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Is the deep earth rigid as a ‘steel ball’ or is it able to flow viscously like a ‘sea of lava’ ? What forces create the low standing oceans and the high standing continents ? What forces hold-up the mountains or conversely holds-down deep basins ?
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Is the deep earth rigid as a ‘steel ball’ or is it able to flow viscously like a ‘sea of lava’ ? • What forces create the low standing oceans and the high standing continents ? • What forces hold-up the mountains or conversely holds-down deep basins ? • What is the earth’s figure best represented as a sphere or a flattened ellipsoid ? • What causes the stranded shorelines Scandanavia (uplift evidence) ? • How does measured gravity relate to the mode of compensation of the earth surface? • How strong in compression/tension/shear is the earth’s crust and lithosphere ? • What are the rheologic laws that govern the deformation (stress/strain) of the shallow and deep portions of the planet ? Isostasy answers (?) these questions
Mis-conceptions about crust, lithosphere, asthenosphere* Crust (compositional). The crust is the residue from melting the mantle. Crustal thicknesses is 10 km (oceans) and 30-80 km (continents). Mantle (compositional). The mantle +crust+core = chondrite meteorites. Core (compositional). Made of liquid/solid iron mostly. Lithosphere (strength). Also, called a plate. The strong layer that slides over the asthensophere. The lithosphere is strong because it is colder. Asthenosphere (strength). The mantle just below the lithosphere is often weaker than the deeper mantle due to pressure and temperature effects. * IMHO, this chapter is sloppy in usage of crust, lithosphere, asthenosphere, (viscous) mantle terms.
How would gravity vary over small and large mountains ? 10 km 100 km Remember, a fundamental property of mass is that it has gravity (and inertia). So, the mass of the two mountains (above the level) will increase the gravity recorded by the gravimeter in the balloon. However, what is important is two questions: 1) is the crust strong enough to support the weight of a mountain ? 2) if the crust ‘breaks’, then what forces support the weight of the mountains? Note that mountains A has no change in density beneath the level, but mountain C has a ‘lower density root’ under it. In general, we’ll find that there are two end-member processes that support or compensate the weight of the mountains: the strength of the crust for small mountains, and a bouyant low density root beneath large mountains.
Earth model: an elastic lithosphere (crust), that does not flow (but does break), over a ‘fluid’ asthenosphere/mantle Historically, this earth model has vigorously debated from 1500 until 1930-1960. Some people said the earth’s interior was as strong as a steel ball. They were wrong! Other said, the earth’s interior was liquid. They were right (outer core) and wrong (mantle). The truth is that the mantle is 99.9% solid AND it does flow at 1-10 cm/yr (10-100 km/Ma) rates. This is called convection. It might take millions of years to move things around, but the earth is 4,500 million years old!
Local versus regional compensation • The Lithosphere (crust) is NOT strong enough to support the load (weight) of the mountain. In fact, in the limit, the lithosphere is broken on either side of the load and has a near zero strength. The load is supported by the hydrostatic pressure of the asthenosphere pushing on the bottom of the loaded block. • Gravity effect • Zero free air anomaly over load • Positive Bouguer anomaly over load • The Lithosphere (crust) is strong enough to support the load (weight) of the mountain. But, the lithospheric strength is finite and the surface of the lithosphere is bowed down ‘regionally’ to support the load. • Gravity effect • Positive free air anomaly over load • Zero Bouguer anomaly over load
Regional compensation of Hawaiian Island Chain Note the strong correlation between the topography and the free air gravity profile. This is because this topography is NOTisostatically compensated but ‘regional’ compensated by the strength of the lithosphere. Also, note the downwarps to either side of the big island caused by the load that down-flexes the lithosphere (see Fig. 9.10).
Volcanic loads vs. Seismic evidence Modelling gravity over Hawaiian Chain
what is a buoyancy force ? A buoyancy force arises when a solid block (boat, mountain) is placed into an (ideal)-liquid. The buoyancy force is specified by Archimede’s Principle which states: the decrease in weight of the block equals the weight of the liquid displaced by the submerged portion of the body. An ideal-liquid is simple in that the only force is transmits is pressure which means that an ideal-liquid CANNOT support any shear stresses. The pressure in a liquid is: P= depth * liquid-density * little-g (N/m2). The sign of the density contrast between the block and the liquid determines whether the block floats (block density less than liquid) or sinks (block density greater than liquid). Note that the weight of the block (a) decreases as the block is lower into the fluid (b) and when the block is floating (c) the effective weight becomes zero as the buoyancy force supports the weight of the block!. Note that the magnitude of the buoyancy force is equal to the weight of the liquid displaced that fills the jar.
Layered floating blocks and gravity Figure 9.3 shows two blocks with the same density that are floating in a liquid. Note that when a few layers of block (a) are removed, hence reducing the blocks height (mass), then the block floats at a new level to maintain isostatic equilibrium. Also, note that block (b) extends less above the liquid surface because there is LESS fluid volume displaced by the shorter block. One could also view this plot as adding layers (mass) to block (b) which causes block (a) to float with a higher surface above the liquid. Measuring gravity at points A,B,C finds no change in gravity! This is because the blocks are all in isostatic equilibrium which means that the total mass of the block and liquid beneath each blocks is the same! (I am missing a detail here, what is that?) Remember that the liquid must be denser than the blocks for the blocks to float. Therefore, the shallower depth of the liquid under block (b) adds mass to this column to make it the same as block (c).
Deriving the isostatic mass and height equations To calculate the isostatic balance between two blocks (A and B), the height and weight (force) equations must be derived. To do this, first the upper-level and lower-level must be defined. We assume that the atmosphere is always at the top of each block and that its weight, hence density, is negligible (assume zero). One must always choose the upper-level to be ABOVE the top of either block! For the lower-level, one must always choose this depth to be at the base of the deepest block. We also assume that the asthenospheric ‘fluid’ (that the blocks float in) is at the base of each block.
Specifying the height and weight equations The Weight and Height equations are defined as: We know have two equations and two unknows that can be solved algebraically.
Example: add 2 km ice to top of block To the left block two km of ice are added. This causes the bottom of the block to sink into asthenosphere by ha (km) as shown by the right side block. Given that 2 km of ice cause the block to sink .56 km, then the former air/sediment surface sank by 2-0.56 = 1.44 km. The height equation gives this result formally.
Isostasy of filling a lake with sediment Notice there are two unknowns in this problem: the thickness of the new sediments (hs) and the amount the block sinks into the asthenosphere (ha ). Amazing! Due to isostasy the 2 km lake filled with 3.14 km of sediment.
Airy and Pratt end-member isostasy models This was a big debate in 1855 after a British gravity/geodetic survey in Indian. Mr. Pratt suggested that mountains do NOT have roots but instead the topography is compensated by a less dense (hence lighter) block. And, that all topography was compensated at the same depth. Mr. Airy suggested that mountains had thick low density roots supporting mountains and that the depth of compensation was NOT constant!
Who was correct ? Airy was mostly correct about what supports large (wide) mountains, but it took until the 1970’s to prove this with seismic work that measured the thickness of the crust and lithosphere beneath mountains. Pratt was correct in that the difference between the low standing ocean basins and the high standing continents is partially due to the fact that oceans have dense gabbroic composition crust whereas continents have lighter ‘Andesitic’ composition crust.
Free-air/Bouguer/Airy-isostatic gravity with and without compensation Important is to WHY the gravity effects of the two mass anomalies makes the above table is true. What happens if I remove the area above the red line from the blocks ?
Glacial isostatic adjustment UM viscosity
Water height in oceans is proportional to gravity field By radar mapping the ocean surface, the gravity field is being measured (also current pressures).
Figure of the earth • Terms to know: • Spherical radius • Equatorial radius • Polar radius • Reference ellipsoid • Geoid (Grav. Potential) • None-spherical shape makes (and spin) make the gravity vary as IGF. • Knowing that the earth rotates once a day around its spin axis. • Why is the Earth a flattened ellipsoid?
Isostasy quotes (1) That part of the surface of any heavy body will become more distant from the centre of its gravity which becomes of greater lightness. The earth therefore, the element by which the rivers carry away the slopes of mountains and bear them to the sea, is the place from which gravity is removed: it will make itself lighter……The summits of the mountains in course of time rise continually (da Vinci, 1505). The mountains, I think, are to be explained chiefly as due to thermal expansion of material at depth, whereby the rock layes near the surface are lifted up. The uplifting does not mean the inflow or addition of material at depth, the void within the mountain compensates for the overlying mass (Boscovich, 1755). The state of the Earth’s crust lying upon the lava may be compared with perfect correctness to the state of a raft of timber floating upon water; in which, if we remark one log whose surface floats much higher than the upper surfaces of the others, we are certain that its lower surface lies deeper in the water than the lower surfaces of the others (Airy 1855). The amount of matter in any vertical column drawn from the surface to a level surface below the crust is now and ever has been, approximately the same in every part of the Earth (Pratt, 1861).
Isostasy quotes (2) The crust must be in a condition of approximate hydrostatical equilibrium, such that any considerable addition of load will cause any region to sink, or any considerable amount deduced off an area will cause it to rise……..the crust is analogous to the case of a broken-up area of ice, refrozen and floating upon water. (Fisher, 1881). The hypothesis (interior contraction by secular cooling) is nothing but a delusion and a snare, and the quicker it is thrown aside and abandoned, the better it will be for geological science (Dutton, 1882). In an unpublished paper I have used the terms isostatic and isostasy to express that condition of the terrestrial surface which follow from the floatation of the crust upon a liquid or highly plastic substratum…….isobaric would have been a preferable term, but it is preoccupied in hypsometry………….For this condition of equilibrium of figure, to which gravitation tends to reduce a planetary body, irrespective of whether it is homogeneous or not, I propose the name isostasy (Dutton 1882). An Airy theory is untenable……The Pratt theory is the only one so far that is sound……..It seems safe to assert that the teory of isostasy has been proven……….. (Bowie 1927). Convenience of computation, and perhaps tradition, rather than any physical probability, has been the chief reasons for the attention given to Pratt’s hypothesis, instead of Airy’s (Jeffreys 1926).
Isostasy quotes (3) Various geological observations and deductions, which the geologists regard as established facts (horizontal shortening), seems inconsistent with the isostatic theory (Chamberlin 1932). Geologists often ask too much of the principle of isostasy. When they find that it will not explain all earth movements, they think it is not a true principle (Reid 1922). Mountains, mountain ranges, and valleys of magnitude equivalent to mountains, exist generally in view of the rigidity of the Earth’s crust; continents and plateaus and oceanic basins exist in virtue of isostatic equilibrium in a crust heterogeneous wrt density (Gilbert 1889). The success of the isostatic hypothesis in reducing gravity anomalies is to show that isostatic adjustment in the earth’s crust is nearly perfect (Gilbert 1913). The excesses and deficits of mass……..will be a more accurate measure of the capacity of the rigid crust to carry without viscous yielding loads which have borne through geological time, hidden loads whose magnitudes in many regions appear to mask by contrast the present relief between mountains and valleys……….The deep zone is the hydraulic agent which converts the gravity of the excess matter in the heavy column into a force acting upwards against the lighter column….By this means even the continental interiors are kept in isostatic equilibrium with the distant ocean basins (Barrell 1914). No question that a mountain’s load is distributed beyond the area of its base (Putnam 1935).
Comparison of astronomic and geodetic determined latitude The keynote of isostasy is a working towards equilibrium. Isostasy is not a process that disturbs equilibrium, but one that restores equilibrium.
