🌍Geophysics Unit 3 – Gravity and Geodesy

What's This Unit All About?

• Explores the fundamental principles and applications of gravity and geodesy in the context of geophysics
• Focuses on understanding the Earth's gravity field, its variations, and how it relates to the planet's shape, internal structure, and dynamics
• Covers key concepts such as gravitational potential, gravity anomalies, and geodetic reference systems
• Examines the techniques used to measure and model the Earth's gravity field, including satellite-based methods and ground-based surveys
• Discusses the implications of gravity and geodesy in various geophysical applications, such as resource exploration, natural hazard assessment, and Earth system monitoring

Key Concepts and Definitions

• Gravity: The force of attraction between two masses, governed by Newton's law of universal gravitation
• Gravitational potential: The work required to move a unit mass from infinity to a given point in a gravitational field
• Geoid: An equipotential surface that closely approximates the mean sea level and represents the shape of the Earth
• Gravity anomaly: The difference between the observed gravity at a location and the theoretical gravity predicted by a reference model
• Geodesy: The science of accurately measuring and understanding the Earth's geometric shape, orientation in space, and gravity field
• Reference ellipsoid: A mathematical model that approximates the shape of the Earth, used as a reference for geodetic calculations
• Isostasy: The state of gravitational equilibrium between the Earth's crust and the underlying mantle, assuming a fluid-like behavior over geological timescales

Historical Background

• Early observations of the Earth's shape and gravity by ancient Greek scholars, such as Eratosthenes and Aristotle
• Newton's formulation of the law of universal gravitation in the 17th century, providing a mathematical foundation for understanding gravity
• The development of geodetic techniques in the 18th and 19th centuries, including triangulation and leveling surveys
• The establishment of the first international scientific organizations dedicated to geodesy, such as the International Association of Geodesy (IAG) in 1864
• The advent of satellite-based methods in the 20th century, revolutionizing the study of Earth's gravity field and shape
  • Launch of dedicated gravity field missions, such as CHAMP (2000), GRACE (2002), and GOCE (2009)
  • Improved global gravity field models and insights into Earth's interior structure and dynamics

Earth's Gravity Field

• Varies in strength and direction across the Earth's surface due to factors such as latitude, elevation, and mass distribution
• Influenced by the Earth's rotation, causing a centrifugal force that opposes gravity and leads to an equatorial bulge
• Affected by the uneven distribution of mass within the Earth, including the core, mantle, and crust
• Exhibits anomalies due to local variations in density, such as those caused by mountains, ocean trenches, and subsurface geological structures
• Continuously evolving due to processes such as glacial isostatic adjustment, sea-level change, and tectonic deformation
• Described using spherical harmonic expansions, which decompose the gravity field into a series of wavelengths and amplitudes

Geodetic Measurements and Techniques

• Terrestrial techniques:
  • Gravity measurements using absolute and relative gravimeters
  • Leveling surveys to determine height differences and establish vertical datums
  • GNSS (Global Navigation Satellite System) positioning for precise point coordinates
• Airborne and shipborne surveys:
  • Gravity measurements using specialized gravimeters mounted on aircraft or ships
  • Allows for regional-scale mapping of gravity anomalies and crustal structure
• Satellite-based methods:
  • Satellite altimetry to measure the shape of the ocean surface, which is closely related to the geoid
  • Satellite gravimetry missions (CHAMP, GRACE, GOCE) to map the global gravity field with unprecedented accuracy and resolution
  • Satellite laser ranging (SLR) to precisely track the orbits of satellites and infer changes in the Earth's gravity field over time

Applications in Geophysics

• Exploration geophysics:
  • Mapping subsurface density variations to identify potential oil, gas, and mineral resources
  • Detecting geological structures such as faults, folds, and sedimentary basins
• Solid Earth geophysics:
  • Investigating the structure and composition of the Earth's interior, including the crust, mantle, and core
  • Studying plate tectonics, earthquakes, and volcanic activity
• Hydrological and cryospheric applications:
  • Monitoring changes in groundwater storage, soil moisture, and snow/ice mass using time-variable gravity measurements (GRACE mission)
  • Assessing the impacts of climate change on the Earth's water cycle and sea-level rise
• Geodynamics:
  • Understanding the Earth's dynamic processes, such as mantle convection, glacial isostatic adjustment, and tidal deformation
  • Investigating the coupling between the solid Earth, oceans, and atmosphere

Mathematical Models and Calculations

• Newton's law of universal gravitation: $F = G \frac{m_1 m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the objects, and $r$ is the distance between their centers
• Gravitational potential: $V(r) = -\frac{GM}{r}$, where $V(r)$ is the potential at a distance $r$ from a point mass $M$, and $G$ is the gravitational constant
• Poisson's equation: $\nabla^2V = -4\pi G\rho$, relating the gravitational potential $V$ to the density distribution $\rho$, where $\nabla^2$ is the Laplace operator
• Spherical harmonic expansion of the gravitational potential: $V(r,\theta,\lambda) = \frac{GM}{r} \sum_{n=0}^{\infty} \sum_{m=0}^{n} (\frac{R}{r})^n P_{nm}(\cos\theta) (C_{nm} \cos m\lambda + S_{nm} \sin m\lambda)$, where $R$ is the reference radius, $P_{nm}$ are the associated Legendre functions, and $C_{nm}$ and $S_{nm}$ are the spherical harmonic coefficients
• Geodetic reference systems and transformations, such as the International Terrestrial Reference Frame (ITRF) and the Earth Gravitational Model (EGM)

Current Research and Future Directions

• Development of next-generation satellite missions for gravity field mapping, such as GRACE-FO (launched in 2018) and future concepts like GRACE-I and MAGIC
• Improvement of global gravity field models, incorporating data from multiple satellite missions and ground-based measurements
• Integration of gravity data with other geophysical observations (seismic, magnetic, electromagnetic) for a more comprehensive understanding of the Earth's interior
• Advancements in computational methods and data processing techniques, enabling higher-resolution and more accurate gravity field solutions
• Interdisciplinary research on the interactions between the solid Earth, oceans, atmosphere, and cryosphere, using gravity as a unifying observation
• Application of gravity and geodesy to the exploration of other planetary bodies, such as the Moon, Mars, and icy satellites of the outer solar system
• Contributions to the United Nations Sustainable Development Goals, particularly in the areas of water resources management, natural hazard mitigation, and climate change adaptation