Isostasy – Concept and Theories of Airy and Pratt

Isostasy is the state of gravitational equilibrium between Earth's crust (lithosphere) and mantle such that the crust "floats" at an elevation that depends on its thickness and density. Isostasy is a dynamic process. As the Earth changes, the crust and mantle must adjust to maintain equilibrium. For example, when glaciers melt, they remove weight from the crust. This causes the crust to rise. Conversely, when glaciers form, they add weight to the crust, causing it to sink. Isostasy can also be affected by tectonic activity, such as the formation of new mountains or the subduction of oceanic crust.

Development of the Isostasy Concept

Here are some of the key developments in the understanding of Isostasy:

 

v    1735: Pierre Bouguer measures the gravitational pull of the Andes Mountains and finds that it is weaker than expected.

v    1855: George Biddell Airy and John Henry Pratt propose two different hypotheses to explain Isostasy.

v    1882: American geologist Clarence Dutton coins the term "Isostasy."

v    1909: Finnish geodesist Weikko Aleksanteri Heiskanen refines Airy's hypothesis and proposes a new model of Isostasy.

v    1910: American geodesist John Fillmore Hayford refines Pratt's hypothesis and proposes a new model of Isostasy.

v    1960s: Geologists began to use gravity measurements to study Isostasy in more detail.

v    1970s: The theory of plate tectonics is developed, which provides a new framework for understanding Isostasy.

 

The basic principle of Isostasy is that the lithosphere will adjust its elevation to achieve equilibrium, much like how a floating object in a fluid will adjust its position to balance its weight and buoyancy. Here's how it works:

 

1. Crustal Thickness: Different regions of the Earth's crust have varying thicknesses due to geological processes such as mountain building, erosion, and deposition.
2. Buoyancy: The lithosphere, including the Earth's crust and a portion of the uppermost mantle, is less dense than the underlying asthenosphere. This buoyant force is what allows the lithosphere to float on the asthenosphere.
3. Isostatic Adjustment: When there is an imbalance in the distribution of mass within the lithosphere (e.g., due to the addition or removal of material through processes like erosion, sedimentation, or tectonic activity), the lithosphere will adjust its elevation to achieve a state of equilibrium. Thicker regions of the crust will "float" higher; while thinner regions will "sink" lower.

 

Theory of George Airy

 

George Biddell Airy, a prominent English mathematician and astronomer, made significant contributions to the theory of Isostasy in the mid-19th century. His work laid the groundwork for our modern understanding of Isostasy and how it relates to the Earth's crust and mantle. Here's a summary of George Airy's theory of Isostasy:

George Airy's theory of isostasy, which he proposed in 1855, is based on the following

 

Assumptions:

 

Ø    The Earth's crust is a rigid shell that floats on a denser mantle.

Ø    The crust has a uniform density throughout.

Ø    The crust and mantle are in Isostatic equilibrium, meaning that the upward buoyant force of the crust is balanced by the downward force of gravity.

 

This means that columns of crust and mantle with the same area have the same mass, regardless of their elevation. This is why mountains have deep roots that extend into the mantle. The roots of the mountains help to compensate for the weight of the mountain range above.

 

Key Points of Airy’s Concept:

 

1. Floating Crust: Airy proposed that the Earth's crust, composed of lighter rocks (often referred to as "sial" - from silicon and aluminium), floats on a denser, semi-fluid layer of material (referred to as "sima" - from silicon and magnesium) in the Earth's mantle.
2. Compensation: Airy's theory included the idea of compensation, where variations in the thickness of the Earth's crust would be compensated for by differences in the depth of the crust's roots into the denser mantle. Thicker crustal regions would have deeper roots.
3. Isostatic Equilibrium: Airy suggested that the Earth's crust is in a state of Isostatic equilibrium when the weight of the crust is balanced by the buoyant force from the mantle. This equilibrium results in the stability of the crust.
4. Application of Floatation Principle: Airy likened the concept of Isostasy to the principle of floatation, where objects in a fluid will displace an amount of fluid equal to their own weight. This analogy helped to explain the concept of crustal roots.
5. Density Considerations: Airy assumed that the density of different columns of the Earth's crust remains the same, even though their thickness or length may vary. This concept was used to explain how different landforms like mountains, plateaus, and plains are supported by underlying mantle material.

FIGURE: Isostatic balance. (A) Wood blocks float in water with most of their bulk submerged.  (B) The lithosphere “floats” on the asthenospheric mantle in approximately the same way. The thicker the block, the deeper it extends into the asthenosphere. (Carlson et al.)

 

Significant Aspects of Airy's Theory:

 

1. Foundation of Isostasy: Airy's theory laid the foundation for the concept of isostasy, which remains a fundamental principle in geology and geophysics. It provided an early framework for understanding the equilibrium and balance of the Earth's lithosphere and its relationship with the underlying mantle.
2. Compensation and Crustal Roots: Airy introduced the idea of compensation, explaining how thicker crustal regions have deeper roots into the mantle, and thinner regions have shallower roots. This concept helped explain variations in topography, including the existence of mountains and their deep roots.
3. Analogies for Understanding: Airy used analogies like the principle of floatation to make complex geological concepts more accessible to a broader audience. This made his ideas easier to grasp and communicate.

 

Drawbacks and Limitations of Airy's Theory:

 

1. Simplistic Assumptions: Airy's theory made simplifying assumptions that do not fully reflect the complexity of the Earth's crust and mantle. For example, it assumed uniform density throughout the crust, which is not the case in reality.
2. Neglect of Mantle Rheology: Airy's theory did not consider the viscosity or flow properties of the mantle, which we now know to be important factors in understanding the behaviour of the lithosphere. Modern Isostatic models incorporate mantle viscosity and flow.
3. Temperature Considerations: Airy's theory did not account for the increase in temperature with depth in the Earth's mantle. At the extreme depths proposed for some crustal roots (e.g., Himalayas), the temperatures would be too high for the maintenance of solid rock, leading to melting.
4. Variability of Crustal Composition: Airy's theory assumed that the entire crust had uniform density. In reality, the composition of the Earth's crust varies, with different types of rocks having different densities.
5. Simplified Geophysical Models: Airy's theory was developed before the advent of modern geophysical techniques such as seismic imaging and gravity measurements. These techniques have provided more accurate data about the Earth's interior, allowing for the development of more sophisticated models.

 

In summary, while George Biddell Airy's theory of Isostasy was a significant step forward in understanding the Earth's lithosphere and its relationship with the mantle, it had limitations due to its simplifications and the lack of comprehensive geophysical data available during his time. Modern Isostatic models have built upon his foundational ideas while incorporating a more nuanced understanding of geological and geophysical processes, such as mantle rheology, temperature gradients, and variations in crustal composition.

 

Theory of Archdeacon Pratt 

 

Pratt's theory of Isostasy is a model that explains the vertical movements of the Earth's crust based on the concept of compensation. According to this theory, the Earth's crust floats on a more dense mantle, and the weight of the crust is balanced by the buoyant force of the mantle. This balance is known as Isostasy.

ASSUMPTION

Here is a brief overview of each assumption:

 

v     Local Compensation: Pratt assumed that Isostatic compensation occurs within relatively small regions, typically on the order of tens to hundreds of kilometers. This is in contrast to the global compensation model proposed by Airy.

v     Floatation Principle: Pratt envisioned the lithosphere as floating on the denser asthenosphere, much like an iceberg floats on water. This is a key assumption of all theories of Isostasy.

v     Airy's Principle of Isostasy: Pratt adopted Airy's principle that the depth of compensation is proportional to the height of the topography above sea level. This means that taller mountains have deeper roots than lower mountains.

v     Rigidity of the Lithosphere: Pratt assumed that the lithosphere is a rigid plate that behaves elastically in response to loading and unloading. This assumption has been challenged by more recent research, which suggests that the lithosphere is more viscoelastic in nature.

v     Continental Crust vs. Oceanic Crust: Pratt recognized that continental crust is less dense than oceanic crust. He attributed this difference in density to the presence of thicker, more buoyant continental roots.

  

Key Points of His Theory:

 

1. Gravitational Deflection: Pratt's theory originated from his observation of a significant difference in the gravitational deflection (the angle at which a plumb line deviates from the vertical due to gravity) during a geodetic survey in the Kaliana and Kalianpur regions.
2. Density Variation with Height: Pratt noticed that the density of the Earth's materials varied with height above the Earth's surface. He found that in general, the density of the rocks and materials decreased as you moved from the Earth's surface to higher elevations. This led him to conclude that there is an inverse relationship between the height of geological features (like mountains, plateaus, and plains) and their respective densities.
3. Compensation Level: Pratt introduced the concept of a "level of compensation." Above this level, there is variation in the density of different geological columns, but there is no change in density below this level. In other words, density remains relatively constant within a single geological column but changes when you move to different columns above the compensation level.
4. Uniform Depth with Varying Density: Pratt's central idea can be summarized as "uniform depth with varying density." He believed that equal surface areas should underlie equal masses along the line of compensation. This means that if two geological columns have equal surface areas but different heights, the density of the taller column should be less than the density of the shorter one to balance out their masses along the "line of compensation".
5. Not the Law of Floatation: Pratt's concept of Isostasy is related to the "law of compensation" rather than the "law of floatation." In other words, geological features, such as mountains or plateaus, are supported because their masses are equal along the line of compensation, even though their densities may vary.
6. Comparison with Airy's Theory: Pratt's theory differs from Sir George Airy's theory of Isostasy. Airy's theory postulated a uniform density with varying thickness of geological features, while Pratt proposed a uniform depth with varying density.

 Pratt's theory of Isostasy is supported by a variety of evidence, including:

 

v     The observation that mountains have roots that extend deep into the Earth's mantle.

v     The observation that the Earth's crust rebounds after being unloaded, such as when a glacier melts.

v     The observation that the Earth's crust subsides when loaded, such as when a large ice sheet forms.

 

Pratt's theory of Isostasy is an important concept in geology, and it helps us to understand the dynamic nature of the Earth's crust.

 

Significance:

 

1. Understanding Earth's Structure: Pratt's theory played a crucial role in advancing our understanding of the Earth's internal structure. It provided insights into how mass is distributed within the lithosphere and how it affects the gravitational field of the Earth.
2. Explanation of Topographic Features: The theory explains why different geological features, such as mountains, plateaus, and plains, can exist and be supported. It helps clarify how the Earth's crust and upper mantle adjust to these variations in mass.
3. Geodetic Applications: Pratt's concept of Isostasy has practical applications in geodesy, cartography, and surveying. It helps geodetic surveyors correct for the variations in gravity when making precise measurements of the Earth's surface.
4. Tectonic Processes: Isostasy is related to tectonic processes, as it helps explain the uplift and subsidence of landmasses over geological time scales. It contributes to our understanding of the dynamic nature of the Earth's crust.

 

Drawbacks and Limitations:

 

1. Simplification: Pratt's theory is a simplified model of the Earth's complex behaviour. It assumes that geological columns adjust to maintain equilibrium only along a single line of compensation, which might not be entirely accurate in some geological settings.
2. Ignores Some Factors: The theory primarily focuses on variations in density and assumes that the lithosphere behaves as a viscous fluid over long time scales. It doesn't consider other factors that can influence topography, such as variations in temperature or the presence of rigid structures in the mantle.
3. Inapplicability to All Geologic Settings: Pratt's concept of Isostasy is more suitable for explaining the behaviour of large-scale geological features like mountain ranges and plateaus. It may not be as applicable to smaller-scale features or regions with complex geological histories.
4. Not a Complete Model: While Pratt's theory is a valuable concept, it is not a complete model for understanding the Earth's complex geodynamic processes. Modern geophysics incorporates additional factors, such as plate tectonics, mantle convection, and seismic data, to provide a more comprehensive picture of Earth's behaviour.

 

In summary, Archdeacon Pratt's theory of Isostasy has had a significant impact on our understanding of the Earth's structure and the distribution of mass beneath its surface. It is a useful concept in geology and geophysics, particularly for explaining the support and equilibrium of geological features. However, it is essential to recognize its limitations and consider more comprehensive models when studying complex geological phenomena.

What is Isostatic Adjustment?

 

Isostatic adjustment is the process by which the Earth's crust rises and falls in response to changes in the weight above it. This can be caused by a variety of factors, such as the melting of glaciers, the deposition of sediment, or the construction of large dams and reservoirs.

Isostatic adjustment is a very slow process, typically taking place over thousands to millions of years. However, it can have a significant impact on the landscape over time. For example, the land in Scandinavia is still rising in response to the melting of the glaciers that covered the region during the last ice age.

Here are some examples of Isostatic adjustment:

 

◍     The land in Scandinavia is still rising in response to the melting of the glaciers that covered the region during the last ice age.

◍     The land in the Mississippi River Delta is sinking due to the weight of the sediment deposited by the river.

◍     The land around the Hoover Dam is sinking due to the weight of the water in the reservoir.

◍     The land in the Netherlands is subsiding due to the extraction of groundwater and natural gas.

◍     The land in the Arctic is sinking due to the loss of sea ice.

 

Isostatic adjustment is an important process that helps to maintain the Earth's balance. It is also a process that we need to be aware of in order to plan for the future and mitigate the risks associated with it.

Comparison between Airy's theory and Pratt's theory

 

Aspect	Airy's Theory	Pratt's Theory
Primary Focus	Uniform density with varying thickness of features	Uniform depth with varying densities of materials
Density Variation	Assumes constant density within geological columns	Assumes density varies with height above a level of compensation
Explanation of Support	Geological features supported by buoyancy	Geological features supported by equal mass along the line of compensation due to density variations
Compensation Depth	The depth at which the lithosphere achieves equilibrium	Depth at which density variations balance out mass
Application	Suitable for explaining variations in the thickness of the Earth's crust	Suitable for explaining variations in the density of geological materials
Relationship with Floatation	Directly related to the concept of buoyancy	Not directly related to the concept of buoyancy
Complexity	A simpler model, assumes a constant density	A more complex model, accounts for density variations
Limitations	Does not account for variations in material properties other than density	Assumes a single line of compensation, which may not be valid in all geological settings
Geological Features	Suitable for understanding mountain ranges and variations in crust thickness	Suitable for understanding the support and equilibrium of geological features with varying densities
Modern Usage	Still used in simplified geophysical models	Incorporated into more comprehensive models of Earth's structure and dynamics