90 years of seismic exploration

Today is an important day for applied geoscience. For one thing, it’s St Barbara’s Day. For another, 4 December is the anniversary of the first oil discovery drilled on seismic reflection data.

During World War 1 — thanks to the likes of Reginald Fessenden, Lawrence Bragg, Andrew McNaughton, William Sansome and Ludger Mintrop — acoustics emerged as a method of remote sensing. After the war, enterprising scientists looked for commercial applications of the technology. The earliest geophysical patent application I can find is Fessenden’s 1917 award for the detection of orebodies in mines, and Mintrop applied for a surface-based method in 1920, but the early patents pertained to refraction and diffraction experiments. The first reflection patent, US Patent no. 1,843,725, was filed on 1 May 1929 by John Clarence Karcher… almost 6 months after the discovery well was completed.

It’s fun to read the patent. It begins

This invention related to methods of and apparatus for determining the location and depth of geological formations beneath the surface of the earth and particularly to the determination of geological folding in these sub-surface formations. This invention has special application in the location of anticlines, faults and other structure favorable to the accumulation of petroleum.

Figures 4 and 5 show what must be the first ever depiction of shot gathers:

Figure 5 from Karcher’s patent, ‘Determination of subsurface formations’. It illustrates the arrivals of different wave modes at the receivers.

Karcher was born in Dale, Indiana, but moved to Oklahoma when he was five. He later studied electrical engineering and physics at the University of Oklahoma. Along with William Haseman, David Ohearn, and Irving Perrine, Karcher formed the Geological Engineering Company. Early tests of the technology took place in the summer of 1921 near Oklahoma City, and the men spent the next several years shooting commercial refraction surveys around Texas and Oklahoma — helping discover dozens of saltdome-related fields — and meanwhile trying to perfect the reflection experiment. During this period, they were competing with Mintrop’s company, Seismos.

The first well

In 1925, Karcher formed a new company — Geophysical Research Corporation, GRC, now part of Sercel — with Everette Lee DeGolyer of Amerada Petroleum Corporation and money from the Viscount Cowdray (owner of Pearson, now a publishing company, but originally a construction firm). Through this venture, Karcher eventually prevailed in the race to prove the seismic reflection method. From what I can tell, HB Peacock and/or JE Duncan successfully mapped the structure of the Ordovician Viola limestone, which overlies the prolific Simpson Group. On 4 December 1928, Amerada completed No. 1 Hallum well near Maud, Oklahoma.

The locations (as best I Can tell) of the first test of reflection seismology, the first seismic section, and the first seismic survey that led to a discovery. The map also shows where Karcher grew up; he went to university in Norman, south of Oklahoma City..

st-barbara-wusel007-CC-BY-SA.png

Serial entrepreneur

Karcher was a geophysical legend. After Geophysical Research Corporation, he co-founded Geophysical Service Incorporated (GSI) which was the origin of Texas Instruments and the integrated circuit. And he founded several explorations companies after that. Today, his name lives on in the J. Clarence Karcher Award that SEG gives each year to one or more stellar young geophysicists.

It seems appropriate that the oil discovery fell on the feast of St Barbara, the patron saint of miners and armorers and all who deal in explosives, but also of mathematicians and geologists. If you have a bottle near you this evening, raise a glass to St Barbara and the legion of geophysicists that have made seismic reflection such a powerful tool today.


Source material

On principles and creativity

I recently heard a quote that resonated with me:

 
Bernbach_principles.png
 

I grapple with this sentiment whenever I feel the selfish twinge of hesitation to donate money to Wikipedia or QGIS, or pay page fees for open access to an article, or otherwise cough up for my convictions.

Curious about who had uttered this wisdom, I looked it up. Turns out it was Bill Bernbach, celebrated advertiser, and supposedly an inspiration for the Don Draper character in Mad Men.

Bernbach_beetle_small.png

One of the founders of Doyle Dane Bernbach, now known as DDB, he brought bare-faced truth to the forefront in advertising, calling VW Beetles 'small', and proudly declaring Avis 'number 2'. He basically invented Apple's entire aesthetic in the late 50's , about four decades before Apple started to 'Think Different'.

He said some other true things. This could be about scientific communication:

The truth isn't the truth until people believe you, and they can't believe you if they don't know what you're saying, and they can't know what you're saying if they don't listen to you, and they won't listen to you if you're not interesting, and you won't be interesting unless you say things imaginatively, originally, freshly.

Now 'science' and 'truth' are not the same thing, so I don't want to try to claim that this sums things up perfectly, but I think the general point is important and we'll be better scientists if we live by it.

And I like this one too:

 
Bernbach_creativity.png
 

Too many organizations, and individuals, think their advantage must come from money, or secrecy, or patents, or other obvious, easily copied, things. But thinking about your creative edge first makes you take care of important things, and stop worrying about unimportant things.

I think this is an important idea, because creativity is, almost by definition, uncopyable. It feels like a slippery thing to build a company on or strategize about because while there's a limitless supply of the stuff, it's hard to maintain — and exploit. Creativity for its own sake is almost useless, but combined with a "Just ship it!" mentality, it's an unstoppable force.


The image of Bill Bernbach and the VW Beetle ad are both copyright of DDB Worldwide Communications Group and low-res images are used here in accordance with fair use rules. 

Finding Big Bertha with a hot wire

mcnaughton-canada-war-museum.jpg

Sunday will be the 131st birthday of General Andrew McNaughton, a Canadian electrical engineer who served in the Canadian Expeditionary Force in the First World War. He was eventually appointed commander of the Canadian Corps Heavy Artillery and went on to serve in the Second World War as well.

So what is a professional soldier doing on a blog about geoscience? Well, McNaughton was part of the revolution of applied acoustics and geophysics that emerged right before and after the First World War.

Along with eminent British physicist Lawrence Bragg, engineer William Sansome Tucker, and physicist Charles Galton Darwin (the other Charles Darwin's grandson), among others, McNaughton applied physics to the big problem of finding the big noisy things that were trying to blow everyone up. They were involved in an arms race of their own — German surveyor Ludger Mintrop was trying to achieve the same goal from the other side of the trenches.

Big_Bertha.jpg

After gaining experience as a gunner, McNaughton became one of a handful of scientists and engineers involved in counter-battery operations. Using novel ranging techniques, these scientists gave the allied forces a substantial advantage over the enemy. Counter-battery fire became an weapon at pivotal battles like Vimy Ridge, and certainly helped expedite the end of the war.

If all this sounds like a marginal way to win a battle, stop think for a second about these artillery. The German howitzer, known as 'Big Bertha' (left), could toss an 820 kg (1800 lb) shell about 12.5 km (7.8 miles). In other words, it was incredibly annoying.


Combining technologies

Localization accuracy on the order of 5–10 m on the large majority of gun positions was eventually achieved by the coordinated use of several technologies, including espionage, cartography, aerial reconnaissance photography, and the new counter-measures of flash spotting and sound ranging.

Flash spotting was more or less just what it sounds like: teams of spotters recording the azimuth of artillery flashes, then triangulating artillery positions from multiple observations. The only real trick was in reporting the timing of flashes to help establish that the flashes came from the same gun.

Sound ranging, on the other hand, is a tad more complicated. It seems that Lawrence Bragg was the first to realize that the low frequency sound of artillery fire — which he said lifted him off the privy seat in the outhouse at his lodgings — might be a useful signal. However, microphones were not up to the task of detecting such low frequencies. Furthermore, the signal was masked by the (audible) sonic boom of the shell, as well as the shockwaves of passing shells.

Elsewhere in Belgium, William Tucker had another revelation. Lying inside a shack with holes in its walls, he realized that the 20 Hz pressure wave from the gun created tiny puffs of air through the holes. So he looked for a way to detect this pulse, and came up with a heated platinum wire in a rum jar. The filament's resistance dropped when cooled by the wavefront's arrival through an aperture. The wire was unaffected by the high-frequency shell wave. Later, moving-coil 'microphones' (geophones, essentially) were also used, as well as calibration for wind and temperature. The receivers were coupled with a 5-channel string galvanometer, invented by French engineers, to record traces onto 35-mm film bearing timing marks:

sound-ranging-traces.png

McNaughton continued to develop these technologies through the war, and by the end was successfully locating the large majority of enemy artillery locations, and was even able to specify the calibre of the guns and their probable intended targets. Erster Generalquartiermeister Erich Ludendorff commented at one point in the war: 

According to a captured English document the English have a well- developed system of sound-ranging which in theory corresponds to our own. Precautions are accordingly to be taken to camouflage the sound: e.g. registration when the wind is contrary, and when there is considerable artillery activity, many batteries firing at the same time, simultaneous firing from false positions, etc.

An acoustic arsenal

Denge_acoustic_mirrors_March-2005_Paul-Russon.jpg

The hot-wire artillery detector was not Tucker's only acoustic innovation. He also pioneered the use of acoustic mirrors for aircraft detection. Several of these were built around the UK's east coast, starting around 1915 — the three shown here are at Denge in Kent. They were rendered obselete by the invention of radar around the beginning of World War Two.

Acoustic and seismic devices are still used today in military and security applications, though they are rarely mentioned in applied geophysics textbooks. If you know about any interesting contemporary uses, tell us about it in the comments.


According to Crown Copyright terms, the image of McNaughton is out of copyright. The acoustic mirror image is by Paul Russon, licensed CC-BY-SA. The uncredited/unlicensed galvanometer trace is from the excellent Stop, hey, what's that sound article on the geographical imaginations blog; I assume it is out of copyright. The howitzer image is out of copyright.

This post on Target acquisition and counter battery is very informative and has lots of technical details, though most of it pertains to later technology. The Boom! Sounding out the enemy article on ScienceNews for Students is also very nice, with lots of images. 

90 years of well logs

Today is the 90th anniversary of the first well log. On 5 September 1927, three men from Schlumberger logged the Diefenbach [sic] well 2905 at Dieffenbach-lès-Wœrth in the Pechelbronn heavy oil field in the Alsace region of France.

The site of the Diefenbach 2905 well. © Google, according to  terms .

The site of the Diefenbach 2905 well. © Google, according to terms.

 
Pechelbronn_log_plot.png

The geophysical services company Société de Prospection Électrique (Processes Schlumberger), or PROS, had only formed in July 1926 but already had sixteen employees. Headquartered in Paris at 42, rue Saint-Dominique, the company was attempting to turn its resistivity technology to industrial applications, especially mining and petroleum. Having had success with horizontal surface measurements, the Diefenbach well was the first attempt to measure resistivity in a wellbore. PROS went on to become Schlumberger.

The resistivity prospecting system had been designed by the Schlumberger brothers, Conrad (1878–1936, a professor at École des Mines) and Maurice (1884–1953, a mining engineer), over the period from about 1912 until 1923. The task of adapting the technology was given to Henri Doll (1902–1991), Conrad's son-in-law since 1923, and the Alsatian well was to be the first field test of the so-called "electrical coring" method. The client was Deutsche Erdöl Aktiengesellschaft, now DEA of Hamburg, Germany.

As far as I can tell, the well — despite usually being called "the Pechelbronn well" — was located at the site of a monument at the intersection of Route de Wœrth with Rue de Preuschdorf in Dieffenbach-lès-Wœrth, about 3 km west of Merkwiller-Pechelbronn. Henri Doll logged the well with Roger Jost and Charles Scheibli. Using rudimentary equipment, they logged about 145 m of the 488-metre hole, starting at 279 m MD, taking a reading every metre and plotting the log by hand. Yesterday I digitized this log; download it in LAS format here


Pechelbronn_thumbnail.png

The story of what the Schlumberger brothers and Henri Doll achieved is fascinating; I recommend reading Don Hill's brief history (2012) — it's free to read at Wiley. The period of invention that followed the Pechelbronn success was inspiring.

If you're looking at well logs today, take a second to thank Conrad, Maurice, and Henri for their remarkable idea.

PS If you're interested in petroleum history, the AOGHS page This Week is worth a look.


The French television programme Midi en France recorded this segment about the Pechelbronn field in 2014. The narration is in French, "The fields of maize gorge on sunshine, the pumps on petroleum...", but there are some nice pictures to look at.

References and bibliography

Clapp, Frederick G (1932). Oil and gas possibilities of France. AAPG Bulletin 16 (11), 1092–1143. Contains a good history of exploration and production from the Oligocene sands in Pechelbronn, up to about 1931 (the field produced up to 1970). AAPG Datapages.

Delacour, Jacques (2003). Une technique de prospection minière et pétrolière née en Pays d'Auge. SABIX 34, September 2003. Available online.

École des Mines page on Conrad Schlumberger at annales.org.

Hill, DG (2012). Appendix A: Historical Review (Milestone Developments in Petrophysics). In: Buryakovsky, L, Chilingar, GV, Rieke, HH, and Shin, S (2012). Petrophysics: Fundamentals of the Petrophysics of Oil and Gas Reservoirs, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118472750.app1. A nice potted history of well logging, including important dates.

Musée Français du Pétrole website, http://www.musee-du-petrole.com/historique/

Pike, B and Duey, R (2002). Logging history rich with innovation. Hart's E&P Magazine. September 2002. Available online. Interesting article, but beware: there are one or two inaccuracies in this article, and I believe the image of the well log is incorrect.

The Computer History Museum

Mountain View, California, looking northeast over US 101 and San Francisco Bay. The Computer History Museum sits between the Googleplex and NASA Ames. Hangar 1, the giant airship hangar, is visible on the right of the image. Imagery and map data © Google, Landsat/Copernicus.

A few days ago I was lucky enough to have a client meeting in Santa Clara, California. I had not been to Silicon Valley before, and it was more than a little exciting to drive down US Route 101 past the offices of Google, Oracle and Amazon and basically every other tech company, marvelling at Intel’s factory and the hangars at NASA Ames, and seeing signs to places like Stanford, Mountain View, and Menlo Park.

I had a spare day before I flew home, and decided to visit Stanford’s legendary geophysics department, where there was a lecture that day. With an hour or so to kill, I thought I’d take in the Computer History Museum on the way… I never made it to Stanford.

The museum

The Computer History Museum was founded in 1996, building on an ambition of über-geek Gordon Bell. It sits in the heart of Mountain View, surrounded by the Googleplex, NASA Ames, and Microsoft. It’s a modern, airy building with the museum and a small café downstairs, and meeting facilities on the upper floor. It turns out to be an easy place to burn four hours.

I saw a lot of computers that day. You can see them too because much of the collection is in the online catalog. A few things that stood out for me were:

No seismic

I had been hoping to read more about the early days of Texas Instruments, because it was spun out of a seismic company, Geophysical Service or GSI, and at least some of their early integrated circuit research was driven by the needs of seismic imaging. But I was surprised not to find a single mention of seismic processing in the place. We should help them fix this!

The disappearing lake trick

On Sunday 20 November it's the 36th anniversary of the 1980 Lake Peigneur drilling disaster. The shallow lake — almost just a puddle at about 3 m deep — disappeared completely when the Texaco wellbore penetrated the Diamond Crystal Salt Company mine at a depth of about 350 m.

Location, location, location

It's thought that the rig, operated by Wilson Brothers Ltd, was in the wrong place. It seems a calculation error or misunderstanding resulted in the incorrect coordinates being used for the well site. (I'd love to know if anyone knows more about this as the Wikipedia page and the video below offer slightly different versions of this story, one suggesting a CRS error, the other a triangulation error.)

The entire lake sits on top of the Jefferson Island salt dome, but the steep sides of the salt dome, and a bit of bad luck, meant that a few metres were enough to spoil everyone's day. If you have 10 minutes, it's worth watching this video...

Apparently the accident happened at about 0430, and the crew abandoned the subsiding rig before breakfast. The lake was gone by dinner time. Here's how John Warren, a geologist and proprietor of Saltworks, describes the emptying in his book Evaporites (Springer 2006, and repeated on his awesome blog, Salty Matters):

Eyewitnesses all agreed that the lake drained like a giant unplugged bathtub—taking with it trees, two oil rigs [...], eleven barges, a tugboat and a sizeable part of the Live Oak Botanical Garden. It almost took local fisherman Leonce Viator Jr. as well. He was out fishing with his nephew Timmy on his fourteen-foot aluminium boat when the disaster struck. The water drained from the lake so quickly that the boat got stuck in the mud, and they were able to walk away! The drained lake didn’t stay dry for long, within two days it was refilled to its normal level by Gulf of Mexico waters flowing backwards into the lake depression through a connecting bayou...

The other source that seems reliable is Oil Rig Disasters, a nice little collection of data about various accidents. It ends with this:

Federal experts from the Mine Safety and Health Administration were not able to apportion blame due to confusion over whether Texaco was drilling in the wrong place or that the mine’s maps were inaccurate. Of course, all evidence was lost.

If the bit about the location is true, it may be one of the best stories of the perils of data management errors. If anyone (at Chevron?!) can find out more about it, please share!

Hooke's oolite

52 Things You Should Know About Rock Physics came out last week. For the first, and possibly the last, time a Fellow of the Royal Society — the most exclusive science club in the UK — drew the picture on the cover. The 353-year-old drawing was made by none other than Robert Hooke

The title page from  Micrographia , and part of the dedication to Charles II.  You can browse the entire book at archive.org.

The title page from Micrographia, and part of the dedication to Charles II. You can browse the entire book at archive.org.

The drawing, or rather the engraving that was made from it, appears on page 92 of Micrographia, Hooke's groundbreaking 1665 work on microscopy. In between discovering and publishing his eponymous law of elasticity (which Evan wrote about in connection with Lamé's \(\lambda\)), he drew and wrote about his observations of a huge range of natural specimens under the microscope. It was the first time anyone had recorded such things, and it was years before its accuracy and detail were surpassed. The book established the science of microscopy, and also coined the word cell, in its biological context.

Sadly, the original drawing, along with every other drawing but one from the volume, was lost in the Great Fire of London, 350 years ago almost to the day. 

Ketton stone

The drawing on the cover of the new book is of the fractured surface of Ketton stone, a Middle Jurassic oolite from central England. Hooke's own description of the rock, which he mistakenly called Kettering Stone, is rather wonderful:

I wonder if anyone else has ever described oolite as looking like the ovary of a herring?

These thoughtful descriptions, revealing a profundly learned scientist, hint at why Hooke has been called 'England's Leonardo'. It seems likely that he came by the stone via his interest in architecture, and especially through his friendsip with Christopher Wren. By 1663, when it's likely Hooke made his observations, Wren had used the stone in the façades of several Cambridge colleges, including the chapels of Pembroke and Emmanuel, and the Wren Library at Trinity (shown here). Masons call porous, isotropic rock like Ketton stone 'freestone', because they can carve it freely to make ornate designs. Rock physics in action!

You can read more about Hooke's oolite, and the geological significance of his observations, in an excellent short paper by material scientist Derek Hull (1997). It includes these images of Ketton stone, for comparison with Hooke's drawing:

Reflected light photomicrograph (left) and backscatter scanning electron microscope image (right) of Ketton Stone. Adapted from figures 2 and 3 of Hull (1997). Images are © Royal Society and used in accordance with  their terms .

Reflected light photomicrograph (left) and backscatter scanning electron microscope image (right) of Ketton Stone. Adapted from figures 2 and 3 of Hull (1997). Images are © Royal Society and used in accordance with their terms.

I love that this book, which is mostly about the elastic behaviour of rocks, bears an illustration by the man that first described elasticity. Better still, the illustration is of a fractured rock — making it the perfect preface. 



References

Hall, M & E Bianco (eds.) (2016). 52 Things You Should Know About Rock Physics. Nova Scotia: Agile Libre, 134 pp.

Hooke, R (1665). Micrographia: or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses, pp. 93–100. The Royal Society, London, 1665.

Hull, D (1997). Robert Hooke: A fractographic study of Kettering-stone. Notes and Records of the Royal Society of London 51, p 45-55. DOI: 10.1098/rsnr.1997.0005.

Poisson's controversial stretch-squeeze ratio

Before reading this, you might want to check out the previous post about Siméon Denis Poisson's life and career. Then come back here...


Physicists and mathematicians knew about Poisson's ratio well before Poisson got involved with it. Thomas Young described it in his 1807 Lectures on Natural Philosophy and the Mechanical Arts:

We may easily observe that if we compress a piece of elastic gum in any direction, it extends itself in other directions: if we extend it in length, its breadth and thickness are diminished.

Young didn't venture into a rigorous formal definition, and it was referred to simply as the 'stretch-squeeze ratio'.

A new elastic constant?

Twenty years later, at a time when France's scientific muscle was fading along with the reign of Napoleon, Poisson published a paper attempting to restore his slightly bruised (by his standards) reputation in the mechanics of physical materials. In it, he stated that for a solid composed of molecules tightly held together by central forces on a crystalline lattice, the stretch squeeze ratio should equal 1/2 (which is equivalent to what we now call a Poisson's ratio of 1/4). In other words, Poisson regarded the stretch-squeeze ratio as a physical constant: the same value for all solids, claiming, 'This result agrees perfectly' with an experiment that one of his colleagues, Charles Cagniard de la Tour, recently performed on brass. 

Poisson's whole-hearted subscription to the corpuscular school certainly prejudiced his work. But the notion of discovering of a new physical constant, like Newton did for gravity, or Einstein would eventually do for light, must have been a powerful driving force. A would-be singular elastic constant could unify calculations for materials soft or stiff — in contrast to elastic moduli which vary over several orders of magnitude. 

Poisson's (silly) ratio

Later, between 1850 and 1870, the physics community acquired more evidence that the stretch-squeeze ratio was different for different materials, as other materials were deformed with more reliable measurements. Worse still, de la Tour's experiments on the elasticity of brass, upon which Poisson had hung his hat, turned out to be flawed. The stretch-squeeze ratio became known as Poisson's ratio not as a tribute to Poisson, but as a way of labeling a flawed theory. Indeed, the falsehood became so apparent that it drove the scientific community towards treating elastic materials as continuous media, as opposed to an ensemble of particles.

Today we define Poisson's ratio in terms of strain (deformation), or Lamé's parameters, or the speed \(V\) of P- and S-waves:

 
 

Interestingly, if Poisson turned out to be correct, and Poisson's ratio was in fact a constant, that would mean that the number of elastic constants it would take to describe an isotropic material would be one instead of two. It wasn't until Augustin Louis Cauchy used the notion of a stress tensor to describe the state of stress at a point within a material, with its three normal stresses and three shear stresses, did the need for two elastic constants become apparent. Tensors gave the mathematical framework to define Hooke's law in three dimensions. Found in the opening chapter in any modern textbook on seismology or mechanical engineering, continuum mechanics represents a unique advancement in science set out to undo Poisson's famously false deductions backed by insufficient data.

References

Greaves, N (2013). Poisson's ratio over two centuries: challenging hypothesis. Notes & Records of the Royal Society 67, 37-58. DOI: 10.1098/rsnr.2012.0021

Editorial (2011). Poisson's ratio at 200, Nature Materials10 (11) Available online.

 

Great geophysicists #13: Poisson

Siméon Denis Poisson was born in Pithiviers, France, on 21 June 1781. While still a teenager, Poisson entered the prestigious École Polytechnique in Paris, and published his first papers in 1800. He was immediately befriended — or adopted, really — by Lagrange and Laplace. So it's safe to say that he got off to a pretty good start as a mathematician. The meteoric trajectory continued throughout his career, as Poisson received more or less every honour a French scientist could accumulate. Along with Laplace and Lagrange — as well as Fresnel, Coulomb, Lamé, and Fourier — his is one of the 72 names on the Eiffel Tower.

Wrong Poisson

In the first few decades following the French Revolution, which ended in 1799, France enjoyed a golden age of science. The Société d’Acrueil was a regular meeting of savants, hosted by Laplace and the chemist Claude Louis Berthollet, and dedicated to the exposition of physical phenomena. The group worked on problems like the behaviour of gases, the physics of sound and light, and the mechanics of deformable materials. Using Newton's then 120-year-old law of gravitation as an analogy, the prevailing school of thought accounted for all physical phenomena in terms of forces acting between particles. 

Poisson was not flawless. As one of the members of this intellectual inner circle, Poisson was devoted to the corpuscular theory of light. Indeed, he dismissed the wave theory of light completely, until proven wrong by Thomas Young and, most conspicuously, Augustin-Jean Fresnel. Even Poisson's ratio, the eponymous elastic modulus, wasn't the result of his dogged search for truth, but instead represents a controversy that drove the development of the three-dimensional theory of elasticity. More on this next time.

The workaholic

Although he did make time for his wife and four children — but only after 6 pm — Poisson apparently had little time for much besides mathematics. His catchphrase was

Life is only good for two things: doing mathematics and teaching it.

In the summer of 1838, he learned he had a form of tuberculosis. According to James (2002), he was unable to take time away from work for long enough to recuperate. Eventually, insisting on conducting the final exams at the Polytechnique for the 23rd year in a row, he took on more than he could handle. He died on 20 April 1840. 


References

Grattan-Guinness, I. (1990). Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics. Vol.1: The Setting. Springer Science & Business Media. 549 pages.

Ioan James, I (2002). Remarkable Mathematicians: From Euler to Von Neumann. Cambridge University Press, 433 pages.

The University of St Andrews MacTutor archive article on Poisson.

Great geophysicists #12: Gauss

Carl Friedrich Gauss was born on 30 April 1777 in Braunschweig (Brunswick), and died at the age of 77 on 23 February 1855 in Göttingen. He was a mathematician, you've probably heard of him; he even has his own Linnean handle: Princeps mathematicorum, or Prince of mathematicians (I assume it's the royal kind, not the Purple Rain kind — ba dum tss).

Gauss's parents were poor, working class folk. I wonder what they made of their child prodigy, who allegedly once stunned his teachers by summing the integers up to 100 in seconds? At about 16, he was quite a clever-clogs, rediscovering Bode's law, the binomial theorem, and the prime number theorem. Ridiculous.

His only imperfection was that he was too much of a perfectionist. His motto was pauca sed matura, meaning "few, but ripe". It's understandable how someone so bright might not feel much need to share his work, but historian Eric Temple Bell reckoned that if Gauss had published his work regularly, he would have advanced mathematics by fifty years.

He was only 6 when Euler died, but surely knew his work. Euler is the only other person who made comparably broad contributions to what we now call the exploration geophysics toolbox, and applied physics in general. Here are a few: 

  • He proved the fundamental theorems of algebra and arithmetic. No big deal.
  • He formulated the Gaussian function — which of course crops up everywhere, especially in geostatistics. The Ricker wavelet is a pulse with frequencies distributed in a Gaussian.
  • The gauss is the cgs unit of magnetic flux density, thanks to his work on the flux theorem, one of Maxwell's equations.
  • He discovered the Cauchy integral theorem for contour integrals but did not publish it.
  • The 'second' or 'total' curvature — a coordinate-system-independent measure of spatial curvedness — is named after him.
  • He made discoveries in non-Euclidean geometry, but did not publish them.

Excitingly, Gauss is the first great geophysicist we've covered in this series to have been photographed (right). Unfortunately, he was already dead. But what an amazing thing, to peer back through time almost 160 years.

Next time: Augustin-Jean Fresnel, a pioneer of wave theory.