Regional Isostasy: supporting a volcano

Since my participation in the Vening Meinesz project (Read about it in some of my earlier posts), I am reading a lot about this interesting person and his scientific findings. One of his greatest achievements to science is the theory of "Vening Meinesz isostasy" or "regional isostasy". This is a model that I use in my research and it is quite powerful but greatly overlooked. Therefore I thought it would be a good thing to write about here on my blog.

The word isostasy, I would think, is not something you would use in a normal conversation. However, you are reading the blog of a scientific geek (Aren't all geeks scientific, hmmmm), so now you will.

It all started with a man taking a bath. This man was given the assignment to solve a problem for his king. The assignment was to find out if the new crown of the king was made of pure gold. The king suspected the goldsmith of using silver. Archimedes (the man) was asked to do this without melting it. A difficult question in those old times.

Thinking long and hard, Archimedes did not solve the problem. So he decided to take a bath (scientific and engineering problem solving are done best in the bathroom). Submerging in the water he noticed that the water level was rising. This observation made him solve the difficult question of the king. Enthusiastic, he ran outside shouting "I found it", or "Eureka", totally naked (every scientist should do this, I think it is liberating).

The Archimedes principle can also be used to calculate when things float. Objects float when the mass of the displaced water by the object is more then the mass of the object itself. When we talk about solid objects, this will mean that they must have a density which is lower than the displaced water. In geoscience we use this principle to study the loading of mountains and ice-sheets.

When a mountain is in isostatic equilibrium, it sort of means that the mountain floats on the fluid mantle material. Ice and mountains have a lower density than the heavy materials in the mantle, which cause them to float. In the late 1800 two scientists devised a theory to explain this phenomenon. Vening Meinesz and Heiskanen wrote a beautiful piece about these two scientists in their book "The Earth and its gravity field":

Quite frequently two scientists working independently discover an important phenomenon or perfect a significant invention simultaneously  It is well known that the English astronomer Adams, in October, 1845, and the French astronomer Leverrier, in the summer of 1846, independently computed the orbital elements of Neptune. Unfortunately for Adams, the new planet was discovered September 23, 1846, on the basis of Leverrier's computations. A similar thing happened in 1868, when the English astronomer Lockyer and the French astronomer Janssen without knowing each other's results invented a method for observing the prominences of the sun, which previously could be studied only during total solar eclipses. In 1892 both the American astronomer Hale and the French astronomer Deslandres invented the spectroheliograph, an important tool in the hands of astronomers. Einstein delivered a paper on his general theory of relativity on November 11, 1915, to the Academy of Sciences in Berlin, and on November 20 of the same year Hilbert gave at the Scientific Association of Göttingen the results of his investigation of a similar theory. (Don't forget the observation of the Jovian moons by Galileo Galilei and Simon Marius, 1610)

   In the same way it happened that on January 25, 1855, the British astronomer G. B. Airy sent to the Royal Society his paper on the same equilibrium problem Pratt discussed before the same society on December 7, 1854.

Both Pratt and Airy had devised a theory that explained, why mountains won't sink under their weight in to the deep depths of the Earth. Pratt's theory states that mountain material have less density than material at coastal areas. This extra light material is more buoyant and is able to support the extra load of a mountain. Airy's theory puts a sub-crustal root beneath the mountain to give it more buoyancy. You can see this a bit like a floating iceberg. I made this following figure to explain Airy isostasy:

The yellow crustal material floats on top of the dens mantle material. Exactly underneath mountains the crust is thicker, having a sub-crustal root. This is called local compensation. Vening Meinesz found out that mountains can also be compensated regionally. This means that not only the area underneath the mountain supports it, but also the region around it. He hypothesized that the crust could endure stresses and distributes the load to other areas around the mountain. This type of compensation is called regional or Vening Meinesz compensation. This is best seen at the islands of Hawaii (which are big mountains):

In this free-air gravity anomaly plot the Hawaiian islands can be seen in the bottom right corner. The gravity high (purple red) is related to the extra mass of the volcanos. The blue area around (less gravity) is due to the bending of the crust. The volcano pushes the oceanic plate downwards. The complete region reacts to compensate the mountain, keeping it up.

In 1926, Vening Meinesz, onboard the Hrs. Ms. submarine K13, observed the gravity field of those islands. With his theory he could describe the observed gravity field almost perfectly. This was not succeeded by others using the Pratt or Airy theory of compensation.

I made the above figures for an ebook describing GOCE satellite gravity results, showing the GOCO03S gravity model (this model was also used to make the first figure) and its Airy isostatic anomaly (thick lines). The thin lines with circles are the observations done by Vening Meinesz 100 years earlier in a cramped metal tube. At 280 km along the profile all anomalies are positive, which can be correlated with the mountain topography (bottom figure, red diamonds are the K13's depth observations done by its sonar crew). Only the green line (Vening Meinesz isostasy) is close to zero. This means that this theory perfectly corrects the gravity field for the mountain and explains the phenomenon. Vening Meinesz's theory is very powerful, however a bit more complex than Pratt and Airy's theory, so it is unfortunately mostly neglected.

In the Netherlands Vening Meinesz is also mostly forgotten, which is a pity, because it was one of our important scientists. Let's get him in our school books ;), start to remember him again...