Great geophysicists #11: Thomas Young

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Painting of Young by Sir Thomas LawrenceThomas Young was a British scientist, one of the great polymaths of the early 19th century, and one of the greatest scientists. One author has called him 'the last man who knew everything'¹. He was born in Somerset, England, on 13 June 1773, and died in London on 10 May 1829, at the age of only 55. 

Like his contemporary Joseph Fourier, Young was an early Egyptologist. With Jean-François Champollion he is credited with deciphering the Rosetta Stone, a famous lump of granodiorite. This is not very surprising considering that at the age of 14, Young knew Greek, Latin, French, Italian, Hebrew, Chaldean, Syriac, Samaritan, Arabic, Persian, Turkish and Amharic. And English, presumably. 

But we don't include Young in our list because of hieroglyphics. Nor  because he proved, by demonstrating diffraction and interference, that light is a wave — and a transverse wave at that. Nor because he wasn't a demented sociopath like Newton. No, he's here because of his modulus. 

Elasticity is the most fundamental principle of material science. First explored by Hooke, but largely ignored by the mathematically inclined French theorists of the day, Young took the next important steps in this more practical domain. Using an empirical approach, he discovered that when a body is put under pressure, the amount of deformation it experiences is proportional to a constant for that particular material — what we now call Young's modulus, or E:

This well-known quantity is one of the stars of the new geophysical pursuit of predicting brittleness from seismic data, and a renewed interested in geomechanics in general. We know that Young's modulus on its own is not enough information, because the mechanics of failure (as opposed to deformation) are highly nonlinear, but Young's disciplined approach to scientific understanding is the best model for figuring it out. 

Sources and bibliography

Footnote

¹ Thomas Young wrote a lot of entries in the 1818 edition of Encyclopædia Britannica, including pieces on bridges, colour, double refraction, Egypt, friction, hieroglyphics, hydraulics, languages, ships, sound, tides, and waves. Considering that lots of Wikipedia is from the out-of-copyright Encyclopædia Britannica 11th ed. (1911), I wonder if some of Wikipedia was written by the great polymath? I hope so.

Filters that distort vision

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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

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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.