CG601 GEODESY 2 Sr Harith Fadzilah Abd Khalid

Topic One Introduction To Physical Geodesy At the end to this topic, student should be: At the end to this topic, student should be: able to explains the earth’s gravity, principle of gravity survey, absolute gravity measurement, relative gravity measurement, gravity data correction, gravity data reduction and introduction to dynamic satellite in geodesy.

Why physical Geodesy? In a quest to determine the shape of the earth, knowledge on the characteristic of the gravity field is needed, such as : Gravity field structure, Gravity field structure, Geoid undulating Geoid undulating Gravimetric vertical deflection, and Gravimetric vertical deflection, and Earth’s flattening Earth’s flattening In physical geodesy context, It is the resultant force of the earth’s attraction force and the centrifugal force due to the earth’s rotation. It is the resultant force of the earth’s attraction force and the centrifugal force due to the earth’s rotation.

A body rotating with the earth experiences the gravitational forces of the earth and of other celestial bodies, as well as the centrifugal force due to the earth's rotation. The resultant force is the force of gravity. It is a function of position, but also undergoes temporal variations Components of the Earth’s Gravitational Field

The unit of acceleration in the Sl-system( Systeme International d'Unites), Markowitz (1973), is ms -2. The acceleration of gravity can be measured with an accuracy of t o ms -2 ; the deviations of the terrestrial gravity field from a "normal earth", in general, remain less than 2 x ms -2. Therefore, the sciences of geodesy and geophysics have until recently adopted the more suitable units mgal = ms - 2, µgal = l0 -8 ms -2 =10 nms -2. They are derived from the unit "gal" (after Galilei) = cm s -2 or 1 gal = 1 cms -2 And the average gravity acceleration of earth is 980 gal = 980 cms -2 = 9.80 ms -2 The unit

Gravity value much influence by : texture and distribution of the earth’s mass variation of the earth rotation due to time factor Measured gravity will contained : location of the observation area/site earth’s mass distribution on the earth’s surface meant for geophysical use. Gravity

(Ocean basins mapped with satellite altimetry. Seafloor features larger than 10 km are detected by resulting gravitational distortion of sea surface. Source: Ocean gravity map

Gravity survey: The measurement of gravity at regularly

Basic Theory of Gravity -Gravitation and gravitational potential - law of universal gravitation

Basic Theory of Gravity - Gravitation and gravitational potential According to Newton’s Law of Gravitation (1687), two point masses m 1 and m 2 attract each other with the gravitational force (attractive force) where, G = gravitational constant, l = distance between point masses K & l = point in opposing directions b = gravitational acceleration or “gravitation”

Basic Theory of Gravity - or simply Newton’s second law : F = ma or in terms of gravity : F = mg Law of universal gravity : The average of g on the earth’s surface is 980 gal where it decrease about 5 gal towards equator.The average of g on the earth’s surface is 980 gal where it decrease about 5 gal towards equator.

Gravitational Potential An irregular earth surface, which no mathematical representation available but it is based on the ‘ equipotential surface ‘ at mean sea level.An irregular earth surface, which no mathematical representation available but it is based on the ‘ equipotential surface ‘ at mean sea level. At any point it is perpendicular to the direction of gravity.At any point it is perpendicular to the direction of gravity.

Gravitational Potential (Cont.) Equipontial surfaces Direction of mass attraction U S

Gravitational Potential (Cont.)

Summary By using the gravimetry technique, the topographic surface can be determined by analyzing the the gravity data.By using the gravimetry technique, the topographic surface can be determined by analyzing the the gravity data. The gravity field (potential force) of a point with m mass is :The gravity field (potential force) of a point with m mass is : U = Gm = constant i.e. r = constant U = Gm = constant i.e. r = constant r The gravity field (potential force) of a non rotated sphere is :The gravity field (potential force) of a non rotated sphere is : U = GM U = GM R The gravity field (potential force) of a rotated sphere is :The gravity field (potential force) of a rotated sphere is : U = - GM + 1 R 2 ω 2 cos 2 φ U = - GM + 1 R 2 ω 2 cos 2 φ R 2 R 2

Summary (cont.) On a rotated ellipsoid surface with angular velocity, ω, the gravity, γ, of a point at latitude, φ, the gravity acceleration is given as (Clairaut,1743):

The International Gravity Standard Formula is given as : Where B 2 and B 4 are constants. For GRS 1967 : B2 = B4 = γ e = Because of the flattening at the poles and the centrifugal acceleration, g, varies on the surface of an earth ellipsoid between 9.78m s -2 (equator) and 9.83ms -2 (pole). Summary (cont.)

Gravity Measurement 2 types:2 types: 1.Absolute Gravity Measurement –The determination of g from the fundamental acceleration quantities length and time. –Done by experts in a laboratory, using special advance and precise instruments. –Quite expensive –Methods : i.Free fall ii.Rise-and-fall iii.Pendulum

Underground Laboratory tomeasure gravity g at very high resolution

Gravity Measurement (cont.) 2.Relative Gravity Measurements -The measurement of a difference in gravity, ∆g by direct or indirect observation. -The observation done by one of the two acceleration quantities time or length kept fixed. -Can be performed with considerably more ease than the ‘absolute’ measurement.

Absolute Gravity Measurement 1.Free Fall Method: Relation between time travelled, t, through distance zRelation between time travelled, t, through distance z

Summary

Absolute Gravity Measurement (cont) 2.Rise and Fall Method: Relation between time travelled, t, through distance zRelation between time travelled, t, through distance z

Absolute Gravity Measurement (cont) 3.Pendulum Method: Relation between time travelled, t, through distance zRelation between time travelled, t, through distance z

Relative Gravity Measurement Two Categories : Two Categories : -Dynamic -Static Measurement : difference in gravity (∆g) Measurement : difference in gravity (∆g) between two stations between two stations Instrument used : Gravimeter Instrument used : Gravimeter

Relative Measurement

1) Dynamic Method - pendulum measurement - the periods of oscillation T1, T2, of the same pendulum are measured - calculation based on : Relative Gravity Measurement - with the invention of the spring gravimeter which is more exact and economical, the pendulum measurements have lost their importance.

2) Static Method – spring gravimeter - based on the principle of a spring balance. - the equilibrium position of a mass is observed as it is influenced by the acceleration of gravity and the counterforce of the elastic spring. - if gravity changes, the spring length will also change in order to reach static equilibrium again. Relative Gravity Measurement (cont.)

Static Method – In ‘V ertical spring balance’, the condition of equilibrium is given by: - by diferentiating the above equation, ∆g) and observed change in gravity (∆g) and observed difference in length ∆l is given by: difference in length ∆l is given by: Relative Gravity Measurement (cont.)

Static Method – In ‘ Lever Spring balance’, the spring counterforce (l-l o ) can act under arbitrary angle on the lever carrying the mass m. - the equilibrium condition for torques reads : Relative Gravity Measurement (cont.)

Methods of Measuring Relative Gravity 1)Traverse method Similar to theodolite traverse Starts at a known reference station (g is avaliable) and closed to the same station other known station. Usually used for measuring the gravity value of an area

2)Profile method Each points will be read twice. Only needs one known reference station (g is avaliable) Will provide more reading for adjustment and better result. Methods of Measuring Relative Gravity (cont.)

3)Star method Needs only one reference station Each point observed, have to referred back to the reference station More time needed, if observed points are quite distant Instrument ‘drift’ can be detected since repeated readings are available Methods of Measuring Relative Gravity (cont.)

4)Step method If precise result needed, this method will be chosen, such as establishing basic gravity network. Each point observed three times Observation can be closed to the starting station or other reference station Able to provide better ‘drift’ information at every measured points Costly in terms of time and money Methods of Measuring Relative Gravity (cont.)

Correction of Observed Gravity Data 1.Correction to Systematic Errors Instrument Height If the instrument placed on different height Free Air Correction Small difference in height : g = 2g o h/R = mgal/m where R – earth’s radius, g o - gravity at equator h – instrument height

Correction of Observed Gravity Data (cont.) 2.Earth’s Tides Earth’s surface subject to deformation cause by tides. This will cause periodical variation in gravity value. The variation is in the radial direction towards earth’s mass centre is around 0.2 mgal Concern only to precise works

Correction of Observed Gravity Data (cont.) 3.Drift Temporal variations arise in the zero reading of the gravimeter Drift is caused by the aging spring as well as uncompensated temperature fluctuations and by elastic aftereffects produced by locking and unlocking the lever

Gravity Data Reduction The variation of gravity is caused by the irregular shape and earth topography shape and earth topography The gravity reduction have to be reffered to a certain reference before any gravity data can be define and Used. The aims of the gravity reduction is to determin the geoid surface. There are several type of reduction, such as: a)Latitude Reduction b)Free air Reduction c)Bouguer reduction, and d)Terrain reduction

Assignment 2 : What are a)Latitude Reduction b)Free air Reduction c)Bouguer reduction, and d)Terrain reduction ?

Gravity Data Reduction

Satellite geodesy Is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques. It belongs to the broader field of space geodesy, which also includes such techniques as geodetic very long baseline interferometry (VLBI) and lunar laser ranging. Traditional astronomical geodesy is not commonly considered a part of satellite geodesy, although there is considerable overlap between the techniques. ** Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. * Very Long Baseline Interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy

The main goals of satellite geodesy are : Determination of the figure of the Earth, positioning, and navigation (geometric satellite geodesy) Determination of Earth's gravity field and geoid (dynamical satellite geodesy) Measurement of geodynamical phenomena, such as crustal dynamics and polar motion. Satellite geodetic data and methods can be applied to diverse fields such as navigation, hydrography, oceanography and geophysics. Satellite geodesy relies heavily on orbital mechanics.

The Jason-1 measurement system combines major geodetic measurement techniques, including DORIS, SLR, GPS, and altimetry.

DORIS - Doppler Orbitography and Radiopositioning Integrated by Satellite Is a French satellite system used for the determination of satellite orbits (e.g. TOPEX/Poseidon) and for positioning. SLR - Satellite Laser Ranging (SLR) a global network of observation stations measure the round trip time of flight of ultrashort pulses of light to satellites equipped with retro reflectors. Satellite altimetry

Laser Ranging System of the geodetic observatory Wettzell, Bavaria. This graph shows the rise in global sea level (in millimeters) measured by the NASA/CNES ocean altimeter mission TOPEX/Poseidon (on the left) and its follow-on mission Jason-1.T Image credit: University of Colorado