8 Isostasy

Dr. Biplab Biswas

The word Isostasy is derived from the Greek word ‘iso-stasios’ which means ‘equal standing’ (in equipoise). The term isostasy was first proposed by an American geologist Clarence Dutton in 1889 to indicate the state of balance which exists between large upstanding areas of the Earth’s surface, mountain ranges and plateaus. The theory says that the less dense materials of the Earth’s surface (sial) must float over the denser magma (sima) of the Earth’s interior. Similarly, as we go deep interior of the Earth’s, we see that there are several concentric layers. The densest material forms the core whereas the Earth’s surface is composed of lightest material. Each layers and the Earth’s surface features are resting on over another with an isostatic adjustment. For example, the average density of the Core is 13.5 gm/cm3; density of Mantle ranges from 3.3 to 5.7 gm/cm3; density of the Continental crust is around 2.7 gm/cm3. The concept of Isostasy is extremely useful to explain ‘glacial adjustment’ taking place in Scandinavian countries after thsede Pliestocene great ice age. The raised beaches of Finland exhibits that an uplift of about 250 metres has taken place during the last 8000 years due to Isostactic adjustment.

In the present module we are going to cover about following aspects of Isostasy:

1.  Development of the Concept

2.  The Concept of Sir George Airy

3.  The Concept of Archdeacon Pratt

4.  The Concept of Hayford and Bowie

5.  The Concept of Jolly

DEVELOPMENT OF THE CONCEPT

The concept of isostasy came in the mind of geologists but the concept grew out of attraction of giant mountainous masses (Fig-1).

Pierre Bouguer during his expedition of the Andes in 1735-45 found that the towering volcanic peak of Chimborazo was not attracting the plumb line, as it should have done. He thus maintained that the gravitational attraction of the Andes ‘is much smaller than that to be expected from the mass represented by these mountains’. Similar discrepancies were noted during the geodetic survey of the Indo-Gangetic plain for the determination of latitudes under the supervision of Sir, George Everest, the then Surveyor General of India in 1859. The difference of latitude of Kalianpur and Kaliana (370 miles apart) was determined by both direct triangulation method and astronomical method.

Fig-1: Deflection of plum bob due to gravity

Kaliana was only 96 km away from the Himalayas. The difference between two results amounted to 5.23 seconds as given bellow:

    Result obtained through triangulation= 5° 23’ 42.294”.

Result obtained through astronomical method = 5° 23’37.058”.

Difference= 5.236”

This discrepancy between two methods was attributed to the less attraction of the Himalayas due to which the plumb bob used in the astronomical determination of latitude was deflected. There are many theories to explain the gravitational attraction and deflection and isostatic balance among the various landforms.

THE CONCEPT OF SIR GEORGE AIRY

According to Airy the inner part of the mountains cannot be hollow; rather the excess weight of the mountains is compensated (balanced) by lighter materials below. According to him the crust of relatively lighter material is floating in the substratum of denser material. In other words, ‘sial’ is floating over ‘sima’.

Thus, the Himalayas are floating in denser glassy magma. According to Airy ‘the great mass of the Himalayas was not only a surface phenomenon – the lighter rocks of which they are composed do not merely rest on the level surface of denser material beneath, but, as a boat in water, sink into the denser material.

In other words, the Himalayas are floating in the denser magma with their maximum portion sunk in the magma in the same way as a boat floats in water with its maximum part sunk in the water. This concept in fact involves the principle of floatation.

For example, an iceberg floats in water in such a way that for every one part to be above water level, nine parts of the iceberg remain below water level. If we assume the average density of the crust and the substratum to be 2.67 and 3.0 respectively, for every one part of the crust to remain above the substratum, nine parts of the crust must be in the substratum.

In other words, the law of floatation demands that ‘the ratio of freeboard to draught is 1 to 9. It may be pointed out that Airy did not mention the example of the floatation of iceberg. He simply maintained that the crustal parts (landmasses) were floating, like a boat, in the magma of the substratum.

It we apply the law of floatation, as stated above, in the case of the concept of Airy, then we have to assume that for the 8,848 meters height of the Himalaya there must be a root, 9 times more in length than the height of the Himalaya, in the substratum. Thus, for 8,848 m part of the Himalaya above, there must be downward projection of lighter material beneath the mountain reaching a depth of 79,632m (roughly 80,000 m).

Joly applied the principle of floatation for the crust of the Earth taking the freeboard to draught ratio as 1 to 8. According to him ‘for every emergent part of the crust above the upper level of the substratum there are eight parts submerged’. If we apply Joly’s view of floatation to the concept of Airy, there would be downward projection of the Himalaya up to a depth of 70,784m (8848m x 8) in the substratum.

Thus, according to Airy the Himalayas were exerting their real attractional force because there existed a long root of lighter material in the substratum which compensated the material above. Based on above observation Airy postulated that ‘if the land column above the substratum is larger, its greater part would be submerged in the substratum and if the land column is lower, its smaller part would be submerged in the substratum.’ According to Airy, the density of different columns of the land (e.g. mountains, plateaux, plains etc.) remains the same. In other words, density does not change with depth, that is, ‘uniform density with varying thickness’ .(fig. -2).

This means that the continents are made of rocks having uniform density but their thickness or length varies from place to place. In order to prove this concept Airy took several pieces of iron of varying lengths and put them in a basin full of mercury. These pieces of iron sunk up to varying depths depending on their lengths. The same pattern may be demonstrated by taking wooden pieces of varying lengths. If we put them into the basin of water these would sink in the water according to their Fig- 2: Model of Isostasy of Airy lengths (Fig-2).

Fig- 2: Model of Isostasy of Airy lengths (Fig-2).

Though the concept of Sir George Airy commands great respect among the scientific community but it also suffers from certain defects and errors. If we accept the Airy’s views of isostasy, then every upstanding part must have a root below in accordance with its height.

Thus, the Himalayas would have a root equivalent to 79,632m (if we accept the freeboard to draught ratio as 1 to 9) or 70,784m (if the freeboard to draught ratio is taken as 1 to 8). It would be wrong to assume that the Himalaya would have a downward projection of root of lighter material beneath the mountain reaching such a great depth of 79,634m or 70,784m because such a long root, even if accepted, would melt due to very high temperature prevailing there (as temperature increases with increasing depth at the rate of 1°c per 32m).

So, there are some alternative models (Fig-3) to explain the isostatic adjustment of the landforms of the Earth’s surface and related gravitational deflection.

THE CONCEPT OF ARCHDEACON PRATT

While studying the difference of gravitational deflection of 5.236 seconds during the geodetic survey of Kaliana and Kalianpur, Archdeacon Pratt calculated the gravitational force of the Himalaya after taking the average density of the Himalaya as 2.75 and came to know that the difference should have been 15.885 seconds. Paratt said that “In order to measure angle to a star a surveyor must determine the horizontal plane if horizontal plane between two sites were askew so must be the vertical direction”.

    He, then, studied the rocks (and their densities) of the Himalaya and neighbouring plains and found that the density of each higher part is less than a lower part. In other words, the density of mountains is less than the density of plateau, that of plateau is less than the density of plain and the density of plain is less than the density of oceanic floor and so on. This means that there is inverse relationship between the height of the reliefs and density.

According to Pratt there is a level of compensation above which there is variation in the density of different columns of land but there is no change in density below this level. Density does not change within one column but it changes from one column to other columns above the level of compensation.

‘Fig- 4: Line of Compensation

Thus, the central theme of the concept of Pratt on isostasy may be expressed as ‘uniform depth with varying density’. According to Pratt equal surface area must underlie equal mass along the line of compensation. This statement may be explained with an example (Fig-4).

There are two columns, A and B, along the line of compensation. Both the columns, A and B, have equal surface area but there is difference in their height. Both the columns must have equal mass along the line of compensation, so the density of column A should be less than the density of column B so that the weight of both the columns become equal along the line of compensation.

Thus, Pratt’s concept of inverse relationship between the height of different columns and their respective densities may be expressed in the following manner- ‘bigger the column lesser the density and smaller the column, greater the density.’ According to Pratt density varies only in the lithosphere and not in the pyrosphere and barysphere

Thus,  Pratt’s  concept  of isostasy was related to the ‘law of compensation’ and NOT to ‘the law of floatation.’ According to Pratt different relief features are standing only because of the fact that their respective mass is equal along the line of compensation because of their varying densities. This concept may be explained with the help of an example (Fig- 5 ).

Bowie has opined that though Pratt does not believe in the law of floatation, as stated by Sir George Airy but if we look, minutely, into the concept of Pratt we certainly find the glimpse of law of floatation indirectly. Similarly, though Pratt does not believe directly in the concept of ‘root formation’ but very close perusal of his concept on isostasy, does indicate the glimpse of such idea (root formation) indirectly.

While making a comparative analysis of the views of Airy and Pratt on isostasy Bowie has observed that ‘the fundamental difference between Airy’s and Pratt’s views is that the former postulated a uniform density with varying thickness, and the latter a uniform depth with varying density (Steers,1937). Fig-3 explains the fundamental difference between the concepts of Airy and Pratt on isostasy.

THE CONCEPT OF HAYFORD AND BOWIE

Hayford and Bowie have propounded their concepts of isostasy almost similar to the  concept  of  Pratt.  According  to  them  there  is  a  plane  where  there  is  complete compensation of the crustal parts. Densities vary with elevations of columns of crustal parts above this plane of compensation.

The density of the mountains is less than the ocean floor. In other words, the crus is composed of lighter material under the mountains than under the floor of the oceans.

There is such a zone below the plane of compensation where density is uniform in lateral direction.

Thus, according to Hayford and Bowie there is inverse relationship between the height of columns of the crust and their respective densities (as assumed by Pratt) above the line of compensation. The plane of compensation (level of compensation) is supposedly located at the depth of about 100 km. The columns having the rocks of lesser density stand higher than the columns having the rocks of higher density. This statement may be understood with the help of fig. 6.

There are four imaginary columns (interior plain, plateau, coastal plain and offshore region) which reach at the level of compensation. Their height varies but they are balanced by their varying densities. ‘The assumption is that the varying volume of matter in the several columns is compensated by their density, in such a fashion that they exert equal downward pressure at the level of compensation and thus balance one another’

Below given figure explains the above concept. It is apparent from fig. 6. that different columns of equal cross-section cut from various metals and ores having varying densities are seen floating in a basin of mercury but all of them reach the same line (level of compensation) and thus exert equal weight along the line of compensation.

Fig-6: The Concept of Isostasy given by Hayford and Bowie

Bowie made a comparative study of the views of Airy and Pratt on isostasy and concluded that there was a great deal of similarity in their views. In fact, ‘both the views appeared to him similar but not the same.’

Bowie could observe a glimpse of the concept of root formation and law of floatation of Airy, though indirectly, in the views of Pratt. The concept of Hayford and Bowie, that the crustal parts (various reliefs) are in the form of vertical columns, is not tenable because the crustal features are found in the form of horizontal layers.

THE CONCEPT OF JOLLY

Joly, presented his views on isostasy in the year 1925. He disapproved the view of Hayford and Bowie about the existence of level of compensation at the depth of about 100 km on the ground that the temperature at this depth would be so high that it would cause complete liquefaction and thus level of compensation would not be possible.

He further refuted the concept of Hayford and Bowie that ‘density varies above the level of compensation but remains uniform below the level of compensation’ on the ground that such condition would not be possible in practice because such condition would be easily disturbed by the geological events and thus the level of compensation would be disturbed.

According to Joly there exists a layer of 10-mile (16 km) thickness below a shell of uniform density. The density varies in this zone of 10-mile thickness. It, thus, Joly assumed the level of compensation as not a linear phenomenon but a zonal phenom-enon. In other words, he did not believe in a ‘line (level) of compensation’ rather he believed in a ‘zone of compensation’ (of 10-mile thickness)

Thus, we also find a glimpse of the law of floatation (it may be noted that Joly did not mention this, we only infer the idea of floatation from Joly’s concept) and his concept is closer to the Airy’s concept rather than the concept of Hayford and
Bowie.

‘This is in close agreement with floatation idea; the areas of low density in the 10-inile layer correspond with downward projections of the light continental crust, while those of high density represent the intervening areas filled with material of the heavier under-stratum’ (Fig-7).

References

• Singh Savindra.2012: Geomorphology,  Arti Printers, Allahabad.
• Khullar .D.R.2011: Physical Geography, Kalyani Publishers, Noida.
• J.A. Steers, 1937, Unstable Earth, Kalyani Publisher pp-74-75