Thursday, April 19, 2007

When the earth moves, his name is on everyone's lips

kw: book reviews, nonfiction, seismology, earthquakes, biographies

As a Geology student in about 1970, one big, big thing they drummed into us about earthquakes was the difference between Intensity, which is different at every point, and Magnitude, which is a characteristic of the total event. When an earthquake happens, a section of a fault—a large crack in the rocks of the earth's crust—experiences displacement. By displacement, I refer to the relative motion of rocks on the opposite sides of a flattish area. This area can be small, perhaps the size of a strip of roadway a block long; the relative motion may also be small, perhaps a few inches; in such a case, unless you happen to be lying down right above that section of the fault, you won't feel it. A small quake like this occurs, at the fault, in a second or less.

On the other hand, a section of fault a thousand kilometers long and twenty miles wide may erupt with relative motion of ten meters or more. Such an event is among the largest earthquakes possible, and can destroy most structures in any nearby (100 km, perhaps) cities and shift landscape features over a huge area. Such large slippage also takes longer, from a few seconds to a minute.

February 9, 1971 (3 months after my birthday...I won't say which) I awoke at 6AM sharp when my water bed sloshed and almost dumped me on the floor. I turned on the radio, grabbed a field notebook, and began to take notes. I lived in Alhambra, California at the time, 38 km from Sylmar, where the earthquake occured. Central Alhambra is built on well-consolidated sediments, so the shaking didn't damage my house much—just a few new cracks. Nearby areas built on looser soils, which shook more as the waves passed through, had much more damage.

It wasn't my first earthquake, just the most memorable. The other well-remembered event occurred nearly three years earlier, April 8, 1968, about 6:30 pm. I was at my parents' home for dinner. I'd just left the table to get something from the pantry, and found myself swaying while haning onto the pantry door. I looked toward the table, and the hanging lamp was swaying. My parents and brothers were quite still, with wide eyes. Then a "SPLOP" against the back door announced that a lot of water from the swimming pool had decided to form a mini-tsunami across the back yard. We were in Arcadia, 205 km from Borrego Mountain, so the motions were smoother and gentler, and no damage resulted (to us).

These two earthquakes were of nearly the same "size", with magnitudes of 6.6 (1971) and 6.5 (1968). Yet because of their different distances, the intensity of motion I experienced was quite different. I could not have remained standing had I been awake during the 1971 quake, but I was able to let go of the pantry door and stand in 1968.

OK, what does "magnitude mean"? The answer has everything to do with Charles Richter, as explained very well in the new biography "Richter's Scale: Measure of an Earthquake; Measure of a Man" by Susan Elizabeth Hough, a USGS seismologist and a fine writer. Her explanation of "the Richter scale" focuses on the work Dr. Richter did to produce it, not on the technical details of its use. So, I'll take a bit of a digression here.

As I mentioned early on, earthquakes range from stupendous catastrophes over huge areas to tiny events hardly distinguishable from footfalls. A small thump you can barely hear with your ear to the ground causes ground "motion" that is measured in microns, while the Sylmar earthquake caused the dirt at the tops of hills to jump several feet into the air, and moved some houses right off their foundations into the yard nearby.

In the 1930s, the standard instrument for recording earthquake motions was the Anderson-Wood Seismograph. These days, seismographs record their data digitally, on tape or CDs...or DVDs I suppose. But the principle is the same. A small motion of a sensor is amplified so you can see it. Instruments intended to record stronger events use much less amplification, or even "de-amplify" the motion. The A-W instrument recorded with a light beam on a piece of film, so you had to develop the film, then you could make measurements. Seismology was smelly work.

Basically, after many measurements of many recordings, and taking the suggestion of his colleague Beno Gutenberg of using logarithms, Richter devised a method of reducing the measurements to a standard form. Thus, an earthquake could eventually be given a single number, a Magnitude, that recorded its strength.

A word about logarithms: they are the way our bodily senses work, so it is good to know how they work. If you have one light on in a room and turn on another of equal brightness, the light is twice as bright, and you can easily tell the difference. If you turn on a third, similar light, it is harder to tell the difference. If you have nine lights on, and turn on a tenth, you may find it hard to see the difference without carefully turning it off and on and off and on again as you look at some object all ten are illuminating. But if you have ten bulbs on and turn on ten more, the difference seems the same as when you had one on and turned on another. In other words, doubling the amount of light causes a similar response in you, regardless of the starting light level.

This allows you to see well in a room lighted by one or two 40-watt fluorescent tubes, yet go right outdoors, blink once or twice, and see quite well in full sunlight, though it is a thousand times as bright. There are ten steps of two that cover a range of 1000:1 (actually 2x2x2x2x2x2x2x2x2x2 = 1,024), and if you ask people how bright the sunlight is, compared to a well-lit room, many will say, "Ten times." In terms of the number two, ten is the logarithm of 1,024. This is nature's way to compensate for sensations that cover a very large range. But note: heat doesn't work like this, so don't try to make something "ten times hotter" and touch it! (The range of temperature we can endure without damage ranges from about 0 to 60 degrees Celsius, or 32 - 140 deg F. But in terms of absolute temperature in a physics sense, the range is ~270 to ~330 Kelvins, or about 1.2:1).

So, you take a seismogram and measure the biggest wiggle, or half the distance from the biggest plus to the biggest minus (the full-scale range). You take its logarithm. Shall we use powers of two? It turns out we are less sensitive to motion than to light. We feel one "shake" is significantly bigger than another when the motion is ten times greater. We can detect smaller differences, but it takes most folks some thought to decide if a shaking that is three times another is really that much different, as long as both are relatively small. So Richter decided that a magnitude of 4 would be ten times the motion of a magnitude of 3.

Specifically, as measured on an A-W seismograph set for recording quakes at moderate distance, he chose a 1mm wiggle of the light trace as a basis. Then, when the instrument was 100 km from the epicenter (the location directly above the piece of a fault that moved), a 1mm wiggle would be given a magnitude of 3. At that distance, then, a barely-recordable quake, with a wiggle just 0.01mm, would have a magnitude of 1.

How to correct for distance? Nobody knows when and where a quake will occur, so you take the recording from the instrument wherever it may be. My two most memorable quakes occurred 38 and 305 km from where I was when they occurred. Since they were both about 6.5 in magnitude, they'd have caused a wiggle of more than 3 meters on an A-W seismograph. The film is only 0.4 meters wide, so that wouldn't work anyway. But if the amplification setting is 100 times smaller (the machine then set for recording larger ground motions), the wiggle would be 32mm.

Do you know the inverse-square law? Simply put, if you are twice as far from a source of energy, its intensity is one-fourth, and so on. So a standard A-W seismograph at 305 km from the Borrego Mountain earthquake, in my parent's dining room, would have shown a wiggle of 3200/(3.05*3.05) or 340mm. Large, but it does fit on the film. At the lower setting of the instrument, a 3.4mm wiggle would be seen.

There's another factor to look at. Distance can be measured pretty accurately from a seismogram. Earthquakes make two large waves, a P wave and an S wave. P is for Pressure, and causes squeezing and its reverse in the rocks it passes through. It arrives first. S is for Shear or Shaking, and is a side-to-side motion. It arrives later. The factor for figuring distance (in the western U.S.) is 9.7: if the S-P arrival is 10 seconds, the earthquake epicenter is 97 km away.

A little algebra, with the setting of M=3, A=1mm, D=100km, and the inverse-square law, yields the following equation, where "log" is a "common logarithm", to base 10:

M = log(A) + 2log(D) - 1

Now let's apply it. This example of a seismogram from a modern instrument has the following characteristics:

  • Biggest wiggle: 245mm
  • S-P time difference: 39sec (p arrives at t=0)
  • The distance to the epicenter is thus 39*9.7 = 380km (rounded from 378)

M = log(245) + 2log(380) - 1 = 2.4 + 5.1 - 1 = 6.5

The nomograph in this illustration can do these calculations for you. Try it out. Draw a line from 245 on the right to 380 on the left, and read M in the middle scale.

As it was initially defined, Richter's magnitude scale worked in the range from 1 to 6, for earthquakes in southern California. He continued to revise it, particularly as better instruments were developed, and seismologists have not stood still since his death in 1985. Modern, wide-range instruments of great sensitivity allow a magnitude and location (by triangulation from several instruments) to be assigned quickly. However, a measure of total energy, produced by Moment-Magnitude calculations, is now used to assign a final number to an earthquake. While a difference of magnitude means a difference of 10 in distant ground motions, it means a difference of 30 in total energy released. Thus, while a "sixer" causes 100,000 times as much ground motion as a "one" at 100km distance, it has 24.3 million times the energy.

This is because of two effects. Firstly, an earthquake of magnitude 6 causes shaking over an area of a square mile or so that is as great as the earth's surface can support: accelerations of 1-2 g. This is why hilltops can be thrown into the air in quakes like that in 1971. Larger earthquakes have this level of intensity spread out over greater and greater areas, so a "big one" with a magnitude of 8, with 900 times the energy of a "sixer", will devastate an area of a couple thousand square miles, and knock down some stuff over an area even larger. The biggest earthquake recorded, with a magnitude of 9.5 in Chile in 1960 (May 22), devastated towns and cities throughout the country, and in nearby Argentina, Bolivia, and Peru. But the ground motions of a 9.5 are not a great deal larger in linear size than those of a 6.5. Ground waves a few meters high seem to be the maximum.

Secondly, when you are too close to a large source of energy, the inverse-square law is not accurate. The fault that ruptured in 1960 offshore of Chile must have been half the length of the country of more, perhaps 2,500 km. If you were on the East coast of Argentina, perhaps 1,000km away, the ends of the fault rupture would be 1,600km distant. It's like trying to measure the brightness of a light bulb when you are two millimeters from the filament. You had to be in China or Europe to get an accurate record! At that distance, the greater size of the fault of a really big quake causes the instrument to record a larger excursion than if the quake were a 6 or so, even though someone near the epicenter of both quakes would find it hard to tell the difference (as she dodges falling masonry!).

Thus, an "instant" measure that indicates 8 really means something closer to 9 when all such factors are taken into account. Well, one can tell I savor the technical details. But the summary of these things occupies just one chapter of Dr. Hough's book. The other eighteen chapters detail the life of Caltech's pre-eminent Mystery Man.

Who was Charles F. Richter? He was a most private man. We are incredibly fortunate that he left all his papers to the Caltech archives. Without those, we'd be limited to the stories told by colleagues and a few neighbors, and those are rather thin on the ground. Without those, we'd never know he was a poet and novelist (unpublished); we'd know little of his frequent treks into the mountains; one might stumble on someone who knew him and his wife Lillian as practicing nudists; never would his relationships within the writing circle, particularly writing women, come to light. Without those, including poems in which he laid bare his soul, it would be hard indeed to determine that he suffered from Asperger's Syndrome.

His closest colleagues all regarded him as an odd sort, an eccentric, a mercurial fellow. Few knew of his breakdown at Stanford the one time he tried to move far from his Los Angeles home. Though he traveled the world—a little, on occasion—he was a persistent homebody. His wife took vacations alone, and he usually hiked alone. Even in Caltech circles he stayed in a narrow circle. He seldom went to the campus proper, staying near his office in the Seismological Lab off campus.

Can you tell that I must be at least halfway into Asperger's myself? I can go on for pages and pages in the vein of the first twenty paragraphs, but I find it hard to discuss the man. Psychologically, there are two big differences I can point to (besides the obvious one that he was a true genius, and I am at best a polymath). I have lived in many places, primarily because my family moved eight times before I moved out. Also, while I, as one AS writer states it, felt "like a Martian among Earthlings", I decided as a teenager to produce the personality I clearly lacked. I deliberately gave over a number of IQ points to "social processing", so I could, with only the smallest time lag, respond as expected in social situations I often didn't understand. It took decades, into my late 40s, before I found, hidden under the artificial personality, that a real one had slowly grown. So, the social integration that takes most folks 15-18 years took me 45-50.

It seems Charlie Richter never had this insight, or never thought it worth the hard work. He was frank to the point of bluntness or rudeness when he wasn't making an effort to be accommodating...and he didn't suffer fools gladly. However, he was perceptive enough to give a fellow a couple tries to prove he was a fool before he whisked him out of his life.

The author seems to believe, and with her I agree, that AS was an asset, giving Richter the focus and relentless energy to do the huge numbers of hand calculations that led to the simple formula I show above (or one much like it) 1935, when even mechanical-gear calculators were not to be found! His greatest work was done in a time that "computer" was a job description for a woman paid a little more than a secretary's wage to do pen-and-paper calculations for a scientist. Richter did his own computing.

The formidable memory characteristic of AS was an asset throughout his life. Knowledge is always a salable commodity. In the Caltech community, where knowledge is more valued than among the "great unwashed," Richter would have had to be a lot odder than he was to be unwelcome. Health and mental problems he may have had, but he lived to age 85, and was beloved by those who knew him, an odd duck, but one worth knowing.

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