrating strings, getting Euler (and Bernoulli) close to a general solution of the wave equation. They missed the mark, however, leaving it to Jean-Baptiste le Rond d'Alembert. 
• optics (also wave behaviour). Though many of Euler's ideas about dispersion and lenses turned out to be incorrect (e.g. Pedersen 2008, DOI 10.1162/posc.2008.16.4.392), Euler did at least progress the idea that light is a wave, helping scientists move away from Newton's corpuscular theory.

The moment of Euler's death was described by the Marquis de Condorcet in a eulogy:

He had full possession of his faculties and apparently all of his strength... after having enjoyed some calculations on his blackboard concerning the laws of ascending motion for aerostatic machines... [he] spoke of Herschel's planet and the mathematics concerning its orbit and a little while later he had his grandson come and play with him and took a few cups of tea, when all of a sudden the pipe that he was smoking slipped from his hand and he ceased to calculate and live.

"He ceased to calculate," I love that.

Blurry vision and refractive power

I'm getting LASIK eye surgery today, so I've been preparing myself by learning about the eye's optics, and the surgical procedure that enhances handicapped eyes like my own. Unsurprisingly, there are some noteworthy parallels with seismic.

The eye as a gather

The human eye is akin to a common-depth point (CDP) gather. Both are like cameras constructed to focus rays at an imaging point. The retina, in the case of the eye; the reflection boundary in the case of the gather. In the eye, there are exactly four refracting interfaces at which light rays bend towards the midline and ultimately converge on the retina. In the earth, there an unknown number of interfaces, surely more than four.

Myopia, or near-sightedness, is the condition where images are focused just in front of the retina. Hyperopia, or far-sightedness, is the condition where the eyeball is too short and images would be focused behined the retina. The structure and density of the tissues in the eye have to be aligned just so, for perfect vision. If any combination of them are out of whack, you get blurry vision. Really blurry, in my case.

Characterizing blurry vision can be thought of as a two step process of measurement and validation. First, measurements of the refractive power of the eye are made with an autorefractor; quantifying the amount of first order correction needed. The correction is applied, verified, and fine-tuned by a qualitative visual assessment test. The measurement gets you close to the perfect correction; any residual adjustments may be negligible or imperceptible. And the patient, a subjective observer, is the final judge of clarity and quality of vision.

Four corrections

There are at least four ways to correct for common vision problems. Each is a different way to force the ray geometry:

• refract the light before it enters the eye (glasses),
• refract the light just above the cornea (contact lenses), 
• change the shape of the cornea using LASIK or PRK surgery, or 
• change the shape or structure of the lens (cataract surgery or implants). 

If the earth were an eye

Seismic processing is the act of measuring the refractive structure of the earth, and correcting for it's natural blurryness. Static correction, is done first in an effort to align the rays into a plane wave before it enters the 'eye'. Seismic velocity analysis is carried out on the rays, as a crude measurement of the earth's 'refractive power'. Migration, is the process of forcing geometries, mathematically instead of surgically, in order to rearrange ray paths to improve focusing. Generally speaking it's the same two-step process: measurement and validation. As with the eye, the quality of the final image is a perceptual one, coming down to subjective visual assessment. But unlike the eye, fortunately, multiple observers can share the same image, talk about it even. Changing the entire discussion about what acuity really means.

The process of vision correction goes sequentially from low order to high order. In the next post I will talk about higher order anomalies within the eye, that, once corrected, can cause super-human vision. Measurements and maps of how the eye sees show surgeons how to correct optical images. In the same vein, measurements and maps of how the seismic experiment sees, show geophysicists how to correct images in the seismic realm.

Rocks, pores and fluids

At an SEG seismic rock physics conference in China several years ago, I clearly remember a catch phrase used by one of the presenters, "It's all about rocks, pores, and fluids." He used it several times throughout his talk as an invocation for geophysicists to translate their seismic measurements of the earth into terms that are more appealing to others. Nobody cares about the VP/VS ratio in a reservoir. Even though I found the repetition slightly off-putting, he succeeded—the phrase stuck. It's all about rock, pores, and fluids.

Fast forward to the SEG IQ Earth Forum a few months ago. The message reared its head again, but in a different form. After dinner one evening, I was speaking with Ran Bachrach about advances in seismic rock physics technology: the glamour and the promise of the state-of-the-art. It was a topic right up his alley, but suprisingly, he seemed ambivalent and under-enthused. Which was unusual for him. "More often than not," he said, "we can get all the information we need from the triple combo." 

What is the triple combo? 

I felt embarrased that I had never heard of the term. Like I had been missing something this whole time. The triple combo is the standard set of measurements used in formation evaluation and wireline logging: gamma-ray, porosity, and resistivity. Simply put, the triple combo tells us about rocks, pores, and fluids. 

I find it curious that the very things we are interested in are impossible to measure directly. For example:

• A gamma-ray log measures naturally occuring radioactive minerals. We use this to make inferences about lithology.
• A neutron log measures Compton scattering in proportion to the number of hydrogen atoms. This is a proxy for pores.
• A resistivity log measures the conductivity of electrical current. We use this to tell us about fluid type and saturation.

Subsurface geotechnology isn't only about recording the earth's constituents in isolation. Some measurements, the sonic log for instance, are useful because of the fact that they are an aggregate of all three.

The well log is a section of the Thebaud_E-74 well available from the offshore Nova Scotia Play Fairway Analysis.

Update on 2013-01-18 00:32 by Evan Bianco

Part two of this post elaborates on the measurements that are an aggregate of all three.

Must-read geophysics blogs

Tuesday's must-read list was all about traditional publishing channels. Today, it's all about new media.

If you're anything like me before Agile, you don't read a lot of blogs. At least, not ones about geophysics. But they do exist! Get these in your browser favourites, or use a reader like Google Reader (anywhere) or Flipboard (on iPad).

Seismos

Chris Liner, a geophysics professor at the University of Arkansas, recently moved from the University of Houston. He's been writing Seismos, a parallel universe to his occasional Leading Edge column, since 2008.

MyCarta

Matteo Niccoli (@My_Carta on Twitter) is an exploration geoscientist in Stavanger, Norway, and he recently moved from Calgary, Canada. He's had MyCarta: Geophysics, visualization, image processing and planetary science, since 2011. This blog is a must-read for MATLAB hackers and image processing nuts. Matteo was one of our 52 Things authors.

GeoMika

Mika McKinnon (@mikamckinnon), a geophysicist in British Columbia, Canada, has been writing GeoMika: Fluid dynamics, diasters, geophysics, and fieldwork since 2008. She's also into education outreach and the maker-hacker scene.

The Way of the Geophysicist

Jesper Dramsch (@JesperDramsch), a geophysicist in Hamburg, Germany has written the wonderfully personal and philosophical The Way of The Geophysicist since 2011. His tales of internships at Fugro and Schlumberger provide great insights for students.

VatulBlog

Maitri Erwin (@maitri), an exploration geoscientist in Texas, USA. She has been blogging since 2001 (surely some kind of record), and both she and her unique VatulBlog: From Kuwait to Katrina and beyond defy categorization. Maitri was also one of our 52 Things authors. 

There are other blogs on topics around seismology and exploration geophysics — shout outs go to Hypocentre in the UK, the Laboratoire d'imagerie et acquisition des mesures géophysiques in Quebec, occasional seismicky posts from sedimentologists like @zzsylvester, and the panoply of bloggery at the AGU. Stick those in your reader!

Must-read geophysics

If you had to choose your three favourite, most revisited, best remembered papers in all of exploration geophysics, what would you choose? Are they short? Long? Full of math? Well illustrated? 

Keep it honest

Barnes, A (2007). Redundant and useless seismic attributes. Geophysics 72 (3). DOI:10.1190/1.2716717
Rarely do we see engaging papers, but they do crop up occasionally. I love Art Barnes's Redundant and useless seismic attributes paper. In this business, I sometimes feel like our opinions — at least our public ones — have been worn down by secrecy and marketing. So Barnes's directness is doubly refreshing:

There are too many duplicate attributes, too many attributes with obscure meaning, and too many unstable and unreliable attributes. This surfeit breeds confusion and makes it hard to apply seismic attributes effectively. You do not need them all.

And keep it honest

Blau, L (1936). Black magic in geophysical prospecting. Geophysics 1 (1). DOI:10.1190/1.1437076
I can't resist Ludwig Blau's wonderful Black magic geophysics, published 77 years ago this month in the very first issue of Geophysics. The language is a little dated, and the technology mostly sounds rather creaky, but the point, like Blau's wit, is as fresh as ever. You might not learn a lot of geophysics from this paper, but it's an enlightening history lesson, and a study in engaging writing the likes of which we rarely see in Geophysics today...

And also keep it honest

Bond, C, A Gibbs, Z Shipton, and S Jones (2007), What do you think this is? "Conceptual uncertainty" in geoscience interpretation. GSA Today 17 (11), DOI: 10.1130/GSAT01711A.1
I like to remind myself that interpreters are subjective and biased. I think we have to recognize this to get better at it. There was a wonderful reaction on Twitter yesterday to a recent photo from Mars Curiosity (right) — a volcanologist thought it looked like a basalt, while a generalist thought it more like a sandstone. This terrific paper by Clare Bond and others will help you remember your biases!

My full list is right here. I hope you think there's something missing... please edit the wiki, or put your personal favourites in the comments. 

The attribute figure is adapted from from Barnes (2007) is copyright of SEG. It may only be used in accordance with their Permissions guidelines. The Mars Curiosity figure is public domain. 

Update on 2013-01-11 13:29 by Matt Hall

The next post is more must-read geophysics, this time in the blogosphere. Enjoy!

Ten ways to spot pseudogeophysics

Geophysicists often try to predict rock properties using seismic attributes — an inverse problem. It is difficult and can be complicated. It can seem like black magic, or at least a black box. They can pull the wool over their own eyes in the process, so don’t be surprised if it seems like they are trying to pull the wool over yours. Instead, ask a lot of questions.

Questions to ask

1. What is the reliability of the logs that are inputs to the prediction? Ask about hole quality and log editing.
2. What about the the seismic data? Ask about signal:noise, multiples, bandwidth, resolution limits, polarity, maximum offset angle (for AVO studies), and processing flow (e.g. Emsley, 2012).
3. What is the quality of the well ties? Is the correlation good enough for the proposed application?
4. Is there any physical reason why the seismic attribute should predict the proposed rock property? Was this explained to you? Were you convinced?
5. Is the proposed attribute redundant (sensu Barnes, 2007)? Does it really give better results than a less sexy approach? I’ve seen 5-minute trace integration outperform month-long AVO inversions (Hall et al. 2006).
6. What are the caveats and uncertainties in the analysis? Is there a quantitative, preferably Bayesian, treatment of the reliability of the predictions being made? Ask about the probability of a prediction being wrong.
7. Is there a convincing relationship between the rock property (shear impedance, say) and some geologically interesting characteristic that you actually make decisions with, e.g. frackability.
8. Is there a convincing relationship between the rock property and the seismic attribute at the wells? In other words, does the attribute actually correlate with the property where we have data?
9. What does the low-frequency model look like? How was it made? Its maximum frequency should be about the same as the seismic data's minimum, no more.
10. Does the geophysicist compute errors from the training error or the validation error? Training errors are not helpful because they beg the question by comparing the input training data to the result you get when you use those very data in the model. Funnily enough, most geophysicists like to show the training error (right), but if the model is over-fit then of course it will predict very nicely at the well! But it's the reliability away from the wells we are interested in, so we should examine the error we get when we pretend the well isn't there. I prefer this to witholding 'blind' wells from the modeling — you should use all the data. 

Lastly, it might seem harsh but we could also ask if the geophysicist has a direct financial interest in convincing you that their attribute is sound, as well as the normal direct professional interest. It’s not a problem if they do, but be on your guard — people who are selling things are especially prone to bias. It's unavoidable.

What do you think? Are you bamboozled by the way geophysicists describe their predictions?

References
Barnes, A (2007). Redundant and useless seismic attributes. Geophysics 72 (3), p P33–P38. DOI: 10.1190/1.2370420.
Emsley, D. Know your processing flow. In: Hall & Bianco, eds, 52 Things You Should Know About Geophysics. Agile Libre, 2012. 
Hall, M, B Roy, and P Anno (2006). Assessing the success of pre-stack inversion in a heavy oil reservoir: Lower Cretaceous McMurray Formation at Surmont. Canadian Society of Exploration Geophysicists National Convention, Calgary, Canada, May 2006. 

The image of the training error plot — showing predicted logs in red against input logs — is from Hampson–Russell's excellent EMERGE software. I'm claiming the use of the copyrighted image is fair use.  

Great geophysicists #6: Robert Hooke

Robert Hooke was born near Freshwater on the Isle of Wight, UK, on 28 July 1635, and died on 13 March 1703 in London. At 18, he was awarded a chorister scholarship at Oxford, where he studied physics under Robert Boyle, 8 years his senior. 

Hooke's famous law tells us how things deform and, along with Newton, Hooke is thus a parent of the wave equation. The derivation starts by equating the force due to acceleration (of a vibrating particle, say), and the force due to elastic deformation:

where m is mass, x is displacement, the two dots denote the second derivative with respect to time (a.k.a. acceleration), and k is the spring constant. This powerful insight, which allows us to compute a particle's motion at a given time, was first made by d'Alembert in about 1742. It is the founding principle of seismic rock physics.

Hooke the geologist

Like most scientists of the 17th century, Hooke was no specialist. One of his best known works was Micrographia, first published in 1665. The microscope was invented in the late 1500s, but Hooke was one of the first people to meticulously document and beautifully draw his observations. His book was a smash hit by all accounts, inspiring wonder in everyone who read it (Samuel Pepys, for example). Among other things, Hooke described samples of petrified wood, forams, ammonites, and crystals of quartz in a flint nodule (left). Hooke also wrote about the chalk formations in the cliffs near his home town.

Hooke went on to help Wren rebuild London after the great fire of 1666, and achieved great respect for this work too. So esteemed is he that Newton was apparently rather jealous of him, and one historian has referred to him as 'England's Leonardo'. He never married, and lived in his Oxford college all his adult life, and is buried in Bishopsgate, London. As one of the fathers of geophysics, we salute him.

The painting of Hooke, by Rita Greer, is licensed under a Free Art License. It's a interpretation based on descriptions of him ("his chin sharp, and forehead large"); amazingly, there are no known contemporary images of him. Hear more about this.

You can read more about the relationship between Hooke's law and seismic waves in Bill Goodway's and Evan's chapters in 52 Things You Should Know About Geophysics. Download their chapters for free!

Units of geological time

I have an exercise in my writing course on scientific units. The last question is about units of geological time, and it always starts a debate. I favour ka, Ma, and Ga for all dates and spans of time, but I've never gone unchallenged. People like Ma BP, mya, m.y., myr, and lots of other things, and I've heard all sorts of rules for when to use which, and why. The sort of rules you can't quite remember the crucial details of.

Twitter isn't for everyone, but I think it has some real strengths — it's a great filter, a reliable connection finder, and a brilliant place to ask questions. So I asked Twitter, and compiled the responses in a storyboard:

The story exposed a useful blog post, an attempt to standardize (Aubry et al., 2009, Stratigraphy 6 (2), 100–105], another attempt [Holden et al., 2011, IUPAC–IUGS recommendation], and a firm rebuttal from Nick Christie-Blick. Many thanks to all my Twitter friends — one of whom I've actually met IRL!

Bottom line — there are regional variations and personal preferences. There's no consensus. Make your choice. Write unambiguously.

Segmentation and decomposition

Day 4 of the SEG Annual Meeting in Las Vegas was a game of two halves: talks in the morning and workshops in the afternoon. I caught two signal processing talks, two image processing talks, and two automatic interpretation talks, then spent the afternoon in a new kind of workshop for students. My highlights:

Anne Solberg, DSB, University of Oslo

Evan and I have been thinking about image segmentation recently, so I'm drawn to those talks (remember Halpert on Day 2?). Angélique Berthelot et al. have been doing interesting work on salt body detection. Solberg (Berthelot's supervisor) showed some remarkable results. Their algorithm:

1. Compute texture attributes, including Haralick and wavenumber textures (Solberg 2011)
2. Supervised Bayesian classification (we've been using fuzzy c-means)
3. 3D regularization and segmentation (okay, I got a bit lost at this point)

The results are excellent, echoing human interpretation well (right) — but having the advantage of being objective and repeatable. I was especially interested in the wavenumber textures, and think they'll help us in our geothermal work. 

Jiajun Han, BLISS, University of Alberta

The first talk of the day was that classic oil industry: a patented technique with an obscure relationship to theory. But Jiajun Han and Mirko van der Baan of the University of Alberta gave us the real deal — a special implementation of empirical mode decomposition, which is a way to analyse time scales (frequencies, essentially), without leaving the time domain. The result is a set of intrinsic mode functions (IMFs), a bit like Fourier components, from which Han extracts instantaneous frequency. It's a clever idea, and the results are impressive. Time–frequency displays usually show smearing in either the time or frequency domain, but Han's method pinpoints the signals precisely:

That's it from me for SEG — I fly home tomorrow. It's tempting to stay for the IQ Earth workshop tomorrow, but I miss my family, and I'm not sure I can crank out another post. If you were in Vegas and saw something amazing (at SEG I mean), please let us know in the comments below. If you weren't, I hope you've enjoyed these posts. Maybe we'll see you in Houston next year!

More posts from SEG 2012.

The images adapted from Berthelot and Han are from the 2012 Annual Meeting proceedings. They are copyright of SEG, and used here in accordance with their permissions guidelines.

Update on 2012-11-09 05:08 by Matt Hall

I just stumbled on another blog post about SEG! Laurent Duval has lots to read on his geophysicsy blog. Add it to your reader.

I was especially pleased to see him writing about Chuck Mosher's talk on the generalized windowed transform, because I was ill-equipped to write about it*, though it seemed 'important'. 

* I know what you're thinking — that doesn't usually stop me.

Brittleness and robovibes

Day 3 of the SEG Annual Meeting was just as rammed with geophysics as the previous two days. I missed this morning's technical program, however, as I've taken on the chairpersonship (if that's a word) of the SEG Online Committee. So I had fun today getting to grips with that business. Aside: if you have opinion's about SEG's online presence, please feel free to send them my way.

Here are my highlights from the rest of the day — both were footnotes in their respective talks:

Brittleness — Lev Vernick, Marathon

Evan and I have had a What is brittleness? post in our Drafts folder for almost two years. We're skeptical of the prevailing view that a shale's brittleness is (a) a tangible rock property and (b) a function of Young's modulus and Poisson's ratio, as proposed by Rickman et al. 2008, SPE 115258. To hear such an intellect as Lev declare the same today convinced me that we need to finish that post — stay tuned for that. Bottom line: computing shale brittleness from elastic properties is not physically meaningful. We need to find more appropriate measures of frackability, [Edit, May 2015; Vernik tells me the following bit is the opposite of what he said, apologies for my cloth ears...] which Lev pointed out is, generally speaking, inversely proportional to organic content. This poses a basic conflict for those exploiting shale plays. [End of public service announcement.]

Robovibes — Guus Berkhout, TU Delft

At least 75% of Berkhout's talk went by me today, mostly over my head. I stopped writing notes, which I only do when I'm defeated. But once he'd got his blended source stuff out of the way, he went rogue and asked the following questions:

1. Why do we combine all seismic frequencies into the device? Audio got over this years ago (right).
2. Why do we put all the frequencies at the same location? Viz 7.1 surround sound.
3. Why don't we try more crazy things in acquisition?

I've wondered the same thing myself — thinking more about the receiver side than the sources — after hearing about the brilliant sampling strategy the Square Kilometer Array is using at a PIMS Lunchbox Lecture once. But Berkhout didn't stop at just spreading a few low-frequency vibrators around the place. No, he wants robots. He wants an autonomous army of flying and/or floating narrow-band sources, each on its own grid, each with its own ghost matching, each with its own deblending code. This might be the cheapest million-channel acquisition system possible. Berkhout's aeronautical vibrator project starts in January. Seriously.

More posts from SEG 2012.

Speaker image is licensed CC-BY-SA by Tobias Rütten, Wikipedia user Metoc.