CG601 GEODESY 2Sr Harith Fadzilah Abd Khalid

Topic OneIntroduction To Physical Geodesy

At the end to this topic, student should be:

able to explains the earths 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,Geoid undulatingGravimetric vertical deflection, andEarths flattening

In physical geodesy context, It is the resultant force of the earths attraction force and the centrifugal force due to the earths 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 variationsComponents of the Earths 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 10-7 t o 10-8 ms-2 ; the deviations of the terrestrial gravity field from a "normal earth", in general, remain less than 2 x 10-3 ms-2.

Therefore, the sciences of geodesy and geophysics have until recently adopted the more suitable units

mgal = 10-5 ms- 2, gal = 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 earths mass variation of the earth rotation due to time factor

Measured gravity will contained :

location of the observation area/site earths mass distribution on the earths 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: http://www.ngdc.noaa.gov/mgg/bathymetry/predicted/explore.HTMLOcean gravity map

Gravitysurvey: The measurementofgravityat regularly

Basic Theory of GravityGravitation and gravitational potential law of universal gravitation

Basic Theory of Gravity- Gravitation and gravitational potentialAccording to Newtons Law of Gravitation (1687), two point masses m1 and m2 attract each other with the gravitational force (attractive force)where,G = gravitational constant,l = distance between point massesK & l = point in opposing directions

b = gravitational acceleration or gravitation

Basic Theory of Gravity or simply

Newtons second law : F = ma or in terms of gravity : F = mgLaw of universal gravity :

The average of g on the earths 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. At any point it is perpendicular to the direction of gravity.

Gravitational Potential (Cont.)

Gravitational Potential (Cont.)

Gravitational Potential (Cont.)

SummaryBy 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 :

U = Gm = constant i.e. r = constant rThe gravity field (potential force) of a non rotated sphere is :

U = GM RThe gravity field (potential force) of a rotated sphere is : U = - GM + 1 R22cos2 R 2

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

The International Gravity Standard Formula is given as :

Where B2 and B4 are constants.For GRS 1967 :B2 = 0.0053024B4 = 0.0000058 e = 978.032

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:

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 expensiveMethods : Free fallRise-and-fallPendulum

Underground Laboratory tomeasure gravity gat very high resolution

Gravity Measurement (cont.)

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

Free Fall Method:Relation between time travelled, t, through distance z

Summary

Absolute Gravity Measurement (cont)

Rise and Fall Method:Relation between time travelled, t, through distance z

Absolute Gravity Measurement (cont)

Pendulum Method:Relation between time travelled, t, through distance z

Relative Gravity Measurement

Two Categories : DynamicStatic Measurement : difference in gravity (g) between two stations

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 Vertical spring balance, the condition of equilibrium is given by:

- by diferentiating the above equation, change in gravity (g) and observed difference in length l is given by:Relative Gravity Measurement (cont.)

Static Method In Lever Spring balance, the spring counterforce (l-lo) 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 GravityTraverse method

Similar to theodolite traverseStarts 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

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.)

Star method

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

Step method

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

Correction of Observed Gravity DataCorrection to Systematic Errors

Instrument HeightIf the instrument placed on different heightFree Air CorrectionSmall difference in height :

g = 2goh/R = + 0.3086 mgal/m

where R earths radius, go - gravity at equator h instrument height

Correction of Observed Gravity Data (cont.)Earths Tides

Earths surface subject to deformation cause by tides.

This will cause periodical variation in gravity value.

The variation is in the radial direction towards earths mass centre is around 0.2 mgal

Concern only to precise works

Correction of Observed Gravity Data (cont.)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 topographyThe gravity reduction have to be reffered to a certainreference before any gravity data can be define and Used. The aims of the gravity reduction is to determinthe geoid surface. There are several type of reduction, such as:

Latitude ReductionFree air ReductionBouguer reduction, and Terrain reduction

Assignment 2 : What are Latitude ReductionFree air ReductionBouguer reduction, and Terrain reduction ?

Gravity Data Reduction

Satellite geodesy

Is the measurement of the form and dimensions of theEarth, 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 geodeticvery long baseline interferometry (VLBI) andlunar laser ranging.

Traditional astronomical geodesy isnotcommonly considered a part of satellite geodesy, although there is considerable overlap between the techniques.** Interferometryrefers to a family of techniques in whichelectromagnetic wavesare superimposed in order to extract information about the waves. An instrument used to interfere waves is called aninterferometer.* Very Long Baseline Interferometry (VLBI)is a type ofastronomical interferometryused inradio astronomy

The main goals of satellite geodesy are:

Determination of the figure of the Earth, positioning, and navigation (geometric satellite geodesy)

Determination ofEarth's gravityfield andgeoid (dynamical satellite geodesy)

Measurement ofgeodynamical phenomena, such ascrustal dynamicsandpolar motion.

Satellite geodetic data and methods can be applied to diverse fields such asnavigation,hydrography,oceanographyandgeophysics.

Satellite geodesy relies heavily onorbital mechanics.

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

DORIS - Doppler Orbitography and Radiopositioning Integrated by Satellite Is aFrenchsatellite system used for the determination of satellite orbits(e.g.TOPEX/Poseidon) and forpositioning.SLR - Satellite Laser Ranging(SLR) a global network of observation stations measure the round trip time of flight of ultrashort pulses oflight tosatellitesequipped 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 theNASA/CNESocean altimeter missionTOPEX/Poseidon(on the left) and its follow-on missionJason-1.

Image credit: University of Colorado