3.3 Isostasy and its applications

Isostasy explains how Earth's crust floats on the mantle, balancing weight and buoyancy. This concept is crucial for understanding gravity anomalies, crustal thickness variations, and vertical motions of the Earth's surface.

Geophysicists use different models to describe isostasy, including Airy, Pratt, and flexural approaches. These models help interpret gravity data, estimate crustal properties, and unravel the Earth's dynamic processes like mountain building and basin formation.

Isostasy: Concept and Principles

Isostatic Equilibrium and Compensation

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• Isostasy is the state of gravitational equilibrium between Earth's crust and mantle where the crust "floats" on the mantle according to its density and thickness
• The principle of isostasy states that the Earth's crust is in a state of buoyant equilibrium, with the lighter crust floating on the denser mantle, similar to the way an iceberg floats on water
• Isostatic equilibrium is achieved when the weight of the crust is balanced by the buoyancy force provided by the mantle, resulting in no net vertical force acting on the crust
• The depth at which isostatic equilibrium occurs is called the depth of compensation, which varies depending on the crustal thickness and density (Moho discontinuity)

Isostatic Adjustments and Disturbances

• Isostatic adjustments occur when the equilibrium is disturbed by processes such as erosion, deposition, glaciation, or deglaciation, causing the crust to rise or sink to restore the balance
• Examples of isostatic adjustments include post-glacial rebound after the melting of ice sheets (Scandinavia, Canada) and the subsidence of sedimentary basins due to the weight of accumulated sediments (Gulf Coast, North Sea)
• Isostatic disturbances can also be caused by tectonic processes such as mountain building (Himalayas, Andes) or the emplacement of dense igneous intrusions (Bushveld Complex, South Africa)
• The timescale of isostatic adjustments depends on the viscosity of the mantle and the size of the disturbance, ranging from thousands to millions of years

Models of Isostasy

Airy and Pratt Isostatic Models

• The Airy isostatic model assumes that the crust has a uniform density and that variations in crustal thickness are compensated by changes in the depth of the crust-mantle boundary (Moho)
  • In the Airy model, mountains have thicker crustal roots extending into the mantle, while oceanic crust is thinner
  • Examples of regions where the Airy model applies include the Himalayan Mountains and the Andes Mountains
• The Pratt isostatic model assumes that the crust has a uniform thickness but varies in density, with less dense crust underlying mountains and denser crust underlying lowlands and oceans
  • In the Pratt model, the density of the crust varies laterally to maintain isostatic equilibrium
  • Examples of regions where the Pratt model applies include the Basin and Range Province in the western United States and the East African Rift System

Flexural Isostatic Model and Combined Approaches

• The Vening Meinesz (flexural) isostatic model considers the crust as an elastic plate that can bend and flex under the weight of surface loads, such as mountains or ice sheets
  • The flexural model accounts for the strength and rigidity of the lithosphere, which can support some degree of non-isostatic loading
  • Examples of regions where the flexural model applies include the Hawaiian Islands and the Fennoscandian Shield
• In reality, the Earth's isostatic behavior is a combination of these models, with the relative importance of each model varying depending on the geological setting and the spatial scale considered
  • Combined approaches, such as the Airy-Heiskanen and Pratt-Hayford models, incorporate elements of both the Airy and Pratt models to better represent the Earth's isostatic behavior
  • The choice of the appropriate isostatic model depends on factors such as the tectonic setting, the age and composition of the crust, and the availability of geophysical data

Isostasy and Gravity Anomalies

Gravity Anomalies and Their Relationship to Isostasy

• Gravity anomalies are differences between the observed gravity and the expected gravity based on a reference model, such as the Earth's ellipsoid
• Isostatic compensation of the crust affects the distribution of mass and, consequently, the gravity field measured at the Earth's surface
• Positive gravity anomalies can indicate an excess of mass, such as dense rocks or uncompensated topography, while negative gravity anomalies can indicate a mass deficit, such as low-density rocks or overcompensated topography
• The relationship between isostasy and gravity anomalies allows geoscientists to infer the crustal structure and density variations in a region

Types of Gravity Anomalies and Their Calculation

• Free-air gravity anomalies are calculated by removing the effect of elevation (free-air correction) from the observed gravity, revealing the gravitational effect of the total mass beneath the observation point
• Bouguer gravity anomalies are calculated by removing the effect of topography (Bouguer correction) from the free-air anomaly, revealing the gravitational effect of the subsurface density variations
• Isostatic gravity anomalies are calculated by removing the effect of the assumed isostatic compensation model from the Bouguer anomaly, revealing the gravitational effect of any departures from the isostatic equilibrium
• The analysis of gravity anomalies can provide insights into the crustal structure, density variations, and the state of isostatic equilibrium in a given region
• Examples of regions with significant gravity anomalies include the Tibetan Plateau (positive free-air anomaly) and the Mid-Atlantic Ridge (negative Bouguer anomaly)

Applying Isostatic Principles

Crustal Thickness and Density Estimation

• Isostatic principles can be used to estimate the crustal thickness and density variations in a region, based on the observed topography and gravity anomalies
• By assuming an isostatic compensation model (Airy, Pratt, or flexural), geoscientists can calculate the expected crustal thickness and density distribution that would satisfy the isostatic equilibrium
• These estimates can be compared with seismic data (seismic refraction or receiver function analysis) to validate the isostatic models and refine the understanding of the crustal structure

Vertical Motions and Sedimentary Basin Evolution

• Isostatic compensation models can be used to predict the vertical motions of the crust in response to changes in surface loading, such as the rebound of the crust after the melting of ice sheets (post-glacial rebound)
  • Examples of regions experiencing post-glacial rebound include Scandinavia, Canada, and Antarctica
• Isostatic considerations are important in understanding the formation and evolution of sedimentary basins, as the weight of the sediments can cause the basin to subside and the surrounding areas to uplift
  • The subsidence of sedimentary basins due to sediment loading is called sedimentary isostasy, and it plays a crucial role in the accumulation and preservation of thick sedimentary sequences (Gulf Coast, North Sea)

Mountain Building and Geodynamic Modeling

• Isostatic principles can be applied to the study of mountain building processes (orogenesis), as the thickening of the crust during collision or compression can lead to isostatic uplift and the formation of high-elevation plateaus
  • Examples of mountain ranges formed by isostatic uplift include the Tibetan Plateau and the Altiplano-Puna Plateau in the Central Andes
• Understanding isostatic principles is crucial for geodynamic modeling, as it helps to constrain the forces and processes that control the evolution and deformation of the Earth's crust and lithosphere
  • Isostatic compensation is incorporated into numerical models of lithospheric deformation, such as thin-sheet models and finite element models, to simulate the long-term behavior of the crust under tectonic loading