Wednesday, January 20, 2010

The Lord of Earthquakes



(Lisbon Cathedral in the wake of the terrible 1755 earthquake that destroyed the city)


"Civilization exists by geologic consent, subject to change without notice."
-Will Durant

Cusco

In June of 2009, I spent a few days in the Andean city of Cusco, Peru. Cusco was the capital of the Inca Empire and it has become one of the world's real adventure travel nexus points, with expeditions of various kinds being launched from the city. We were there to acclimate to the higher altitude and sightsee for a short period before hiking the famous Inca Trail, the stone path that begins near "Kilometer 88"and then moves up and down through the Andes like a long serpent, past snow-capped mountains and cloud-high camp sites and picturesque ruins, before ultimately coming to the "Sun Gate" pass that looks down upon Machu Picchu.

I had read that Cusco was located in a region of substantial seismic activity, and that the irregularly-shaped, giant blocks of the Sacsayhuaman walls outside of the city, some of which are estimated to weigh over 360 tons, may have been organized according to cyclopean construction principles meant to give them an increased resistance to earthquakes. It was fascinating, then, to see first-hand how Spanish Catholicism, brought to Peru by the conquistadores and missionaries, cross-pollinated with the region's natural disasters to create a local mythology that was unique to Cusco.




(Plaza de Armas, Cusco, Peru---June 2009)













A short walk from our base at the Libertador, down a narrow alley that featured modern storefronts and restaurants built on top of Inca block walls, we found the large, rectangular plaza de armas that is typically found in cities of this lineage. Dominating the plaza was the Cathedral of Cusco, an imposing and beautiful work of architecture that essentially combines three large churches into one. Inside the cathedral was the Lord of the Earthquakes.

In 1650, Cusco was hit by one of the major earthquakes that appear to devastate the city every 200-300 years. Legend has it that the cathedral and Inca heritage sites were spared when an effigy of Christ that was donated by Carlos V of Spain was taken from the church and into the streets, miraculously causing the violent tremors to subside. The Lord of The Earthquakes---also called "The Dark Christ" because of its black color---is venerated in Cusco and is removed from the cathedral once a year for a special ceremony.



"Dark Christ" procession, Cusco








Gutenberg-Richter

If there is an empirical "Lord of the Earthquakes", it is a mathematical expression known as the Gutenberg-Richter Law. Gutenberg-Richter is a power law, a class of statistical distributions that features very large "tail", or extreme, events. These tail events are so big that they have profound effects on the average behavior we expect from the whole system over time.

We have seen power laws before. Changes in financial market prices appear to obey one. The top-grossing 5% of movies accounted for 50% of all box office revenues in the period 2000-2005, and film workers obey a power law called "Solla Price", which holds that 50% of the work being done in the profession is done by the square root of the number of participants. Company sizes follow a power law called Zipf's Law: just .3% of U.S. firms generated 65% of all sales in 2005.

The laws extend to areas of individual human performance as well: Charles Murray, in his tour de force Human Accomplishment, found that excellence in fields as diverse as the arts, professional golf, and peer-reviewed scientific research follow power laws, which he described as a "...a type of hyperbolic distribution---highly skewed right, with an elongated tail". To cite just one example: 53% of professional golfers---all of them elite players---fail to win even a single tournament during their careers, and then we get a Jack Nicklaus who wins 71 of them. (There are some very interesting theories about how individual talents---"component skills"---may follow Gaussian bell curves, but can mix together in interesting ways to create power law-monster performers. "Ammon's Turnip" and relevant observations by Francis Galton and William Shockley can provide insights here. We'll return to this subject later for a discussion of how a 007, Jason Bourne, or even Batman could conceivably exist in the real world, although it is statistically unlikely that the human race could generate more than a handful of such individuals).

Gutenberg-Richter is the relevant power law for this discussion, because it describes a range of earthquake destructiveness magnitudes and their relative frequencies. The frequencies of earthquake types, placed in these destructive-energy classes, vary according to a demonic mathematical scaling relationship. The majority of earthquakes will be quite minor, but there will be a long tail to the distribution that will feature extreme seismic events in greater frequencies than we would get if earthquakes were normally distributed.

One of the features of power law distributions that makes them maddeningly difficult to study at the micro level is that they appear to be a product of what physicist Per Bak has termed "self-organized criticality" ("SOC"). A system that has reached a critical state can be thought of as being "loaded": a small perturbation can cause the system to suddenly exhibit wildly volatile behavior. Bak's traditional example is that of a sandpile: for a long time, additional grains of sand dropped on the sandpile simply form new layers of building material, causing the pile to grow higher and higher. At some point, however, an additional grain meets a sandpile that has entered a critical state. This final grain of sand causes the structure to behave violently, with responses that may range from a small avalanche of sand to the total collapse of the entire structure---the response can be modeled with a power law distribution. What we cannot predict is what the size of the response will be in any given instance, although we can say that a larger, higher sandpile has the potential to create a more spectacular collapse.

We will deal with this issue of criticality again and again on Bastiat Blogger. For an immediate example of a system with the potential to go critical, the market for crude oil can begin to behave chaotically---wild price excursions become possible----as a stable (or perhaps soon to begin declining) supply of crude in the production system meets insatiable demand from the economies of China and India, and the "swing producer" of Saudi Arabia becomes increasingly unable to provide a buffer, particularly after the monster Ghawar field goes into decline.

While Gutenberg-Richter gives a scale for sizes and frequencies, the more widely-known Richter Scale actually articulates what these sizes mean by giving the magnitude---the amount of earth moved by an earthquake---and the energy released. The scale functionally goes from 2 to 9, although a 10 is possible-but-never- recorded (it would represent an "epic", or civilization-destroying, earthquake). The Richter Scale is logarithmic: each upward whole number change increases the amplitude of the earthquake by a factor of 10. A level 9 quake thus has 100 times the amplitude of a level 7. The energy released increases even more dramatically: each upward shift increases the energy released by a factor of about 30, so a level 9 is releasing 900 times the energy of a level 7.

The other important scale used in earthquake measurement is called the Mercalli-Rossi Scale, and it is more of a subjective and anecdotal review of the damage caused. Suffice to say that it is roughly analogous to the Richter Scale in terms of what one would expect: earthquakes that score 7 and above tend to kill a lot of people, particularly if they occur in areas of the world with high population densities and poor building codes. Above 8 and the quakes leave ever fewer structures intact. Earthquakes that have Mercalli-Rossi scores of 9 leave virtually nothing standing.

Subduction Zones

One of the first steps in understanding earthquakes is to try to determine where the geological processes are located that tend to produce them. Overlaying a map of global earthquake activity onto a map of the earth's major geologic plates and tectonic zones will reveal that the most severe earthquakes take place near subduction zones, where one plate is pushed beneath another, rather than near the mid-oceanic ridges, where plates diverge in east-west directions. The reason for the violence of the subduction zone earthquakes has to do with the strength characteristics of rock.

Rock is very strong under non-rotational compression (pushing in), and not very strong under tension (pulling apart). The ancient Greeks realized this when they found that their public buildings tended to collapse unless columns were placed under horizontal lintels at close intervals; if the columns were too far apart, weight pushing down on the lintel---or sometimes just the weight of a lintel itself---would create excess tension and the lintel would crack in its center and bring the whole roof down with it .



(reason why the Parthenon has so many Doric columns-the lintels must be well-supported)


The Romans, however, realized that rocks were stronger under compression than they were under tension. This led them to the Roman arch, a construction technique that created strength in the structure by means of a wedge-shaped keystone that, loaded with weight from above, generated non-rotational compression forces over the span of the arch. An arch between two supports can be made much wider than an equivalently-loaded lintel can be made.



(Roman arches used to construct an aqueduct)





In the oceanic ridge situation, rocks are being pulled apart by tensional forces. Because rocks are not strong under tension, they give quickly---little energy is stored in the process. So earthquakes, like volcano activity, in a place like Iceland will tend to be quite gentle. The major damage caused by a volcano in an oceanic ridge chain like Iceland (or Hawaii, for that matter, although the situation in Hawaii is a bit different because the "hot spot" that has created the Hawaiian Islands is located under oceanic plate rather than at an oceanic ridge) will be created by running lava, not by an exposive eruption.

In a subduction zone, however, rocks are being compressed. These regions feature thrust or reverse faults, where two plates are forced together in collision before one buckles and goes beneath the other. The compression forces here are beyond human comprehension---the forces involved created the Himalayas when the Indian subcontinent collided with Asia.

Rocks are very strong under compression, so it takes a lot of energy to break them that way. They store energy up until they reach their elastic limits, and thus when they do break, they will break very violently. Subduction zones produce the monster earthquakes and volcanic eruptions.

Venomous Sting at The Very End of the Seismic Tail

Incidentally, a variation on this theme may actually be our collective undoing one day. Let us leave earthquakes for a moment and discuss their cousins in geologic violence, volcanic eruptions. The deadliness of volcanic eruptions varies with both the underlying tectonic process (subduction vs. mid-oceanic ridge) and the type of rock that is heated to create magma. The most rare case of eruption---thankfully---occurs when the granitic rock of a continental plate is forced over a subduction factory. Granitic magma can store vast amounts of gas, and pressure can build for very long periods of time. However, when a volcano of this type explodes the results are truly, truly catastrophic: an entire mountain range can be blown up.

A situation of this kind currently exists under Yellowstone National Park. An immense caldera is steadily growing beneath the park, and when it ultimately does go (it may take thousands of years for this to happen---we just don't know) the results will be quite bad. What is happening under Yellowstone is that a hotspot, deep in the earth, is creating a magma plume, a fiery spike that eats its way towards the surface. The magma plume, which is basaltic magma, has hit the granite of the continental plate beneath Yellowstone. The magma has pooled there, eventually creating enough heat to begin melting granite (!). Over time, the process is creating a bubble of granitic magma. When this rising bubble of magma eventually reaches the surface, it will be absolutely apocalyptic, an explosion like no modern human has ever seen. One intriguing possibility is that the eruption will be triggered by a large earthquake in the western United States.

Just to give a sense of scale and some historical precedent here: the biggest volcanic eruption of the last two centuries, the Tambora eruption in Indonesia, displaced approximately 20 cubic kilometers of ash, and caused the planet's climate to measurably cool (1816, the year of the eruption, was termed "the year without a summer"). About 74,000 years ago, Mount Toba in Sumatra erupted and displaced about 800 cubic kilometers of ash (about the same size as the Yellowstone blast of 2.1 million years ago).

More to the point, Toba may have very nearly caused the extinction of the human race: population geneticists have found a mysterious "bottleneck" in our genetic past, a period in which the population of humans on the planet plunged to about 10,000 living adults (this is called the "Toba Catastrophe Theory"). The disaster may also have created isolated, independent population "islands" of genetic diversity that allowed for more rapid mechanisms of genetic drift to work, and thus led to the existence of our modern races.













(picturesque Lake Toba, Sumatra: site of cataclysmic explosion that nearly killed off the human race)



Earthquakes and Shock Waves


The deep place where rocks reach their elastic limits and break is termed the "focus" of the earthquake. The energy that is released at the focus travels outward in "body waves" (seismic shock waves), and the closest surface point to the focus is called the "epicenter". There are two types of body waves---"S" or "shearing" waves that scissor left and right as they travel and can only propagate through solid materials; and "P" or "compression" waves that move backwards and forwards and can propagate through anything.

These things move at extremely high speeds---approximately 18,000 miles per hour. By the time seismic waves are detected, it is almost certainly too late to evacuate an area. It *may* be possible to automatically shut gas mains and stop trains and so on, and this is currently being tried in some locations in Japan.

We can detect seismic waves using a system of sensors that was originally put in place to monitor underground nuclear testing, but our detection equipment is more useful for post-destruction crime scene forensics than it is for providing early-warning alerts. An interesting tangent: attempts have been made to conceal underground nuclear tests by detonating bombs in the immediate aftermaths of earthquakes, the goal obviously being to try to mask the bombs' seismic signatures behind those of the natural processes.

Body waves use up very little energy trying to move rocks around within the crust of the earth as they travel: apparently total rock movement is just a fraction of a milimeter, so it may be best to visualize an almost invisible ripple that shoots through the rock at extreme speeds. When the body waves reach the epicenter, however, that energy is dumped rapidly and a very different kind of shock wave effect----the surface wave---is produced. Surface waves emanate out from the epicenter in an expanding circle of destruction, traveling across the surface of the earth. They have much higher amplitudes than do body waves; at higher Richter scale levels, an observer can actually see a surface wave undulating across the surface.

Surface waves, like body waves, come in two flavors: the ironically-named Love waves move with the horizonal, left-right shearing motion of a pair of scissors being pushed forward; Rayleigh waves move up and down and forward and back, creating an undulating, rolling type of motion in the ground. Both are destructive, but I am told that Love waves are the big killers because buildings just cannot take those quick side-to-side shearing motions (seismologists have a saying: "Earthquakes don't kill people; buildings kill people"). The explanation that I heard for the particular deadliness of the Love surface waves used this example: imagine holding a stack of dominos in the palm of your hand. You could make a rolling motion forward and back, up and down, with your hand and, if the motion was fairly smooth, keep the dominos from falling over. However, move your hand left and then immediately right and the dominos have no chance at all.

Besides their terrifying capacities for tearing buildings down and crushing people or causing them to perish after being buried alive, earthquakes have several other direct kill mechanisms. For instance, they can create tsunamis, like the one that recently killed an estimated 225,000 people in the Indian Ocean (the tsunami was created when a magnitude 9.3 earthquake off the coast of Sumatra, the largest recorded since 1964, released an energy equivalent to almost 10,000 gigatons of TNT, about enough energy to power the entire United States for 400 years. Some estimates, presumably including the aftershock earthquakes that continued for months after the major quake, have raised the total-energy-released number up to approximately 25,000 gigatons). They can break gas mains and create huge fires, like the 1906 earthquake that caused San Francisco to burn for over three days, destroying over 80% of the city (when they break the gas mains, earthquakes also break the water mains and pour rubble into the streets, so that firefighting becomes extremely difficult). If the soil under the buildings is wet, the surface waves can split sand grains apart for an instant, creating an effect called "liquefaction"---momentary quicksand---that can cause buildings to just disappear into the ground. They can also create huge landslides, as they have in Colombia.

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The next entry will focus on what has been learned about earthquake prediction and earthquake-resistant buildings, and on socioeconomic factors that may make earthquake-disaster relief efforts in Haiti more difficult than they otherwise would be.









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