Earth's Gravity Field PDF

EARTH’S GRAVITY FIELD PAGE | 01 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 02 The shape of the Earth is not spherical. The radius at the equator is...

EARTH’S GRAVITY FIELD PAGE | 01 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 02 The shape of the Earth is not spherical. The radius at the equator is larger than at the poles due to the long term effects of the Earth’s rotation. And, at a smaller scale, there is topography—mountains have more mass than a valley and thus the pull of gravity is regionally stronger near mountains. All of these large and small variations to the size, shape, and mass distribution of the Earth cause slight variations in the acceleration of gravity (or the “strength” of gravity’s pull). These variations are measurable by precise instruments, and they manifest themselves by changing the Earth’s liquid environment. Specifically, if one were to remove the tides and currents from the ocean, it would settle onto a smoothly undulating shape (rising where gravity is high, sinking where gravity is low) called “the geoid.” By long-standing scientific convention, the geoid is a surface which defines zero elevation. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 03 For gravity studies on the Earth’s surface, we use instruments called gravimeters to measure the acceleration of gravity. A gravimeter observing over a dense volume of rock will measure a larger local gravity value (which yields a larger geoid undulation). Gravity is measured in units of Gals (named in honor of Galileo), where one Gal equals one cm/sec2. Gravity on Earth’s surface ranges from about 983 Gals near the North Pole to near 977 Gals on equatorial mountaintops. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 04 Geoid determination. After Determine variations of rock 01 the geoid is determined, then other surveys, like 02 densities (as a geologic mapping tool) Global Positioning System (GPS) or differential leveling, can be used to measure surface elevations. Temporal monitoring Metrology laboratories for 03 elevation changes, magma intrusions, or water-table 04 calibrating weighing machines. variations. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 05 The Earth is rotating, which generates a centrifugal force (gravity), "throwing" mass out toward space with the greatest force at the equator (where Earth’s rotation moves bodies at the crust with the greatest speed) and least force at the poles (where Earth’s rotation doesn’t move bodies at the crust at all). The ellipsoidal nature of Earth thus causes variations in gravitational acceleration as a function of an observation point’s latitude. What we call “gravity” is the combination of gravitation (the pull between two masses) and centrifugal force (caused by the spin of the Earth). 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 06 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 07 the force acting on a body on the Earth’s surface Vector quantity Has 3 components: Gravitational force (Earth’s pull) Centrifugal force (Earth’s rotation) Coriolis force (for a moving body, responsible for the geostrophic motion encountered in air or water movement) 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 08 External gravity field
> reference system for most geodetic measurements. Distribution of gravity values + other geodetic measurements shape of the Earth. Geoid > reference surface for heights > level surface of the gravity field. Yields information on the structure and characteristics of the Earth’s interior. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 09 Has a dimension of acceleration Measured in gals, 1 gal = 1 cm / sec-2 Numerical value ≈ 977 (equator) – 983 (poles) Direction of g : direction of plumb line or vertical 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 10 EQUATION 1 This law states that two very small particles of mass (m1) and (m2) respectively, each with dimensions very small compared with the separation (r) of their centers of mass, will be attracted to one another with a force.  2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 11 F = m(a) EQUATION 2 where, m = the mass a = acceleration For a body whose mass (m) is constant, where F (force) and a (acceleration) are both vector quantities. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 12 EQUATION 1 EQUATION 2 EQUATION 3 Newton’s law states that in case of two masses (m1) and (m1) separated by a distance (r) between them, then these two masses attract each other’s by force (F). 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 13 EQUATION 4 EQUATION 5 EQUATION 6 The gravity attraction of the earth varied from point to point on the earth surface, due to that the radius of the earth (r) (which is not constant everywhere on the earth) in addition to the centrifugal force create duo to the rotation of the earth 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 14 Vertical Component Horizontal Component 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 15 EQUATION 7 EQUATION 8 For the other latitude circle of the earth which symbolized by 0, the radius (r) replaced by r cos0 then, the angular acceleration become a cos0 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 16 EQUATION 1 EQUATION 2 The intensity of gravitational field depends only on position, the analysis of such fields can often be simplified by using the concept of potential. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY PAGE | 17 EQUATION 3 EQUATION 4 EQUATION 5 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY : EQUIPOTENTIAL SURFACES AND THE GEOID PAGE | 18 EQUIPOTENTIAL SURFACES AND THE GEOID 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY : EQUIPOTENTIAL SURFACES AND THE GEOID PAGE | 19 A surface where all points on the surface have the same electric potential. This means that at every point on the equipotential surface, a charge will have the same potential energy. The work done in moving a charge between two points on an equipotential surface is zero. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY : EQUIPOTENTIAL SURFACES AND THE GEOID PAGE | 20 A geoid is the irregular-shaped “ball” that scientists use to more accurately calculate depths of earthquakes, or any other deep object beneath the earth’s surface. The geoid is a model of global mean sea level that is used to measure precise surface elevations. 2.1 FUNDAMENTALS OF GRAVITY FIELD THEORY : EQUIPOTENTIAL SURFACES AND THE GEOID PAGE | 21 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EATH AS AN OBLATE SPHEROID PAGE | 22 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 23 any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 24 the force acting on a body on the Earth’s surface Vector quantity Has 3 components: Gravitational force (Earth’s pull) Centrifugal force (Earth’s rotation) Coriolis force (for a moving body, responsible for the geostrophic motion encountered in air or water movement) 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 25 Centrifugal force is a pseudo force in a circular motion which acts along the radius and is directed away from the centre of the circle. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 26 The invisible force that appears to deflect the wind is the Coriolis force. The Coriolis force applies to movement on rotating objects. It is determined by the mass of the object and the object's rate of rotation. causing moving objects like air and water to be deflected from their straight path. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 27 Earth is not a perfect sphere. Its shape is an oblate spheroid. This just means that it flattens at the poles and widens out at the equator. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: EARTH AS AN OBLATE SPHEROID PAGE | 28 Due to its rotation, the equatorial region of Earth experiences a stronger outward force (centrifugal force), causing the planet to flatten at the poles. The centrifugal force acts outward from the rotational axis, causing Earth to bulge at the equator.  2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: NORMAL GRAVITY PAGE | 29 DEFINITION KEY CONCEPTS Normal Gravity: It is the gravitational Reference Ellipsoid: It is a mathematical acceleration experienced at the Earth's model of the Earth's shape used to define surface, approximately 9.81 m/s². normal gravity. Equipotential Surfaces: It is surfaces FORMULA where gravitational potential is constant; one such surface is the reference ellipsoid. Normal gravity can be derived from the normal potential U(x,y,z)U(x,y,z):  2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: NORMAL GRAVITY PAGE | 30 INFLUENCING FACTORS Latitude: Gravity varies slightly from pole to equator due to the Earth's rotation and shape. Altitude: Gravity decreases with height above sea level. Local Geological Variations: Density differences in the Earth's crust can cause anomalies in measured gravity. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: ANOMALOUS GRAVITY PAGE | 31 Anomalous gravity refers to variations in the strength of the gravitational force over the surface of the Earth. These anomalies can be due to unusual concentrations of mass in a region. Anomalous gravity refers to the difference between the actual, measured gravity at a location and the theoretical normal gravity calculated for that location. We calculate gravity anomalies using this equation: GRAVITY ANOMALY OBSERVED REFERENCE GRAVITY GRAVITY 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: ANOMALOUS GRAVITY PAGE | 32 TWO CLASSIFICATION OF GRAVITY ANOMALIES 1. POSITIVE ANOMALY 2. NEGATIVE ANOMALY A positive anomaly refers to a A negative anomaly indicates that measurement that is greater than the observed temperature or the expected or average value, value is cooler or lower than the indicating a deviation from normal baseline conditions. UNITS USED FOR GRAVITY ANOMALIES A common unit of measurement for gravity variations is the milligal. The connection with the SI system is 1 mGal = 10−5 m/s 2. The unit µGal or 10−8 m/s 2 is also used. The units µm/s 2 and GALILEO GALILEI nm/s 2 , which formally belong to the SI system. 2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: ANOMALOUS GRAVITY PAGE | 33  2.2 GEOMETRY OF THE EARTH’S GRAVITY FIELD: ANOMALOUS GRAVITY PAGE | 34 1. FREE AIR GRAVITY ANOMALY The free air gravity anomaly is the measured gravity anomaly after a free- air correction is applied to correct for the elevation at which a measurement is made. This is done by adjusting these 3. ISOSTATIC GRAVITY measurements of gravity to what would have been measured at sea ANOMALY level. Isostatic gravity anomalies provide a measure of the Earth's gravity field free from the gravitational attractions 2. BOUGUER GRAVITY of the topography and its isostatic ANOMALY compensation, most commonly represented by a variation in the Bouguer anomaly refers to the depth of a compensating density contrast. measured gravity that has been adjusted for the expected gravity effects on a planetary scale. This adjustment involves subtracting the normal field or the normal gravity, which is calculated using a specific formula based on the shape and size of the reference ellipsoid.  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 35 PURPOSE OF GRAVITY OBSERVATIONS 1 STUDY OF EARTH'S INTERNAL STRUCTURE 2 GEOID DETERMINATION 3 RESOURCE EXPLORATION Variations in gravity indicate The height of various Gravity measurements differences in the Earth’s internal parts of the geoid provide information density. constantly shifts due to about rocks densities changes in gravitational beneath the ground. force.  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 36 METHODS FOR MEASURING GRAVITY 1 GROUND-BASED OBSERVATIONS Absolute Gravity Measurement Relative Gravity Measurement 2 SATELLITE-BASED OBSERVATIONS 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 37 GRAVIMETERS AND SATELLITE-BASED OBSERVATION  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 38 For gravity studies on the Earth’s surface, we use instruments called gravimeters to measure the acceleration of gravity. A gravimeter observing over a dense volume of rock will measure a larger local gravity value (which yields a larger geoid undulation). Gravity is measured in units of Gals (named in honor of Galileo), where one Gal equals one cm/sec2. Gravity on Earth’s surface ranges from about 983 Gals near the North Pole to near 977 Gals one quatorial mountaintops DACQUEL  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 39 Absolute gravity measurement- measure the size of the entire field. Although these were the first kind of gravity measurements ever made, they are also very difficult to do precisely. There are two primary types of absolute meters: pendulums and falling body instruments Relative gravity measurement- the difference in gravity between two locations. Most of these meters are based upon the principle of a mass on a spring DACQUEL 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 40 When the young French researcher Jean Richer visited French Guyana in 1671 with a pendulum clock, he noticed that the clock ran clearly slower. The matter was corrected simply by shortening the pendulum. The cause of the effect could not be the climatic conditions in the tropics, like the thermal expansion of the pendulum. The right explanation was that in the tropics, gravity g is weaker than in Europe. After his return to France in 1673, Richer had to make his pendulum longer again. The observation is described in just one paragraph in his report Observations astronomiques et physiques faites en l’isle de Caïenne, Richer (1731). DACQUEL  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 41 The instrument contains a vacuum tube, inside of which an object, a prism reflecting light, falls freely. During the fall of the prism, a “cage” with a window in the bottom moves along with the prism inside it without touching it. The main purpose of the cage is to prevent the last remaining traces of air from affecting the motion of the prism. Approaching the bottom, the cage, which moves along a rail under computer control, decelerates, and the prism lands relatively softly on its base. After that, the cage moves back to the top of the tube and a new measurement cycle starts. DACQUEL 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 42 Spring gravimeters and ideal-spring gravimeters are spring-based relative gravimeters. A spring gravimeter (LaCoste-Romberg gravimeter) has good sensitivity even on a mobile platform, but it needs regular recalibration and has the limitations of a mechanical spring, such as aging. An ideal-spring gravimeter (superconducting gravimeter) has the best sensitivity relative to the other gravimeters. However, the ideal-spring gravimeter is limited by the environment, and it is difficult to use on a mobile platform (Lee, J., 2007). DACQUEL 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 43 Satellites used for geodetic observations differ in design, equipment and orbital parameters according to the mission purpose. Satellites can be regarded as moving targets at high altitudes and then used for positioning and navigation. Since the satellite orbits are sensitive to the gravitational field of the Earth, the satellites also serve as a sensors for gravitation. 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 44 Space geodetic techniques are essential for providing accurate and long-term stable global reference frames and observing and understanding Earth's dynamics. Each space geodetic technique is sensitive to different Earth signals, conducts observations with different resolutions in space and time, and provides geodetic products with different latency and quality.  2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 45 Geodetic LEO satellites are preferred for determining Satellites at high altitudes the Earth’s gravity field (as (MEO and GEO) are they are more sensitive to preferred for positioning, as short-wavelength gravity they are less influenced by components) and to map gravitational and air drag the Earth’s surface perturbations (topography, oceans, ice caps, lakes, rivers, and soil moisture 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 46 VLBI SLR DORIS GNSS 2.3 GRAVITY OBSERVATIONS AND INSTRUMENTS PAGE | 47 Satellite-based gravity field observations Satellite altimetry GNSS Radar Occultation Interferometric Synthetic Aperture Radar (InSAR) EARTH’S GRAVITY FIELD PAGE | 48