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What is isostasy? What are the unusual gravity measurements? What are the models of isostasy? Is the Himalayas under isostatic equilibrium? What are the isostatic effects of sedimentation and erosion? What is gravity? How is gravity measured? Written by: LEE Boon­ying 1. What is isostasy? Models of isostasy were proposed more than a century ago to explain unusual gravity
measurements (what is gravity? how is it measured?) made in various parts of the Earth. The
concept of isostasy is that mountains are compensated by masses of smaller density under the
mountains while oceans are compensated by masses of higher density under the water. Viewed in this way, isostasy is simply based on Archimedes' principle ­­­ an immersed object
experiences a buoyant force equal to the weight of the displaced fluid. Back to content 2. What are the unusual gravity measurements? The unusual gravity measurements mentioned above are normally referred to as 'gravity anomalies'. Simply put, it is the difference between a gravity measurement (corrected for various factors) and
the theoretical value. Figure 1 shows plots of the gravity anomaly respectively over the mid­Atlantic ridge, the European
Alps, and the continental margins of southeast Australia. Strikingly, these plots indicate that over the
oceans the anomaly is strongly positive, increasing in magnitude with depth, while over highly
elevated terrain it becomes markedly negative. Figure 1 Back to content 3. What are the models of isostasy? There are several models based on different assumptions regarding the compensation mentioned
under the first question above. The two most commonly mentioned models are:­ (a) Airy's model ­­­ the crust is of variable thickness but of constant density and is thicker under
elevated terrain than under depressions such as oceans. The depth of the underlying 'roots' is
related to the height of the overlying topography. (b) Pratt's model ­­­ the crust is of variable density but its base is at a constant depth below sea
level. Topographic height is related to the crustal density at that point. Figure 2 presents schematic diagrams for the two models. Figure 2 Airy (left) and Pratt (right) models of isostasy [Source ­ Wikipedia] While both models are based on assumptions that are not too realistic, they describe amazingly well
the gravity observed over regions of variable terrain, which indicates that the isostasy concept is
obeyed over much of the world. Back to content 4. Is the Himalayas under isostatic equilibrium? No. Isostasy can only explain part of the rise of the Himalayas. Scientists are still figuring this out. Some propose that the Himalayas is being constantly pushed to ever greater heights by the
northward movement of the Indian Plate (see here). Back to content 5. What are the isostatic effects of sedimentation and erosion? Where sedimentation occurs, the weight of the sediment may cause the crust below to sink. Similarly, where erosion occurs the crust may rebound. Likewise, when ice sheets form the crust may sink. Conversely, when they melt the crust may
rebound, such as what is happening around the Baltic Sea and Hudson Bay area of Canada. Specifically, Scandinavia and Scotland were under more than 300 metres of ice during the ice
ages, and uplift is fastest in the northern Baltic where it is still going on at a rate of about a metre a
century, i.e. roughly one centimetre per year. Like a seesaw, with less burden of ice on the other
side of the landmass, southern Baltic and southern England are now sinking. [Unfortunately, climate
change makes things worse ­­­ global warming makes the oceans warmer, which raises the sea
level due to thermal expansion. Furthermore, the oceans are receiving more and more water from
melting glaciers. Both factors cause the sea level to rise.] Back to content 6. What is gravity? Objects attract one another, for example the attraction between the Sun and the Earth, and that
between the Earth and an object on the Earth's surface. On the Earth's surface, there is another
force, the centrifugal force, which arises from the Earth's diurnal rotation. Gravity is the combined
effect of the attraction (which we call gravitation) and centrifugal forces. Figure 3 (The ellipsoidal shape of the Earth is exaggerated to illustrate the forces.) Many of us are aware that the acceleration due to the Earth's gravity, g, is about 9.8 m/s2. It varies
with latitude and elevation. For instance, the centrifugal force mentioned above is at a maximum at
the equator, acts in the opposite direction and is about 1/3% of the gravitational attraction. Also, g
changes with elevation at a rate of about 3.1 x 10­6/s2. Gravity also varies from place to place on the Earth's surface, reflecting the uneven distribution of
mass in the Earth's crust and mantle. There are also small short­term changes due to the changing
attraction of the Sun and Moon. Back to content 7. How is gravity measured? Gravity can be measured with a pendulum since the period of a pendulum depends only on its length
and on gravity. Gravity is therefore the measurement of a time interval and of length ­­­ the period of
the pendulum and its effective length. There are other less common methods, e.g. by timing a free­
falling object. The above refers to absolute measurement of gravity. Gravity can also be measured in a relative
manner using gravimeters, in which a weight is suspended from a coiled spring whose length
changes in proportion to a change in gravity. While they measure only changes in gravity,
gravimeters are more sensitive to small changes as well as simpler and faster to operate. For this
reason, most gravity measurements are made using gravimeters that measure the gravity relative to
a base station at which the absolute gravity has been measured. Compared with pendulum
apparatus, gravimeters are 3 or 4 orders of magnitude more precise. Figure 4 ­ a photo showing the gravity measurement points on the verandah of the Hong Kong Observatory 1883 Building. On record, the earliest gravity measurements at the Observatory were made in 1933­1935. Gravity is now routinely measured on board artificial satellites. Simply, as a satellite passes over a
gravity anomaly it is accelerated /decelerated in its orbit. While the anomaly itself may be relatively
small, the cumulative acceleration/deceleration of the satellite during successive passes becomes
measurable. Back to content Reference: 1. Wikipedia. 2. "Does anything eat wasps", New Scientist, Profile Books, p.158, 2005. 3. "The Cambridge Encyclopedia of Earth Sciences", D.G. Smiths, Cambridge University Press, 1981.