Gravity Methods Shell Training

Theory of Gravitation

• Newton's Law of Gravity describes the mutual attraction between two masses, represented by the equation ( F = \frac{G m_1 m_2}{R^2} ).
• The universal gravitational constant ( G ) is valued at ( 6.67 \times 10^{-11} , \text{N m}^2 \text{kg}^{-2} ).
• The acceleration due to Earth's gravity ( g ) is approximately ( 9.8 , \text{m/s}^2 ) and is directed toward the Earth's center.

Gravitational Force and Mass

• The gravitational force on an object ( m_0 ) falling towards Earth can be expressed as ( F = mg ).
• Combining ( F = mg ) with Newton's Law gives ( g = \frac{GM}{R^2} ), where ( R ) is Earth's radius and ( M ) is Earth's mass.

Density of Earth

• The average density ( P ) can be calculated as ( P = \frac{3M}{4\pi R^3} ).
• From gravity measurements, the equation ( P = \frac{3g}{4\pi R G} ) allows for the determination of Earth's average density.
• Current measurements show Earth's average density ( \rho ) is ( 5520 , \text{kg/m}^3 ), which is significantly higher than the density of common rocks (2500-3000 kg/m³).

Variations in Gravity

• The value of ( g = 9.8 , \text{m/s}^2 ) is an average; local gravitational anomalies occur due to variations in Earth's density.
• Equation ( g = \frac{4 \pi R G}{3} ) illustrates that gravity depends on both radius and density.
• Local variations in density affect gravity readings, providing insights into subsurface rock structures.

Earth's Shape and Gravity

• The Earth is an ellipsoid, being slightly flattened at the poles, with the equatorial radius approximately ( 21.5 , \text{km} ) longer than the polar radius (6378 km).
• Due to this shape, gravity is slightly stronger at the poles than at the equator since ( g ) is inversely proportional to the square of the radius ( R ).
• The centrifugal force caused by Earth's rotation reduces the effective gravitational force, peaking at the equator and affecting gravity measurements across the surface.

Implication for Geophysical Studies

• Measurement variations in gravity can reveal changes in subsurface rock density, facilitating the understanding of Earth's internal structure.
• The interplay between gravitational pull and centrifugal forces shapes the interpretation of gravity data in geophysical research.

Magnetic Methods

• Magnetic surveying analyzes subsurface geology by identifying magnetic anomalies from the Earth's magnetic field caused by magnetic minerals in rocks.
• Most minerals are non-magnetic; notable exceptions include certain rock types that can create detectable anomalies due to their magnetic properties.
• Rock magnetism includes both magnitude and direction, influenced by the rock’s orientation relative to Earth's magnetic poles.
• Von Wrede pioneered magnetic prospecting in 1843 by using variations in Earth's magnetic field to locate magnetic ores.
• Sir Gilbert's 16th-century research revealed Earth's behavior as a North-South permanent bar magnet.

Principles of Magnetism

• A bar magnet creates a magnetic flux, identifiable by compass needle alignment, with converging poles indicating the magnet's ends.
• Common magnets are dipoles, containing both north-seeking (positive) and south-seeking (negative) poles.
• All materials exhibit magnetic properties at the atomic level; induced magnetization occurs when materials gain magnetic alignment in an external field but lose it when the field is removed.
• Induced magnetization, represented as Ι, correlates to external magnetic field strength (H) with the equation Ι = χH, where χ is the material's susceptibility.

Magnetic Susceptibility

• Susceptibility varies among rock types; it measures how well a material can be magnetized.
• Common rock types exhibit low susceptibility (e.g., sedimentary rocks) to very high susceptibility (e.g., Peridotite).

Classification of Magnetic Materials

• Diamagnetic materials:

  • Full electron shells, no unpaired electrons
  • Produce an opposing magnetic field when exposed to an external field
  • Weakly negative susceptibility

• Paramagnetic materials:

  • Incomplete electron shells
  • Unpaired electrons align with the external field, resulting in positive susceptibility

• Ferromagnetic materials:

  • Metallic elements (e.g., Ni, Co, Fe) allow electron exchange between atoms
  • Strong magnetic behavior and spontaneous magnetization in the presence of a field

Summary of Rock Susceptibility

• Datasets show various ranges of susceptibility for different rock types, indicating variable magnetic properties based on mineral content.
• Rocks like basalt and gabbro can exhibit susceptibility values in the thousands, while sedimentary rocks like limestone remain very low (<1).