Isostacy, Archimeds Principles, Airy Models, Pratt Models ....

1. Name : Manoj Govindrao More
Geophysics I’stYear,
SES, SRTMU Nanded
ISOSTACY
 Introduction :-
Isostasyis a fundamental conceptin the Geology. It is the idea that the
lighter crust must be floating on the denser underlying mantle. It is invoked to
explain how different topographic heights can exists on the Earth's surface.
Isostatic equilibrium is an ideal state where the crust and mantle would settle
into in absence of disturbing forces. The waxing and waning of ice sheets,
erosion, sedimentation, and extrusive volcanism are examples of processesthat
perturb isostasy. The physical properties of the lithosphere (the rocky shell that
forms Earth's exterior) are affected by the way the mantle and crust respond to
these perturbations. Therefore, understanding the dynamics of isostasy helps us
figure out more complex phenomena suchas mountain building, sedimentary
basin formation, the break-up of continents and the formation of new ocean
basins. When attempting to study isostasy, the first scientific principle one
needs to know is Archimedes’ Principle.
Archimedes’Principle. :- It is states that, as an object is partially submerged in
a fluid, the weight of the fluid that is displaced is equal to the weight reduction
of the object. When the weight of the object submerged exactly equalsthe
displaced fluid, the object floats.

2.  Theory :-
This conceptcan be then applied to the Earth. The asthenosphere acts fluidly
and the lithosphere is a rigid bodythat floats on top. The lithosphere is in
isostatic equilibrium, therefore, the mass of the asthenosphere (fluid) displaced
equals the mass of the floating lithosphere (solid). This means that the
asthenosphere under two different isostatic blocks will be at the same pressure.
This allows you to calculate the effects of isostasy due to an increase or
decrease of weight on the surface due to erosion or deposition.
There are two primary models for isostasy.
1) Pratt Model
2) Airy Model
Both the Pratt and Airy models are about local isostasy. There is no rigidity
because any load is perfectly compensated. Both are end member models and
there are others possible. The main difference between the two models is that in
the Airy model all blocks have the same densities but different thicknesses,
whereas in the Pratt model all blocks have different densities but float to the
same depth. Generally speaking though, the Airy model is used for continental
topography, especially mountain ranges; and the Pratt model is used for mid-
ocean ridges. Continental mountain ranges have thick crustal roots which are
more easily explained using the Airy model. In the Airy model, the elevation is
proportional to this root. The higher the elevation is, the thicker the block and
root.
At mid ocean ridges the topography is supported by density changes. This is
due to increased temperature at the ridges which causes the rocks to expand
resulting in a lower density. According to the Pratt model, all blocks float at the
same depth. This depth is where the asthenosphere begins. The difference in
elevations is due to the density of the rocks. Higher elevations indicate lower
density rocks and this higher ground means the lithosphere is thicker. The
compensation depth is always the same in the Pratt model. The height equation
is the same for both models. Below, figure #1 shows the Airy model and figure
#2 shows the Pratt model.

3. The asthenosphere under two different isostatic blocks will be at an equal
pressure. This is due to the fact that the asthenosphere acts fluidly, and a liquid
will flow from high to low pressure. This allows us to calculate the effects of
the isostatic compensation between two blocks. For them to be in isostatic
equilibrium, the pressure at the compensation depth (the bottomof the deepest
lithosphere) must be equal. To calculate the effects of isostasy, it is necessary to
create a height equation, as well as a weight equation. In order to do this you
have to set up two blocks showing both the height and weight. For the height
equation, the distance from the upper to lower level is the same. Likewise, for
the weight equation the weight of the blocks is the same from the upper to lower
level. If this were not true the pressure in the asthenosphere would be different.
Neither model can be applied over a regional scale. Over large expanses the
plate acts elastically. When a weight is added in the center of a plate, it causes a
flexural bulge to form around it. For example mountain chains are areas of
thickened crust and they cause the land around them to sink. This often leads to
the formation of sedimentary basins on the edge of the highlands where
sediments eroded off of the mountain settle in the basin.

4.  Question:-
Why Himalaya have thicker crust ?
 Answer :-
According to Airy model of isostacy, Continental mountain ranges have thick
crustal roots which are more easily explained using the Airy model. In the Airy
model, the elevation is proportional to this root. The higher the elevation is, the
thicker the block and root. Therefore the Himalaya have highest elevation (7200
metres). So, the higher the elevation is, the thicker crust.
 References :-
 Guidance :
Mr. SKG Krishnamacharyulu Sir, Mr. TVK Sir
 Ref. book:
A. B. Watts, Isostasyand Flexure of the Lithosphere (Cambridge, 2001)
 Ref. link :
https://www.britannica.com/science/isostasy-geology
https://www.youtube.com/watch?v=ybd17tx4Tz4