Gravite ölçerler ve çalışma prensipleri
Gravity meters and their workink principles
- Tez No: 39323
- Danışmanlar: PROF.DR. ORHAN BAYKAL
- Tez Türü: Yüksek Lisans
- Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
- Anahtar Kelimeler: Yer çekimi, Ölçme aletleri, Gravity, Measurement devices
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Gravite, dünyanın kütlesinin oluşturduğu çekim kuv¬ veti (gravitasyonel kuvvet) ile dünyanın kendi ekseni etrafında dönmesinin meydana getirdiği merkezkaç kuvvetin bileşkesidir. Yapılan gravite ölçme ve hesap işlerinin tümüne gravimetri denir. Gravimetrideki amaç yeryuvarının şekli ve büyüklüğü ile ilgili problemlerin çözümlenmesidir. Yeryüzünde gra vite ölçmesi demek, yere doğru serbest düşüş yapan^bir cismin ivmesinin ölçülmesi demektir.“Gal”(cm.s ) biriminde olan gravite ivmesi kutuplardan ekvatora gidildikçe küçülür. Bu da yerkürenin kutuplarda basık olduğunun bir göstergesidir. Yapılan tüm gravite ölçmelerinde, enlem etkisi, yükseklik etkisi (serbest hava etkisi+Bouguer et¬ kisi), topoğrafik etki, izostati etkisi, atmosfer etkisi, gel-git etkisi bulunmakta ve bundan dolayı ölçme değerleri¬ ne düzeltmeler getirilmektedir. Gravimetride, mutlak gravite ve bağıl gravite olmak üzere iki çeşit ölçme yöntemi bulunmaktadır. Mutlak gra¬ vite ölçmesi, bir noktada gravite değerinin direkt olarak ölçülmesi anlamına gelmektedir. Serbest düşme yöntemine uygun aletler ve sarkaç donanımlarının kullanılmasıyla mutlak gravite ölçmeleri yapılabilmektedir. Bağıl gravite ölçmesi ise keyfi seçilen bir nokta ile bir baz noktası arasındaki gravite farkının ölçülmesi demektir. Bu tür ölçmelerde ise sarkaçlar, burulma terazisi ve farklı prensiplerde çalışan gravimetreler kullanılmaktadır. Jeodezide kullanılan tüm ölçme aletlerinde olduğu gibi gravimetrelerin de periyodik olarak kalibre edilmesi gerekmektedir. Kalibrasyon için eğim değişimi yöntemi, kütle değişimi yöntemi veya gravite değeri önceden bilinen noktalarda yapılan ölçmelerle kalibrasyon yöntemi kullanılmaktadır. Ayrıca dış etkenlerin ve gel-git olayının neden olduğu alet driftinin çeşitli yöntemler (fark, yıldız, adım ve profil yöntemleri) kullanılarak belirlenmesi gerekmektedir. Bu çalışmada yukarıda sözü edilen konulara genel olarak değinilmiş, özellikle gravimetride kullanılan gravite ölçerlerin çalışma prensipleri ve hata kaynakları ayrıntılı olarak açıklanmıştır.
Özet (Çeviri)
GRAVITY METERS AND THEIR WORKING PRINCIPLES SUMMARY Gravity, which has to be measured on the surface of the earth, contains information about the measurement location (geodetic utilization), about the mass distribu- tion in the interior of.the earth (geophysical utilization) and in the case of repeated measurements, about temporal variations of the earth's body (geodynamical utilization). The first gravity measurements in the 17th and 18th Century are triggered by the development of the mechanics of rigid and deformable bodies. Measurements of the magnitude of the earth's gravitational acceleration have been made since the time of Newton. Developments are governed by the interaction of technological possibilities and scientific objectives in geodesy, where practical tasks in geodetic surveying have an increasing influence. Measurement of acceleration in geodesy is principally intended to solve problems associated with the shape and size of the earth. Gravitation is öne of the fundamental forces in the universe, observed as the attraction between two bodies and according to Newton's law of gravitation, proportional to the product of their masses and inversely proportional to the square of the distance between them, i.e., m-.m,, F= G. -i-/ r where F= the force between two particles of mass m, and m2 r= distance between them G= gravitational constant which was invented with the experiment of torsion balance by Henry Cavendish,in England in 1798. Its value is 6,673x10 m3kg~1s2. Gravity is the force which is the resultant of gravitation, the force exerted by the mass of the Earth, and the centrifugal force, caused by the rotation of the Earth, Centrifugal force, due to the earth's rotation, tends slightly to counteract the force of gravity. Because the earth is a spheroid flattened at the poles and because of the rotation of the earth. the value of_2 gravity iş at a maximum at the poles (983.22 cm.s ) and at a minimum at the eguator (978.03 crn.s“2}. The basic cgs unit of acceleration used to describe gravity is the ”gal“, named for Galileo. 2 l gal = l cm/s l gal = 1.000 milligals (mgal) l gal = 1.000.000 microgals (ygal) 2 5 l m/s = 10 milligals ”Gravitation“ and ”gravity“ are occasionally used as if they were synonymous. Such usage can be misleading. The term gravity is used for both the force and for the acceleration, and for both the vector and its magnitude. The representation of the gravity field and related computations are simplified if we consider the scalar quantity ”potential“ instead of the vector guantity ”acceleration“. Gravity potential, W(r) = V(r) + Z (r) V= gravitational potential Z = centrifugal potential g= gradV + grazZ Gravity measured on the Earth's surface varies with position because the distance of the measurement station from the centre of mass of the Earth is not constant and because of variable topographic attractions. it is necessary, therefore, to reduce the measurements to some standard so as to give a geodetically useful gravity values that is representative över a reasonably large area about the point of observation. in order to compare the pull of gravity from point to point on the Earth, six corrections must be applied to gravimeter measurements. These corrections are latitude, elevation (free,air and Bouguer correction), topographic, isostatic, atmospheric and tidal. Latitude correction: The value of gravity increases with the geographical. latitude. For the latitude dif f erence between two stations, the correction becomes 6 g = 0.8122 sin2 ı/) mgal/km ıj) is the latitude of observation point. This correction must be subtracted from ör added to the measured gravity difference according as the station is on a higher ör lower latitude then the base station. Elevation correction: Free-air correction + Bouguer correction. Free-air correction: A gravimeter can detect the increase in gravitational pull when it is moved as viilittle as a meter from the top of a table to the floor. Therefore, ali measurements must be adjusted för elevation., in order to do so, graviıtıeter readings are adjusted as if they were made at the surface of a reference ellipsoid that lacks topographic variations. The Earth's reference elipsoid corresponds approximately with sea level. This correction is called the free-air correction because it does not take into account the attraction of any earth material above sea level. 6gFA= 0.3086.h mgal h is the elevation from sea level of observation point. This correction is added to observed gravity. Bouguer correction: When a gravimeter reading is adjusted to the reference ellipsoid value, account must be taken of the gravitational attraction exerted by the rock lying between the gravimeter and the ellipsoid. The correction that completes the adjustment for topography is called the Bouguer correction; it has an effect opposite to that of the free-air correction. 6gB= 0.04191.p.h mgal 2.0<p<2.67 gr/cm3 This is subracted because we are effectively removing the material between sea level and the station level. Since the free-air and Bouguer corrections are both proportional to elevation above sea level, it is usual to combine the two into a elevation correction. <sgE= 69FA +69B 6g_= (0.3086.h-0.04191.p.h) mgal E 6g = 0.1967.h mgal Ül Topographic correction: This correction accounts for the attraction of ali material higher than the gravity station and also removes the effect of material. it is always added whether the feature is a hill ör valley. Isostatic correction: The isostatic gravity correction is an ad hoc correction invented to make predicted values of acceleration agree better with measured values. There are many different kinds of isostatic gravity corrections; each kind is character- ristic of a particular theory on how density varies within the crust and upper mantle. Ali the theories postulate that the crust and part of the upper mantle ”float“ on a underlying material of greater density. They differ in viiitheir assumptions regarding the depths to which the floating materials extend, the density of that floating material under the geoid, and in other particulars. These theories about isostatic corrections are Pratt-Hayford, Airy-Heiskanen and Vening Meinesz. Atmospheric correction: The masses on the level surface which passes through the measurement point decrease the value of the gravity as in topografic correction. Atmosphere is also mass and decrease the value of gravity acceleration. Tidal correction: In addition to the attraction of the earth's mass, the attraction of the moon's and sun's mass is considered when we need to measure gravity with very high accuracy. The attraction of the sun and the moon change the gravity at a station during the course of a day. The effect of the moon's and sun's attraction is called the tidal effect, because it is also in connection with the tides. This periodical attraction- tidal force, can be obtained at any point of the earth's surface by subtracting the attraction of the celestial body-in this case, the moon and sun-at the computation point from the attraction of the same bodies at the earth's center. The combined effect of the attraction of the moon and sun depends on the direction of these bodies. There are essentially two types of gravity measurement, absolute and relative. An absolute measurement consists of measuring the value of the acceleration due to gravity at a point, whereas a relative measurement gives only the difference in gravity between two points. Absolute gravity measurement: Nowadays the absolute value of gravity has great importance when creating a gravity net all over the world.Measurements of the absolute value of gravity are required in the determination of a number of physical quantities and in calibrating precision instruments in the laboratory. Two methods have been used for the precise determination of the absolute value of gravity; these are pendulums and the observation of a body free fall. Measurements of a free-falling mass: Suppose that a small objects is released from a stationary position. The earth's gravitational attraction g will cause it to fall a distance z during the lenght of time t according to the well-known formula z= - gt 2 which can be rearranged to obtain g= 2z/t2 IXGravity can be determined simply by timing the fall of object through a measured distance. It will fall 1 meter in slightly less than one-half second, indicating a gravitational acceleration of approximately 9 80 gals close to the earth's surface. One of the most accurate instruments combines two corner cube prisms and a laser. A corner cube prism is designed to produce by internal reflections a beam of reflected light that is parallel to the incident beam. The sharply focused and extremely intense light beam produced by the laser is separated into two perpendicular parts by the beam splitting device at position A. These beams travel to the two prisms where they are internally reflected and then rejoin at position B. There they are directed into a photomultiplier that is sensitive to light intensity. These light beams can be considered as oscillating waves. If both are oscillating in the same way when they join at position B, a particularly bright composite beam is produced. But if they are oscillating in opposition, the composite beam will be dark. Because one of the prisms is falling, its beam oscillations are alternately aligned, and then opposed, to beam oscillations from the stationary prism. Therefore, the composite beam is alternately bright and dark. The cycles of brightness are counted in the photomultiplier apparatus. Because the speed of light and the wavelenght of light produced by the laser are known to high precision, both time and distance can be determined by counting these cycles of brightness. The experiment with a falling corner cube must be done in a vacuum chamber s that air resistance will not slow the motion of the prism. This apparatus is not truly portable or easy to operate. Other devices measure the motion of a free-faaling object by means of laser interferometers. In one system a catapult projects the test mass vertically upward so that it passes through two horizontal light beams separated by a precisely measured distance. Motion of the mass is timed during its upward rise and again during its return fall as its passing interrupts the light beams. Another device records the times that two markers on a vertically falling rod pass a sensor. To find g at other places, we use a different kind of instrument that measures, quite precisely, the change in gravity 6g between one of these observatories and another more remote location. Pendulum measurements: An object suspended from a stationary pivot so that it is free to swing back and forth is called a pendulum. The period (T) of the pendulum is the time required for it to swing through on cycle of motion. The formula relating the pendulum period and the attraction of gravity is T= 2 ir/ 1 /mgh where m is the mass of the pendulum, I is its moment of inertia about the point of suspension, and h is the distance between the point of suspension and the center of mass. Ifthe pendulum consisted of a weightless string fixed at one end and attached to a point mass at the other end, then I/mh would equal the lenght I of that string. Its period would be and g= 4tt2. ±- T Relative gravity' measurements: To achieve the geodetic objective of determining the dimensions and shape of the planet it is necessary to reduce all gravity measurements to a consistent reference standard, a requirement that has become particularly important with the the widespread use of relative gravity meters for both geodetic and geophysical work. All gravity observations should be referred to the same gravity system or datum. In the past, local gravity surveys utilized different and sometimes arbitrary reference stations and values. Local surveys gradually developed into larger national or regional systems, usually referred to a national base station that inturn was directly or indirectly connected to the international absolute base station in Potsdam. With the adoption of the Potsdam absolute value of gravity (<3Potsdam= 981.274 cm.s”2) as an international reference value it became possible through relative gravity measurements to establish national absolute gravity base values in each country. These base values in turn have been used to develop networks of absolute gravity values in each country. An instrument used to measure relative gravity is called a gravimeter. The simplest form of a gravimeter is a pendulum. Pendulum measurements: Relative measurements of the acceleration of gravity by pendula are simpler than absolute measurements. They are based on the correct determination of the oscillation period T of the pendulum at various points of observation, assuming that its reduced length has not changed. If the acceleration of gravity g, is known at an initial point where the oscillation period has been determined to be T,, and if the oscillation period determined at another points is T_, g1= (27r/T1) 2.A and g2= (2tt/t2)2.£ Therefore, g2= g2 (Tl/T2)2 9i 2 2 6g= 4 * (Tj-*J) T2 is obtained. XIIn pendulum observations-absolute and relative alike-the following corrections must be taken into account: clock rate, vacuum (barometric), temperature and amplitude corrections. In addition to these corrections, oscillation period of the pendulum take co-oscillation of the stand, pendulum blade camber and geomagnetic field corrections in relative gravity measurements. Gravimeters: During the last twenty years great advances have been achieved in the construction of gravimeters, which measure directly the change in vertical force on a given mass. Gravimeters are now available which are light and easy to transport, and possess very small temperature variation and high sensitivity, some instruments measuring to a hundredth of a milligal. Gravimeters may be divided into two types: (1) the stable (2) the unstable type. In the stable gravimeters, a mass is suspended from a metallic spring or quartz fibre and a change in gravity displaces this mass, either through an elongation or a twisting of the spring. The displacement required to return the mass to the nominal or null position relates to the change in gravity by a spring constant that is determined through an appropriate calibration process. Typical are the Gulf and Graf-Askania gravimeters designed in the 1930s. In unstable gravimeters, a balancing force is introduced that produces instabilities such that changes in gravity produce much larger displacements from the equilibrium position than in the case of the stable instrument. Some of the most accurate unstable instruments include the LaCoste-Romberg and Worden gravimeters. These instruments designed for field observations. One of the first gravimetric instruments used in gravimetric surveying, was the gravitational torsion balance. Its design was proposed by Eötvös at the end of the 19th century. The gravitational torsion balance can be used to measure the second derivatives of the gravity potential W, W, W, Wa= W -W, from which xz yz xv Yv xx it is then possible to determine the magnitude and direction of the horizontal gradient of the acceleration of gravity and the curvature of the equipotential surface at the point of observation. Gravimeters should be regularly calibrated. Accurate observations at two places at which g is already known give the average value of k over the range covered. This range must not be smaller than the spread of the stations whose readings are to be based on it, nor so large that k is materially variable over the interval. Calibration of gravimeters can be done in three ways: (1) by change of mass, (2) by change of tilt, (3) by measuring at points with known values of the acceleration of gravity. In addition to calibration, drift of the gravimeter is also controlled. Gravimeter drift is the gradual change in the gravity reading over time; this change is xiiunrelated to actual gravity changes. There is inevitably a slow but regular change in the length of the spring. Drift is caused by creep in the gravimeter, external influences and tides. There is evidence that the drift rate depends on whether, or how, the meter is being transported. The drift rate function is defined by repeat readings daily or weekly or as necessary. It is not necessary to use the same station throughout for checking drift. These corrections can be taken directly off the drift curve, keeping in mind that positive drift requires negative correction. One of the following methods must be used to determine the drift easily: - difference method: 1-2-1, 1-2-1-2, 1-2-1-2-1-2, etc. - star method: 1-2-1-3-1-4-1, etc. - step method: 1-2-1-2-3-2-3-4-3, etc. - profile method: 1-2-3-4-... -1 or 1-2-3-4--4-3-2-1, etc. In this study, the subjects are handled which mentioned above. xxii
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