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Chapter 7. Earth’s Field

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1. Overview

2. Earth’s Gravitational Field

3. Earth’s Magnetic Field


a. Calculation of Latitude and Longitude of High Point Stimulation



1. Overview

⑴ Earth’s field : Flow of Earth’s forces

⑵ Fields are divided into gravitational and magnetic fields



2. Earth’s Gravitational Field

⑴ Gravity

① Definition of gravity : Sum of the universal force towards the center of the Earth and the centrifugal force due to Earth’s rotation that objects on Earth receive

② Universal force F is inversely proportional to the square of the distance between two objects and directly proportional to the product of their masses

○ Gravity is maximum at the poles and minimum at the equator

③ Centrifugal force : f = mrω2 (r : distance from the axis of rotation, ω : angular velocity of Earth’s rotation)

○ Centrifugal force is zero at the poles and maximum at the equator

④ Direction of gravity : Toward the center of the Earth at the equator and poles, not toward the center at other places

⑵ Measurement of gravity

① Using gravimeter : Using a sensitive plumb line balance

② Use of pendulum method : The period of a pendulum with length ℓ is as follows

③ Measurement of universal gravitational constant : Measured for the first time by the Cavendish experiment

Figure. 1. Cavendish Experiment

⑶ Gravitational acceleration

① Surface gravitational acceleration

○ Small-scale movements on the Earth’s surface have constant gravity due to nearly constant distance between objects and the Earth

○ Gravitational acceleration varies locally due to differences in underground density and equatorial centrifugal force

② Gravitational acceleration in the atmosphere

③ Gravitational acceleration within the Earth

○ When calculating gravitational acceleration within the Earth, the outer shell beyond a specific point doesn’t have an effect ( principle of similarity)

Figure. 2. Gravitational Acceleration Inside Earth and Shell

○ Assuming constant Earth density, gravitational acceleration is proportional to the distance from the Earth’s center

④ Actual profile of Earth’s gravitational acceleration

Figure. 3. Actual Profile of Earth’s Gravitational Acceleration

⑤ Gravity on the Earth’s surface is 6 times that on the Moon’s surface

⑷ Anomalies in gravity

① Standard gravity : Theoretical value calculated for a uniform ellipsoid closest to the geoid with the same mass as the actual Earth, as a function of latitude (Φ)

② Gravity anomaly = Measured gravity - Standard gravity

○ Positive gravity anomaly : Presence of high-density materials (e.g., iron ore, basalt)

○ Negative gravity anomaly : Presence of low-density materials (e.g., petroleum, halite)

③ Correctional gravity : Gravity on a flat terrain on the geoid

④ Bouguer anomaly = Correctional gravity - Standard gravity

○ Bouguer anomaly appears due to differences in underground material density

○ (+) value in regions with high underground density (mainly ocean), (-) value in regions with low underground density (mainly land)

⑤ Distribution of gravity anomalies : Also called “Potato Model” of gravity anomalies

Figure. 4. Potato Model of Gravity Anomalies

⑸ Role of Gravity

① Forms in the contraction of cold interstellar material → Energy source in Earth’s early formation

⑹ Isostasy

① Theory that low-density lithospheres float on high-density mantle while maintaining equilibrium

② In this equilibrium process, compensatory movement occurs

Theory 1. Pratt’s hypothesis : Different lithospheric densities with the same Moho depth. (Note) Remember as “flat”

Theory 2. Airy’s hypothesis : Same lithospheric density with different Moho depths

Figure. 5. Comparison of Pratt’s and Airy’s Hypotheses

⑤ Actual lithosphere fits with Airy’s hypothesis since it’s divided into continental and oceanic lithospheres, and Pratt’s hypothesis applies to each lithosphere

Figure. 6. Isostasy in Actual Lithosphere

⑺ Motion of Artificial Satellites

① First cosmic velocity : Velocity required for circular motion just above Earth’s surface. About 7.9 km/s

② Second cosmic velocity : Escape velocity required to leave Earth’s gravitational field from its surface. About 11.2 km/s

③ Third cosmic velocity : Escape velocity required to leave the solar system from Earth’s surface. About 16.7 km/s

④ Geostationary satellites

○ Geostationary satellites : Those with an orbital period matching Earth’s rotation period. Otherwise called non-geostationary satellites

○ Geostationary satellites remain fixed over the same point on Earth’s surface



3. Earth’s Magnetic Field

⑴ Overview : Earth can be considered as a magnetic dipole with its South Pole at the geographic North

⑵ Three Elements of Earth’s Magnetism

Figure. 7. Three Elements of Earth’s Magnetism

① Declination (Magnetic Azimuth) : Represented by α

○ The angle formed by the direction of magnetic north (needle’s north) with respect to true north (geographic north)

○ Positive when the needle’s north points east, negative when it points west

② Inclination : Represented by β

○ Angle formed by the inclination of the magnetic needle to the horizontal plane. Also known as the angle between the horizontal magnetic force and the vertical magnetic force

○ Magnetic dip : 0°, North Pole : +90°

○ Increases with latitude

Figure. 8. Inclination Based on Latitude

Arrows point to the geographic North, which is the South Pole of the magnetic dipole

③ Horizontal magnetic force : Represented as A or H

○ Horizontal component of Earth’s magnetic force

○ Maximum at the magnetic equator

○ Horizontal magnetic force H = F cos I, I : Inclination

○ Vertical magnetic force V = F sin I, I : Inclination

⑶ Variations in Earth’s Magnetic Field

① Present Earth’s magnetic field : 2.0 × 10-5 T

② Secular variation : Gradual change in Earth’s magnetic field due to changes in Earth’s interior

○ No periodicity

○ Normal and reversed polarity

Figure. 9. Magnetic Field Lines Profile during Reversed Polarity

Note: Consider that geographic North is the magnetic South

○ Magnetic anomalies measured near the Wrangel Island region

Figure. 10. Magnetic Anomalies Measured near Wrangel Island Region

③ Diurnal variation : Variations in Earth’s magnetic field due to changes in the Sun’s altitude

○ More prominent during daylight than nighttime

④ Magnetic storms : Sudden and rapid changes in Earth’s magnetic field that occur irregularly over several hours to 2-3 days due to solar flares

○ Accompanied by the phenomenon of auroras and the Van Allen belts

Aurora Phenomenon (aurora)

○ Fluorescent phenomenon caused when electrons and ions previously present in solar winds excite atmospheric particles, which emit light afterward

○ Electrons or ions experience a perpendicular Lorentz force to their velocity and magnetic field, resulting in their spiraling path

Figure. 11. Trajectory of Electrons or Ions Generating Aurora

⑷ Causes of Earth’s Magnetism and Van Allen Belts

① Dynamo Theory : Theory that currents generated by the motion of the outer core produce the Earth’s magnetic field

○ (Note) Circular loop of current : Iron ions (Fe2+) do not rotate due to Earth’s rotation, so a North Pole bar magnet is not formed

○ Coriolis force and convection lead to the creation of a South Pole bar magnet (considering geographic North as magnetic South)

Figure. 12. Actual Movement of Fe2+[Note:7]

② Causes of Earth’s magnetic field variations

○ Internal cause : Causes secular variation due to changes in Earth’s interior

○ External cause : Causes diurnal variation, magnetic storms, auroras, etc., due to changes in solar activity

③ Van Allen belts

○ Belt-shaped regions that block solar winds and cosmic rays

○ Inner radiation belt (Internal cause) : Composed mainly of protons, located at around 3,000 km above the Earth’s surface

○ Outer radiation belt (External cause) : Composed mainly of electrons, located at around 15,000 km above the Earth’s surface



Input : 2019.08.16 22:36

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