What is Physical Geodesy? Importance of Physical Geodesy
What is Physical Geodesy
Physical geodesy is the study of the physical qualities of the Earth’s gravitational field, the geopotential, with the goal of applying them to geodesy.
The study is concerned with the Earth’s shape and other spheroidal properties, such as its oblateness or tilt.
Examples of practical applications of physical geodesy are GPS positioning, satellite navigation systems, and estimating surface elevation from satellite imagery.
Physical geodesy is a branch of geodesy, the study of the Earth’s size and shape. Geodesists work to produce maps that depict shapes such as curvature and relief so that they can be used in cartography or engineering projects involving underground structures.
They also construct high-precision geodetic and gravimetric devices, such as the world’s largest triangulation network, the International Terrestrial Reference Frame (ITRF).
Physical geodesy studies the Earth’s gravitational field and its effect on objects within it.
It gives hints about the shape and size of the Earth based on measurements of its gravitational field around some selected point on the surface.
The field strength of gravity is obtained using gravimeters, which measure the weight force (gravitational acceleration) acting on an object as it is dragged across the ground by gravity in different places.
History of Physical Geodesy
The history of physical geodesy begins with work by early Greek and Chinese mathematicians.
The ancient Egyptians developed a technique of measuring the horizontal length of a pyramid by dragging a rope across it in different places, thus establishing the length of the sides twice.
The ancient Greeks measured the heights of pyramids by sighting through high-quality optical devices called oculi, which allowed them to measure high places more accurately than Egyptians.
They also measured heights reliably by constructing pendulums that were suspended on similar cords or cables.
Precision measurements of height were made in the 17th century by English scientist John Michell and Dutch engineer Willebrord Snell.
The first modern geodesic was designed in 1882 by German mathematician Eduard Rheticus.
Physical geodesy techniques are also used to study the Earth’s oblateness.
This is a feature of the Earth’s mass distribution that is associated with a tilt of the Earth whose axis is tilted 23.5° with respect to its orbital plane.
Physical Geodesy Instruments
An optical theodolite measure angles between two visible reference points or reflective prisms. The measured angle can be calibrated to calculate the elevation (height above sea level).
The accuracy of an optical theodolite depends on how well it is calibrated, how well it is maintained, and its horizontal location. The World Geodetic System has two additional variants using radio signals with a precision of one millimeter.
Modern Global Navigation Satellite Systems (GNSS)
GNSS is a set of orbiting satellites that transmit accurate time signals and monitor the Earth’s shape.
Measurements from GPS, GLONASS, and GALILEO can be used to calculate the absolute position of an object on the surface.
The accuracy depends on how well they are calibrated, how well they are maintained, their location, and the quality of their reception by a receiver on the ground.
These satellite-based systems enable objects to be located anywhere in the world with an accuracy of a few centimeters.
Global Positioning System
A GPS device measures three coordinates: latitude, longitude, and altitude. It is accurate to about 5 cm. It is a satellite-based radio positioning system.
Gravity meters (Gravimeters)
Gravimeters measure the gravitational acceleration of a point on the Earth’s surface, resulting in a measurement of g (9.80665 m/s). An average of multiple readings determines the local gravity field, including variation over time.
The simplest type of gravimeter is called a ‘wet’ gravity meter and uses some form of fluid. The denser the fluid, the greater the resulting value will be. These are portable, but low-cost versions are not very accurate.
Satellite Laser Ranging
An optical telescope on Earth tracks a satellite as it orbits and calculates the distance by measuring when light from the satellite is emitted and when it is received. This is called triangulation (a form of trilateration). The method is accurate to about 1 mm.
Global Positioning System (GPS) Receiver
A GPS receiver measures positions and time very accurately by analyzing signals from satellites, but it can only determine elevation within a few tens of meters.
A combination of optical theodolites, wet gravimeters, and GPS receivers allows the determination of surface shape with nanometer accuracy.
A total station is an instrument that measures angles and distances to points on the surface. It is a very accurate instrument for surveying, mapping, and leveling purposes.
The accuracy of a total station depends on its height above sea level, how well it is calibrated, how well it is maintained, and its horizontal location.
Theoretical Concepts in Physical Geodesy:
The theoretical Concepts are as follows:
- Theory of small angles
Geodesists use the principle of small angles to estimate the relative heights of points on a surface (or to estimate the relative height of an altitude within a triangle in measuring distance).
The sum of the angles within a triangle is equal to 180°. So, if A, B, and C form a triangle this formula can be used to calculate the distance between A and B.
- Theory of triangles
Geodesists use the principle of triangles to estimate the relative heights of points on a surface (or to estimate the relative height of an altitude within a triangle in measuring distance).
The sum of the perpendicular distances from each point on a plane (or each vertex) to another point (or other three vertices) must be equal
In physical geodesy, the perpendicular distance is referred to as orthodromic distance.
- Theory of gravity
The sum of the gravitational forces due to the Earth, Moon and Sun has a theoretical value of zero everywhere on the surface. The deviations from this value are known as ‘gravity anomalies’.
The magnetic field of the Earth is also subject to anomalies. These anomalies occur in various shapes and sizes and may be localized or widespread over large areas (or even entire continents).
Derivation of Physical Geodesy Parameters
There are two methods of deriving the parameters in physical geodesy. The first is mathematical and the second is an empirical method.
The first method is more accurate than the second one but quite complicated for less experience geodesist. It involves using the mathematics of spherical trigonometry to determine the shape parameters from measurements.
The Earth’s shape is represented by a mathematical function that has two independent parts corresponding to the elliptic model and oblate spheroidal model.
The results are then compared with actual height values to refine the mathematical model of shape.
The second method is more practical because it uses a series of empirical measurements, which are then mathematically smoothed to create the best possible approximation of the actual shape.
Physical Geodesy Importance
Physical Geodesy is useful in:
- Geographical information system (GIS)
Geographical Information systems are critical to the study of Physical Geodesy. GIS and GPS together enable the collection, storage, and analysis of geodetic data that is used to analyze and display physical features on maps.
Strain is a measure of change in shape over time. Geological forces such as earthquakes, volcanic eruptions and landslides all cause changes in the strain that can be estimated using geodesy techniques.
- Seismic activity
Earthquakes are monitored by seismographs around the world and geodesy techniques aid in the interpretation of these records.
Gravity is a measure of the weight of the mass on Earth’s surface. Geodesy techniques are used to determine gravity accurately, to detect changes in gravity over time, and to determine the size of the gravitational field needed for a geophysical application.
Tide gauges are used to measure tide heights and tides and coastal characteristics. Geodesy techniques are used to determine tide heights, tidal strength, and tidal currents.
- Earth’s motion
Earth’s motion is measured using geodesy techniques because they provide information on changes in the speed of rebound from mass boundaries that can be used to measure the shape of our planet.
- Global Sea level
Seawater is sensitive to variations in global sea level. Geodesy techniques are used to predict sea levels and the locations of future changes. Geodetic measurements also help determine the variations in global sea level with respect to mean sea-level and implications for local challenges such as tidal flooding.
Physical Geodesy Challenges
The challenges encountered in Physical Geodesy are many, they include:
The precision of geodetic measurements is dependent on the accuracy of measurement, the accuracy and uniformity of the measuring equipment, and the stability of any change in shape.
The accuracy of geodetic measurements refers to the spatial resolution and precision in shapes that can be measured. Precision and accuracy combine to determine how much detail can be included in a map. Accuracy is dependent on the size of the repeatability of the measurement.
The cost of geodetic measurements has decreased with recent advances in technology and improvements in satellite accuracy but it still remains high because most measurements must be made in remote areas and require specialized equipment.
It takes time to measure the shape of the Earth. Gravity is the only measurement that can be made continuously in real time with current technology so other data must be stored and analyzed at regular intervals.
- Space complexity
Geodesic measurements are inherently complex because they require measuring in multiple dimensions, so it is difficult to make observations with simple data collection equipment and methods.
Physical Geodesy has a spatial measurement uncertainty that is measured through field observations of deflections in the vertical and horizontal directions. The two different types of deflections are called Geodetic Height and Geodetic Orientation.
Geodetic height is the difference between mean sea level and local vertical height above or below sea level, respectively. Geodetic orientation (in a north-south direction) refers to the angle by which a surface deviates from or deviates to, a true reference ellipsoid.
Physical Geodesy Techniques
There are a variety of techniques that can be used to measure the shape of the Earth, gravity, and dynamics. Some techniques focus on measuring things such as gravitational attraction while others measure the speed of light passing through space.
- Composition of points:
This is the most common and oldest technique. In this method, geodetic lines (surveyed lengths) are used to make a point distribution map of the Earth’s surface.
The distribution of points on the surface represents various types of terrain from topography to ocean floor, lake bottom and ice. This technique is very accurate for large area maps but does not produce local detail or provide orientation information on a small scale.
Measuring gravity provides a global map of the Earth’s interior. Gravity is very stable with time and is found to be constant across the surface of the Earth.
- Satellite tracking:
Geodetic positions are calculated by tracking satellites in orbit. The distances between satellites and receivers are measured using radio signals transmitted from each satellite and receiver.
The shape of the Earth can be determined by measuring distances on multiple paths, in different directions and rotating positions around the center of mass.
- Gravity inversion:
This method seeks to determine the shape of the Earth’s core by measuring gravity profiles. Gravity is measured from select locations on the surface and is inverted to obtain information about the shape of the mantle. The shape of the mantle can be determined by comparing gravity readings in different locations such as those along either side of a ridge or valley.
- Gravity changes:
Changes in gravity can provide information about the shape of the mantle. This technique is used to measure the density of the Earth at several locations across the globe. Differences between these density readings are used to calculate depth and anomalies in gravity.
- Gravity waves:
This method uses GPS occultation data taken by satellites to determine variations in gravity that cannot be explained by other sources. The GPS satellites pass directly over the Earth, but if they are tracked over long enough periods of time, satellites usually pass through one another.
- Gravitational time-transfer:
Using a radio signal transmitted from a satellite to a receiver on Earth, GPS time is calculated. Changes in distance between the transmitter and receiver as determined by gravity can be used to determine the shape of the Earth’s surface.
Has the shape of the Earth changed in the past?
The shape of the surface of Earth is constantly responding to changes in physical processes, such as plate tectonics which creates mountains, earthquakes, volcanoes, and ocean floor formation.
The shape of the Earth’s gravity field has also changed over time due to surface uplift and subsidence (i.e., ice-age glacial loading)
What is classical Physical Geodesy?
Classical physical geodesy is the measurement of gravity and its elastic response on the surface. Gravity is considered to be a completely linear phenomenon, meaning that it has zero curvature.
It is also nonsingular, which means any two locations can be added together to give two locations with the same value of acceleration.
This property implies that the Earth does not change shape when measured or transported by light or gravity waves.
Classical geodesy can measure very large scales and provide a basic set of mapping functions including area, contour and elevation.
What physical geodesy methods are available to us?
We can use GPS and gravity changes to determine the shape of the Earth’s surface, but they do not provide local detail or orientation information.
Passive Measurement: Passive measurements include measuring gravity and GPS tracking of satellites.
Active Measurement: Active measurement methods are used to measure things such as the acceleration of mass and momentum flow on Earth.
Examples include radar reflections, magnetometers, ionospheric propagation, laser ranging, laser interferometry and radar sounding.
What is gravity mean in Physical Geodesy gravity?
Gravity is frequently measured in ms2 units (meters per second squared).
This can alternatively be represented as newtons per kilogram of attracted mass (by multiplying by the gravitational constant G to convert units). Potential is defined as gravity multiplied by distance.
What is cotangent-tangent measurements used in Physical Geodesy?
The principal purpose for measuring gravity changes is to determine how much mass and momentum change is occurring on Earth.
What is the difference between geodesy, geodetic and physical geodesy?
Geodesy: Geodesy is the science and practice of measurement of the Earth’s surface. This can include mapping functions such as elevation, area, and contour.
Geodetic: Geodetic refers to the location on a globe or map that is oriented according to reference ellipsoids. A reference ellipsoid refers to a mathematical model of the shape of Earth that approximates local distances and angles to some degree.
Physical Geodesy: This is a subdivision of geodesy that encompasses measurement and modeling of Earth’s gravity and elastic response.
What is the definition of geoid?
The geoid is a surface that approximates the mean sea level on the Earth (i.e. the elevation of the ocean). The geoid can be measured by determining how far away from land an object sinks after being thrown off the coast.
What is a Geodetic Datum?
An established and essential framework of geodetic observations is used as the basis for precise positioning and measurement. In the past, geometric datums were used to make large-area maps at a 1:50,000 scale.
What are the 3 aspects of geodesy?
Geodesy is the study of properly measuring and comprehending three fundamental aspects of the Earth: its geometric form, orientation in space, and gravitational field—as well as how these qualities change through time.
Geodetic: involves the measurement of large-scale variations in the Earth’s form and gravitational field.
Physical Geodesy: involves measuring and modeling gravity and the elastic response of the Earth.
Can a geoid be an ellipsoid?
The geoid can be approximated by an ellipsoid, although it does not include data for non-spherical variations.