Review: The Wave Watcher's Companion

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The Wave Watcher's Companion: From Ocean Waves to Light Waves via Shock Waves, Stadium Waves, and All the Rest of Life's Undulations
Gavin Pretor-Pinney, Perigee (USA), Bloomsbury (UK), July 2010, $22.95

This book was on my reading list, and then on my shelf, for ages. Now I wish I'd snapped it up and read it immediately. In my defence, the end of 2010 was a busy time for me, what with turning my career upside down and everything, but I'm sure there's a lesson there somewhere...

If you think of yourself as a geophysicist, stop reading this review and buy this book immediately. 

OK, now they've gone, we can look more closely. Gavin Pretor-Pinney is the chap behind The Cloud Appreciation Society, the author of The Cloudspotter's Guide, and co-creator of The Idler Magazine. He not a scientist, but a witty writer with a high curiosity index. The book reads like an extended blog post, or a chat in the pub. A really geeky chat. 

Geophysicists are naturally drawn to all things wavy, but the book touches on sedimentology too — from dunes to tsunamis to seiches. Indeed, the author prods at some interesting questions about what exactly waves are, and whether bedforms like dunes (right) qualify as waves or not. According to Andreas Baas, "it all depends on how loose is your definition of a wave." Pretor-Pinney likes to connect all possible dots, so he settles for a loose definition, backing it up with comparisons to tanks and traffic jams. 

The most eye-opening part for me was Chapter 6, The Fifth Wave, about shock waves. I never knew that there's a whole class of waves that don't obey the normal rules of wave motion: they don't obey the speed limits, they don't reflect or refract properly, and they can't even be bothered to interfere like normal (that is, linear) waves. Just one of those moments when you realize that everything you think you know is actually a gross simplification. I love those moments.

The book is a little light on explanation. Quite a few of the more interesting parts end a little abruptly with something like, "weird, huh?". But there are plenty of notes for keeners to follow up on, and the upside is the jaunty pace and adventurous mix of examples. This one goes on my 're-read some day' shelf. (I don't re-read books, but it's the thought that counts).

Figure excerpt from Pretor-Pinney's book, copyright of the author and Penguin Publishing USA. Considered fair use.

Filters that distort vision

Almost two weeks ago, I had LASIK vision correction surgery. Although the recovery took longer than average, I am seeing better than I ever did before with glasses or contacts. Better than 20/20. Here's why.

Low order and high order refractive errors

Most people (like me) who have (had) poor vision fall short of pristine correction because lenses only correct low order refractive errors. Still, any correction gives a dramatic improvement to the naked eye; further refinements may be negligible or imperceptible. Higher order aberrations, caused by small scale structural irregularities of the cornea, can still affect one's refractive power by up to 20%, and they can only be corrected using customized surgical methods.

It occurs to me that researchers in optometry, astronomy, and seismology face a common challenge: how to accurately measure and subsequently correct for structural deformations in refractive media, and the abberrations in wavefronts caused by such higher-order irregularities. 

The filter is the physical model

Before surgery, a wavefront imaging camera was used to make detailed topographic maps of my corneas, and estimate point spread functions for each eye. The point spread function is a 2D convolution operator that fuzzies the otherwise clear. It shows how a ray is scattered and smeared across the retina. Above all, it is a filter that represents the physical eye.

Point spread function (similar to mine prior to LASIK) representing refractive errors of the cornea (top two rows), and corrected vision (bottom row). Point spread functions are filters that distort both the visual and seismic realms. The seismic example is a segment of inline 25, Blake Ridge 3D seismic survey, available from the Open Seismic Repository (OSR).Observations in optics and seismology alike are only models of the physical system, models that are constrained by the filters. We don't care about the filters per se, but they do get in the way of the underlying system. Luckily, the behaviour of any observation can be expressed as a combination of filters. In this way, knowing the nature of reality literally means quantifying the filters that cause distortion. Change the filter, change the view. Describe the filter, describe the system. 

The seismic experiment yields a filtered earth; a smeared reality. Seismic data processing is the analysis and subsequent removal of the filters that distort geological vision. 

This image was made using the custom filter manipulation tool in FIJI. The seismic data is available from OpendTect's Open Seismic Repository.

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.

Great geophysicists #5: Huygens

Christiaan Huygens was a Dutch physicist. He was born in The Hague on 14 April 1629, and died there on 8 July 1695. It's fun to imagine these times: he was a little older than Newton (born 1643), a little younger than Fermat (1601), and about the same age as Hooke (1635). He lived in England and France and must have met these men.

It's also fun to imagine the intellectual wonder life must have held for a wealthy, educated person in these protolithic Enlightenment years. Everyone, it seems, was a polymath: Huygens made substantial contributions to probability, mechanics, astronomy, optics, and horology. He was the first to describe Saturn's rings. He invented the pendulum clock. 

Then again, he also tried to build a combustion engine that ran on gunpowder. 

Geophysicists (and most other physicists) know him for his work on wave theory, which prevailed over Newton's corpuscles—at least until quantum theory. In his Treatise on Light, Huygens described a model for light waves that predicted the effects of reflection and refraction. Interference has to wait 38 years till Fresnel. He even explained birefringence, the anisotropy that gives rise to the double-refraction in calcite.

The model that we call the Huygens–Fresnel principle consists of spherical waves emanating from every point in a light source, such as a candle's flame. The sum of these manifold wavefronts predicts the distribution of the wave everywhere and at all times in the future. It's a sort of infinitesimal calculus for waves. I bet Newton secretly wished he'd thought of it.