Türkiye astrojeodezik ve astrogravimetrik jeoidinin belirlenmesi

Abstract

Yer gravite alanının deniz yüzeyi ile çakışan eşpotan siy elli yüzeyine jeoid adı verilir. Jeodezinin ana hedeflerinden birisi jeoidi, jeodezik hesapların yapıldığı bir referans elipsoidine göre belirlemektedir. Jeoid belirlemenin esası, üzerinde jeodezik hesapların yapıldığı referans elipsoidi ile jeoid arasındaki uzaklıkların (jeoid yüksekliklerinin) bulunmasıdır. Jeoid yüksekliklerinin belirlenmesi için değişik yöntemler vardır ve bu yöntemler çoğunlukla kullandıkları ölçülerin adlan ile anılırlar. Bu çalışmada astrojeodezik çekül sapmaları ve gravimetrik çekül sapmaları ile gravimetrik jeoid yüksekliklerinin ölçü olarak kullanıldığı astrojeodezik ve astrogravimetrik jeoid belirleme çalışması yapılmıştır. Bu çalışmada, astrojeodezik ve astrogravimetrik jeoid belirlemesinde değişik data gruplarıyla jeoid belirlenmiştir. Astrojeodezik yöntemde astrojeodezik çekül sapmalarından, astrogravimetrik yöntemde ise astrojeodezik çekül sapmalarının yanında gravimetrik çekül sapmalanda kullanılmıştır. Astrojeodezik çekül sapmaları Astronomik enlem ve boylam ile Avrupa 1950 datumundaki (ED-50) jeodezik enlem boylam değerlerinin karşılaştınlmasıyla elde edilmiştir. Gravimetrik çekül sapmaları ise Ag gravite anomalileri, yerpotansiyel katsayıları ve sayısal arazi modeli yardımıyla en küçük karelerle kolokasyon (EKKK) ve N jeoid yüksekliklerinden yararla bikübik splines fonksiyonları ile elde edilmiştir. Daha sonra Astrojeodezik ve astrogravimetrik jeoid hesabı yapılmış ve sonuçlar sunulmuştur. Kullanılan ölçü noktası sıklığının artmasının belirlenen jeoidin doğruluğu üzerinde etkili olduğu görülmüştür. Ayrıca astrojeodezik jeoide getirilen gravimetrik düzeltme ile elde edilen astrogravimetrik jeoidin daha doğru olduğu belirlenmiştir. Ancak astronomi ölçülerinin yeterli sayıda olmadığı da düşünülmektedir.

As it is well known, all geodetic measurements are related to the earth's surface, however computations are performed on an ellipsoid. Geodesists employ various corrections or transformations to reduce their observations onto the ellipsoid. However, some measurements which are made on the earth's surface refer to another surface, the geoid. In geodetic surveying, one normally performs the computation of geodetic coordinates of points on an ellipsoid which closely approximates the size and the shape of the earth in the surveying area. Geoid can be defined as the surface to which the oceans conform over the entire earth. Geoid is an irregular surface due to the uneven distribution of the earth's mass. An ellipsoid, reversely, is a regular surface to which the geodetical calculations refer, and the differences between these two important surfaces are the geoid heights (geoid undulations) or geoid separations which stand for the distance between geoid and ellipsoid. It goes without saying that there is only one geoid for the earth, but an infinite number of ellipsoids. So, it is quite common to depict geoid undulations with reference to a particular ellipsoid, either earth-fixed or not. Geoid is a surface on which every point has the same gravity potential. The direction of the gravity is always perpendicular to surface of geoid. The geoid is assumed to continue under the lands. Despite its great conceptual meaning, determination of geoid is always in the hands of a few specialists in the world. This was due to the practical use of the heights above the mean sea level. It is quite possible to have orthometric corrections if there exist gravity observations around. So, from the practical point of view, people did not attempt to determine the geoid. There are, of course, other reasons why people are so late to determine geoid. These can be classified as the lack of data, ineffective computer facilities, etc. But today, especially with the advent of the Global Positioning System (GPS), it became compulsory to have a high-accurate geoid because GPS gives us ellipsoidal heights which are not used in most of the geodetic activities. It was then necessary to transform ellipsoidal height (h) to the orthometric height (H) by means of the geoid undulation. This VI is why geoid still constitutes one of the major topics of higher geodesy. The increase in the amount of related data and new computer facilities made it possible to determine geoid. There are various methods to determine geoid. These methods are named after the observations on which the determination is based. In this study, astrogeodetic and astrogravimetric geoid determination will be discussed. Astrogeodetic geoid to be explained in this study makes use of the astrogeodetic deflections of the vertical, whereas astrogravimetric geoid is determined by means of astrogeodetic and gravimetric deflections of the vertical as well as gravimetric geoid undulations. As it is seen clearly one can use different types of data separately or completely together. In most cases, the name of the geoid explains the types of the data used in the determination of the geoid. In this study, both the astrogeodetic and the astrogravimetric geoid determination are reviewed and various applications using different groups of data are made for Turkey. In the beginning, coordinate systems related to the astronomic and geodetic observations are discussed briefly. This is obviously necessary to understand the meaning of deflections of the vertical. As it is known, all measurements are made on the physical surface of the earth but computations are referred to the ellipsoid, either earth-fixed or not. Measurements made on the physical surface of the earth are referred to the level surfaces which do not allow to make computations. This is why scientists developed new surfaces which are proper for geodetic calculations. The geodetical problems in Turkey are solved by means of the positions or coordinates of the related points. These coordinates are defined according to the coordinate systems. The coordinate systems can be classified as natural and model(referance) coordinate systems. The coordinate systems give information on the definition of the deflections of the vertical. Deflections of the verticals are absolute or relative depending upon the ellipsoid which is used at geodetical works. Deflections of the vertical is absolute if the elipsoid used is earth-fixed, relative if the ellipsoid is local or relative. Geoids determined by absolute deflections of the vertical are absolute geoid, otherwise relative geoids if the deflections of the vertical are relative. Deflections of the vertical (DOV) are obtained by using different methods depending upon the different types of data. If necessary to make a classification, one can define the types of DOV as, astrogeodetic DOV, gravimetric DOV and topographic-isostatic DOV. Astrogeodetic DOV are obtained by comparing the astronomic latitude , astronomic longitude A by geodetic latitude (p, geodetic longitude A. by the well-known equation