Question

In: Civil Engineering

i. Explain structural components of continents in detail and summarize it in pictorial form ii. Why...

i. Explain structural components of continents in detail
and summarize it in pictorial form
ii. Why the earth has oblate spheroid shape? Explain in
detail

Solutions

Expert Solution

(1)First we will discuss about formation of continents and after that inner structure will be explained.

(1.1) Structure of continents
The surface of continents can be subdivided into several broad regions which were formed at
different times and by different tectonic processes. These broad regions are referred to as
tectonic provinces:
Shields lie at the heart of continents and are their oldest components. Shields are composed of
Precambrian crystalline rocks (metamorphic and igneous rocks). These rocks may have been
deformed during the Precambrian but remained undeformed during the Phanerozoic. Examples of
shields are the Canadian Shield, the African Shield, and the Australian Shield.
Platforms consist of sedimentary layers overlying the Precambrian basement and displaying
relatively minor deformations (e.g. North American Platform, Siberian Platform). Shields and
platforms consist of the most stable parts of continents called cratons. Cratons have not been
significantly affected by mountain building episodes (orogenies) during the Phanerozoic. However,
they may have experienced slow vertical movements due to mantle convection beneath the
lithosphere or to the growth and retreat of ice sheets . Large areas
can be uplifted due to heating by mantle upwelling beneath the lithosphere
. More locally,
magmatic intrusions migrating upward can warp the overlying rock layers. Circular regions of the
lithosphere which have been uplifted are called structural domes (e.g. Cincinnati Arch, USA;
Richat Dome, Mauritania). Rock layers in a structural dome dip away from its center. On the other
hand, regions of the lithosphere which cools and contracts are affected by subsidence and arecalled thermal subsidence basins where abundant sediments can accumulate (e.g. Michigan
Basin, USA; Amadeus Basin, Australia). Unlike domes, rock layers in a thermal subsidence basin
dip toward its center. Intracratonic basins are economically important because they contain large
reservoirs of coal, oil, and natural gas.
Phanerozoic orogens are mountain chains situated along the margins of cratons and produced
by continental collision or ocean-continent subduction. The Appalachian mountains (eastern USA)
and the Ardennes (central Europe) are examples of past orogens related to mountain building
episodes that are no longer active. On the other hand, the Alpine-Himalayan orogen and the Andes
are examples of ongoing mountain building .
Regions of extended crust are regions where the last episode of tectonic deformation is an
extension. Passive margins are regions of extended crust because they are formed after rifting and
the subsequent opening of an ocean basin (e.g. the passive continental margins bordering the
Atlantic Ocean).

1.2

Structure of earth

Structure of Earth

The internal structure of Earth is layered in spherical shells: an outer silicate solid crust, a highly viscous asthenosphere and mantle, a liquid outer core that is much less viscous than the mantle, and a solid inner core. Scientific understanding of the internal structure of Earth is based on observations of topography and bathymetry, observations of rock in outcrop, samples brought to the surface from greater depths by volcanoes or volcanic activity, analysis of the seismic waves that pass through Earth, measurements of the gravitational and magnetic fields of Earth, and experiments with crystalline solids at pressures and temperatures characteristic of Earth's deep interior.

The structure of Earth can be defined in two ways: by mechanical properties such as rheology, or chemically. Mechanically, it can be divided into lithosphere, asthenosphere, mesospheric mantle, outer core, and the inner core. Chemically, Earth can be divided into the crust, upper mantle, lower mantle, outer core, and inner core. The geologic component layers of Earth are at the following depths below the surface:

Depth (km) Layer
0–80 Lithosphere (locally varies between 5 and 200 km)
0–35 ... Crust (locally varies between 5 and 70 km)
35–2,890 Mantle
80–220 ... Asthenosphere
410–660 ... Transition zone
35–660 ... Upper mantle
660–2,890 ... Lower mantle
2,740–2,890 ... D″ layer
2,890–5,150 Outer core
5,150–6,360 Inner core

The layering of Earth has been inferred indirectly using the time of travel of refracted and reflected seismic waves created by earthquakes. The core does not allow shear waves to pass through it, while the speed of travel (seismic velocity) is different in other layers. The changes in seismic velocity between different layers causes refraction owing to Snell's law, like light bending as it passes through a prism. Likewise, reflections are caused by a large increase in seismic velocity and are similar to light reflecting from a mirror.

Earth's crust

The Earth's crust ranges from 5–70 kilometres (3.1–43.5 mi) in depth and is the outermost layer. The thin parts are the oceanic crust, which underlie the ocean basins (5–10 km) and are composed of dense (mafic) iron magnesium silicate igneous rocks, like basalt. The thicker crust is continental crust, which is less dense and composed of (felsic) sodium potassium aluminium silicate rocks, like granite. The rocks of the crust fall into two major categories – sial and sima (Suess, 1831–1914). It is estimated that sima starts about 11 km below the Conrad discontinuity (a second order discontinuity). The uppermost mantle together with the crust constitutes the lithosphere. The crust-mantle boundary occurs as two physically different events. First, there is a discontinuity in the seismic velocity, which is most commonly known as the Mohorovičić discontinuity or Moho. The cause of the Moho is thought to be a change in rock composition from rocks containing plagioclase feldspar (above) to rocks that contain no feldspars (below). Second, in oceanic crust, there is a chemical discontinuity between ultramafic cumulates and tectonized harzburgites, which has been observed from deep parts of the oceanic crust that have been obducted onto the continental crust and preserved as ophiolite sequences.

Many rocks now making up Earth's crust formed less than 100 million (1×108) years ago; however, the oldest known mineral grains are about 4.4 billion (4.4×109) years old, indicating that Earth has had a solid crust for at least 4.4 billion years.

Mantle:

Earth's mantle extends to a depth of 2,890 km, making it the thickest layer of Earth.The mantle is divided into upper and lower mantle,which are separated by the transition zone. The lowest part of the mantle next to the core-mantle boundary is known as the D″ (pronounced dee-double-prime) layer. The pressure at the bottom of the mantle is ≈140 GPa (1.4 Matm).The mantle is composed of silicate rocks that are rich in iron and magnesium relative to the overlying crust. Although solid, the high temperatures within the mantle cause the silicate material to be sufficiently ductile that it can flow on very long timescales.Convection of the mantle is expressed at the surface through the motions of tectonic plates. As there is intense and increasing pressure as one travels deeper into the mantle, the lower part of the mantle flows less easily than does the upper mantle (chemical changes within the mantle may also be important). The viscosity of the mantle ranges between 1021 and 1024 Pa·s, depending on depth.In comparison, the viscosity of water is approximately 10−3 Pa·s and that of pitch is 107 Pa·s. The source of heat that drives plate tectonics is the primordial heat left over from the planet's formation as well as the radioactive decay of uranium, thorium, and potassium in Earth's crust and mantle.

Core:

The average density of Earth is 5.515 g/cm3. Because the average density of surface material is only around 3.0 g/cm3, we must conclude that denser materials exist within Earth's core. This result has been known since the Schiehallion experiment, performed in the 1770s. Charles Hutton in his 1778 report concluded that the mean density of the Earth must be about that of surface rock, concluding that the interior of the Earth must be metallic. Hutton estimated this metallic portion to occupy some 65% of the diameter of the Earth. Hutton's estimate on the mean density of the Earth was still about 20% too low, at 4.5 g/cm3. Henry Cavendish in his torsion balance experiment of 1798 found a value of 5.45 g/cm3, within 1% of the modern value.Seismic measurements show that the core is divided into two parts, a "solid" inner core with a radius of ≈1,220 km and a liquid outer core extending beyond it to a radius of ≈3,400 km. The densities are between 9,900 and 12,200 kg/m3 in the outer core and 12,600–13,000 kg/m3 in the inner core.

(2)

The simplest model for the shape of the entire Earth is a sphere. The Earth's radius is the distance from Earth's center to its surface, about 6,371 kilometers (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth".

The concept of a spherical Earth dates back to around the 6th century BC,but remained a matter of philosophical speculation until the 3rd century BC. The first scientific estimation of the radius of the Earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes's measurement ranging from -1% to 15%.

The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km (3,947 – 3,968 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 kilometers (3,959 mi). Regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km (3,950 – 3,963 mi). The difference 21 kilometers (13 mi) correspond to the polar radius being approximately 0.3% shorter than the equator radius.

Ellipsoid of revolutionEdit

An oblate spheroid, highly exaggerated relative to the actual Earth

A scale diagram of the oblateness of the 2003 IERS reference ellipsoid, with north at the top. The outer edge of the dark blue line is an ellipse with the same eccentricity as that of Earth. For comparison, the light blue circle within has a diameter equal to the ellipse's minor axis. The red curve represents the Karman line 100 km (62 mi) above sea level, while the yellow band denotes the altitude range of the ISS in low Earth

Since the Earth is flattened at the poles and bulges at the Equator, geodesy represents the figure of the Earth as an oblate spheroid. The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other celestial body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid.

An ellipsoid of revolution is uniquely defined by two quantities. Several conventions for expressing the two quantities are used in geodesy, but they are all equivalent to and convertible with each other:

  • Equatorial radius  (called semimajor axis), and polar radius  (called semiminor axis);
  • and eccentricity
  • and flattening

Eccentricity and flattening are different ways of expressing how squashed the ellipsoid is. When flattening appears as one of the defining quantities in geodesy, generally it is expressed by its reciprocal. For example, in the WGS 84 spheroid used by today's GPS systems, the reciprocal of the flattening {1/f} is set to be exactly 298.257223563.

The difference between a sphere and a reference ellipsoid for Earth is small, only about one part in 300. Historically, flattening was computed from grade measurements. Nowadays, geodetic networks and satellite geodesy are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid is intended to model the entire Earth or only some portion of it.

A sphere has a single radius of curvature, which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have constant radius of curvature east to west along parallels, if a graticule is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature {\displaystyle r_{p}} is larger than the equatorial

{\displaystyle r_{p}={\frac {a^{2}}{b}},}

because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north–south radius of curvature at the equator { r_{e}} is smaller than the polar

{ {e}={ {b^{2}}{a}}}

where { a} is the distance from the center of the ellipsoid to the equator (semi-major axis), and { b} is the distance from the center to the pole. (semi-minor axis)

Geoid

It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the geoid. In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (gravitation) and the centrifugal force of the Earth's rotation. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as geoid undulations, geoid heights, or geoid separations, will be irregular as well.


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