Lageos I ve Lageos II için doğruluk analizi

Abstract

Bu çalışmada, LAGEOS - 1 ve LAGEOS - II lazer uydularına yapılan SLR (Satellite Laser Ranging) ölçmelerinin doğrulukları araştırılmış, istasyon nokta konumları belirlenmiş ve farklı bir stokastik model kullanılarak yıllara göre doğruluk analizi yapılmıştır. 1994,1995 ve 1996 yıllarına ait yer istasyon noktalarının SLR verileri NASA-CDDIS'ten (National Aeronautics and Space Administration - Crustal Dynamics Data Information System) elde edilmiş ve MERIT-II format ına çevrilerek RGO (Royal Greenwich Observatory)'da oluşturulan SATAN analiz programında kullanılmıştır. SATAN'ı oluşturan ana programlardan biri olan ORBIT ile uydunun aylık süreç içindeki konumu ve yörüngesi hesaplanmış, Helmert'in varyans analizi yönteminin diğer ana program RGODYN'a entegrasyonu ile nokta konumları ve standart sapmalar hesaplanmıştır. Yapılan analizlerin sonuçları t (student) - testine tabi tutularak karşılaştırılmış, ayrıca LAGEOS - I ve LAGEOS - II için kullanılan benzer noktaların da karşılaştırılması yapılmıştır. Bundan başka, çalışmanın içinde SLR kavramı, ölçme tekniği ve aletleri, getirilen düzeltmeler, verilerin toplanması - sıkıştırılması ve SLR uyduları konularına da geniş olarak yer verilmiştir.

The emergence of satellite geodesy as a useful tool for geophysical research has been stimulated by the development of high-accuracy tracking techniques for determining satellite positions. The most advanced and accurate of these techniques is the satellite laser ranging (SLR). In fact, during just the last 10 years the quality and quantity of SLR data have improved several-fold, as witnessed by their emergence as an increasingly important data set for geodesic and goedynamic studies. SLR can be used for: global and regional positioning, polar motion and earth rotation parameters, determination of the satellite orbits, earth gravity field determination, crustal dynamics studies, solid earth and ocean tides, determination of the conventional terrestrial and conventional celestial reference systems. The advantages of laser measurements reside in the high accuracy and in not having to rely on satellite-borne sources of energy. As in any method which utilizes light, it is necessary that the target can be optically seen. In an SLR measurement the round-trip travel time of a photon pulse from a laser at an observatory to cube corner reflectors located on the satellite is measured. The laser pulse is emitted through the transmitting optics; at the same instant, the time counter begins to record the time. The reflected pulse collected by the receiving telescope is channeled, upon ampilification in a secondary-electron multiplier, to the time counter. The laser and receiving telescope are mounted such that they can automatically follow the satellite, according to the precalculated orbit. Laser ranging is only possible to satellites equipped with appropriate reflectors. The incoming laser light must be sent back in exactly the same direction from which it comes. Such types of reflectors are also called retroreflectors. A retroreflector can be created by cutting an evenly sized pyramid from the corner of a cube. This is why they are often named corner cube reflectors. The measured travel time is converted into a range through the speed of light. The basic observation equation is At d = -.c c ; speed of light (299 792. 458 km/s) Earth's gravitational parameter used in calculations; GM=398600.44 km3/s2 The distance from tracking site to a satellite can be determined to a precision of better than a centimeter using current technology and techniques. Repeated range measurements are made on the satellite by a number of different tracking stations. The acquired range data are combined with a dynamical model for satellite motion to deduce parameters describing the satellite orbit, tracking station coordinates and xi various model parameters. The most important model parameters are geopotential values, polar motion and earth rotation parameters and tidal amplitudes. Although almost all SLR systems are capable of ranging to a variety of satellites, the majority of the observed satellite passes are to LAGEOS I. The Laser Geodynamics Satellite (LAGEOS I) is one of the first artificial passive satellites developed exclusively for geodynamic measurements using laser-ranging techniques. LAGEOS I was launched by NASA from the Western Test Range in California on May 4, 1976. It was carefully designed to minimize aspherical radiative effects and was launched into a high altitude (about 6000 km.) near- circular orbit to diminish the modeling problems associated with the rather poorly known short-wavelength gravity field and errors arising from mismodeled non- conservative forces like atmospheric drag. The satellite is a sphere, 60cm. in diameter, having a mass of about 407 kg. The spherical aluminum outer portion of the satellite has a mass of 117 kg. Embedded within it are 422 cube corner reflectors made of fused silica and four made of germanium. A cylindrical brass inner core of the satellite is 27.5 cm. long and 31.76 cm. in diameter and has a mass of 175 kg. LAGEOS I is in a high inclination orbit (/' = 109.8°) and is therefore viewed by stations deployed over most of the earth's surface on a regular basis. In a cooperative venture between the NASA and the kalian Space Agency (ASI). LAGEOS II was launched on October 23, 1992 with the Space Shuttle. The physical properties are nearly identical to those of LAGEOS-I. The weight is slightly less at 406 kg. The spacecraft will carry 426 optical corner cube retroreflectors. The orbit is a near-circular with an altitude of 5900 km. and an inclination of 52 degress. Other laser satellites are described below in detail. STARLETTE was launched by the French Space Agency CNES (Centre National d' Etudes Spatiales) on February 6, 1975. It was the first satellite to be designed with minimized surface forces in order to allow highly precise laser ranging. The core consists of Uranium 238 with a density of 18.7, formed as an icosahedron with 20 triangular planes. Each triangle carries a spherical aluminium cap with three integrated retroreflectors. STARLETTE is also a sphere, 24cm. in diameter, having a mass of about 47 kg. 60 retroreflectors were adopted on it. it's orbit inclination is 49.8°. Because of the rather low orbit (960 km.), STARLETTE is particularly suitable for the study of solid earth tides and related elasticity models of the earth. The Japanese Experimental Geodetic Satellite (EGS), also named AJISAI, was launched on August 12, 1986 into a circular orbit of 1500 km. altitude and 50° inclination. The orbital period is 1.93 hours. The spherical satellite has a diameter of 214 cm, a mass of 685 kg, and it carries 120 laser reflector assemblies. The satellite can be used for laser range and photographic direction measurements. In January and May 1989 the former Soviet Union launched two spherical satellites, named ETALON-1 and ETALON-2, each time together with two GLONASS satellites into rather high orbits. The characteristic parameters; altitude 19100 km., orbit inclination 65°, diameter of sphere 1.294 m., mass 1.415 kg., 306 reflectors. In satellite geodesy two types of solid state pulsed lasers are used, the ruby laser and the Neodymium-YAG laser. Ruby is the classic material of solid state lasers. It xii is a crystal, absorbing green and blue-violet light and emitting sharp red spectral lines at 694.3 nm. By changing the resonator quality and opening the resonator at the predefined maximum of energy absorption, single laser pulses can be generated with a pulse width of about 10 to 50 nanoseconds and a peak power of 1 Giga Watt. The process is controlled by the so-called Q-switch (Q stands for quality). With a special arrangement of the Q-switch inside the resonator it becomes possible to reduce the pulse width to 2-5 ns. This is, however, the upper limit of performance for a ruby laser. Another way of generating short pulses is the coupling of longitudinal resonator oscillations, the so-called modes, through active modulators, producing a defined sequence of short, high energy pulses. In particular the Neodymium-YAG laser (YAG=Ytrium-Aluminium-Granat) is suited for the mode-coupling. This technique makes a reduction of the pulse width to 100 to 200 picoseconds possible. It also requires less pumping energy and hence provides a better system performance and a higher pulse repetition rate. Finally the frequency is doubled and with a wavelength of 530 nm (green) instead of 1060 nm (infrared), produces better conditions for the reception of return pulses. The achievable range accuracy is strongly correlated with the length and resolution of the laser pulses. Usually the operating laser systems are assigned to one of the following groups (generations), according to their concept and accuracy level First Generation pulse lengths of 10 to 40 ns, corresponding to 1 to 4 m. in range accuracy; mostly ruby laser with Q - switch. Second Generation pulse lengths of 2 to 5 ns, corresponding to 30 to 100cm; application of sophisticated pulse analysis methods. Third Generation pulse lengths of 0.1 to 0.2 ns, corresponding to 1 to 3 cm; mostly mode-locked Nd: YAG laser; single photon detection capability. 1 nano second (ns) = 15 cm. The SLR systems of the first and second generation are almost exclusively equipped with ruby lasers, whereas the third generation systems mostly use the Nd:YAG laser. The range measurements have been processed in the form of so-called "normal points". These synthetic measurements represent, in a condensed form, the tracking information embedded in the many thousands of raw observations that may be acquired during each pass of LAGEOS. One normal point is created for every two minutes of data. The use of normal points has three important advantages: first, the number of data points is dramatically reduced without loss of tracking information. The second advantage is the improved global weighting of the data, since the number of normal points per pass is determined by the lenght of the observation periods only. Finally, the full-rate data screening and normal point generation eliminates bad data points and provides a good estimate of the noise level of the original data; passes with ranging problems can be identified easily and are completely edited out. Satellite laser ranging data processing techniques are generally divided into two categories: long and short arc methods. The long arc technique models the satellite orbit for a few days to a year or more, whereas the short arc deals with a XIII period of a few minutes or even less. Long arc solutions utilize tracking data from a worldwide network of tracking stations. The short arc technique minimizes the effects of orbit errors and gives very precise baselines between the simultaneously observing stations. In order to describe the actual measuring process it is necessary to introduce additional parameters and corrections into the simple basic observation equation. d = -c.At + Ad0 + Ads + Adb +Adr + tj In this equation; At = measured flight time of the laser pulse between the start and the stop signal Ada = eccentricity correction on the ground Ads = eccentricity correction at the satellite. Adb = signal delay in the ground system. Adr- refraction correction 7/ = remaining systematic and random observation errors. The first SLR system was developed at NASA (National Aeronautics and Space Administration) Goddard Space Flight Center (GSFC) in 1964. The NASA Geodynamics Program was initiated in 1979 to coalesce the emerging technologies of Satellite Laser Ranging (SLR), Lunar Laser Ranging (LLR) and Very Long Baseline Interferometry (VLBI) all having the potential for the detection of tectonic plate motion and crustal deformation and the use of satellites for mapping the geopotential fields into a coherent program for the study of the solid Earth. The Geodynamics Program was subdivided into three areas: Earth Dynamics, Crustal Motion and Geopotential Research. A major element of the Geodynamic Program, the Crustal Dynamics Project (CDP) has the primary responsibility for conducting laser ranging measurements on LAGEOS. Numerous other domestic and foreign institutions are cooperating in data collection, analysis and interpretation. The CDP was formed in 1979 to apply space technology, both in the form of satellite laser ranging and very lang baseline interferometry to the measurement of tectonic plate motions, regional crustal deformations, polar motion and earth rotation and other phenomena associated with crustal movements. Twenty-three countries were participating in this program. In the Mediterranean region, the CDP is participating with WEGENER in a Long- term set of SLR measurements. WEGENER is the first European group to study crustal dynamics. It was founded in 1981 to respond to the NASA announcement of opportunity for participation in the Crustal Dynamics Program. The first project of the group was the WEGENER/MEDiterranean LASer ranging project, which was launched in 1985. This project consists of field operation, data analysis and interpretation of the results. Italian, Greek and Turkish groups participated in the xiv operational activities. The first two campaigns were organized in 1987 and 1989 at Turkish sites and equipment was provided by France, Germany, the Netherlands and the U.S.A. The most commonly used satellite for the WEGENER/MEDLAS compaign is LAGEOS-1. The combined NASA and NGS (National Geodetic Survey) programs involved 23 countries in SLR and VLBI observations using 38 fixed and 8 mobile systems. The accuracy of the fixed SLR and VLBI systems was demonstrated at certain sites at the subcentimeter-level. Plans were made for further improvements with the goal of achieving the few mm-level. Mobile systems are:. TLRS-1, TLRS-2, TLRS-3 and TLRS-4 (U.S.A). MTLRS-1 (IfAG, Germany). MTLRS-2 (University of Delft, The Netherlands). HTLRS (Japanese Hydrographic Department). FTLRS (France). SALRO (Saudi Arabia). ITLRS(İtaly) Data Analysis Centers throughout the world and particularly in countries which support SLR Observatories conduct their own individual analyses of the observations. For example, in Tokyo, three analysis methods are used; multi-pass method, SRD (Simultaneous Range Differences) method, Single-pass method. The SLR analysis software CONCERTO developed at CRL (Communications Research Laboratory) is used for the following research of local solutions. This software is based on the physical models which are recommended by IERS Standarts. In France, the CNES/GRGS GINS software has been developed and upgraded over more than 20 years for dynamic space geodesy applications. The core of GINS consists in a iterative least squares adjustment of selected parameters from the observables and uses precise numerical integration. Real - time programs used in Graz (Ranging and Calibration) are written as simple sequential programs, running under DOS. The programs are extremely structured and very easy to maintain- improve-change. The software package for orbital dynamic analysis and least- square parameter estimation SLRP has been developed at the Central Laboratory for Geodesy in Sofia (Bulgaria) since 1987. The program utilizes the state-of-art modeling of the orbit, numerical integration of both the equations of motion and variational equations and the Gauss-Newton estimation technique. The station coordinates, Earth orientation and station velocities have been regularly provided to the IERS (International Earth Rotation Service) since 1992. The analysis with the GEOSAT multi-purpose space geodesy software developed at NDRE (Norwegian Defence Research Establishment) during the last decade. In this software, the most precise reference frames, dynamical models, and measurement models available are used and updated continually as better information comes along. But xv some countries are used SLR analysis programs (GEODYN and SOLVE) of NASA. For example, both GEODYN II and SOLVE II run on the Convex 3840 supercomputer of Delft University of Technology. The GEODYN orbit determination system is based on a Bayesian weighted least squares adjustment of tracking observations to a satellite orbit by using a numerical orbit integration scheme. The system posseses the capability of estimating station locations from multiple arcs of data from several different satellites simultaneously as well as adjusting all components of the earth's orientation. Individual least squares normal matrices are formed from each 30-day segment of observations. These matrices are combined, and a solution parameter subset is selected through the utilization of the SOLVE system. The I.T.U. (Istanbul Technical University) SLR data analysis software is based on the SATAN package (SATellite ANalysis) written at the Royal Greenwich Observatory (RGO), England. The package implemented at I.T.U. consists of two main parts. The first program, ORBIT, calculates the orbit of a satellite and the partial derivatives of the coordinates of the satellite with respect to parameters to be solved for that affect the orbit. These include the start state vector (initial satellite position and velocity), a selected set of parameterised force coefficients such as the solar reflectance coefficient and an along-track acceleration, but not earth rotation parameters (ERPs), individual pass and station parameters or station coordinates. The orbit computation is carried out using the Gauss-Jackson 8 the order numerical integration method, with the step length depending on the satellite orbit being modelled. The forces modelled conform to those recomended in the Project MERIT Standarts. MERIT (an acronym for Monitor Earth Rotation and Intercomparison of Techniques of Observation and Analysis) standarts for common parameters such as solid Earth tides and astronomical constants are accepted internationally. The second program, RGODYN, uses output from ORBIT to compute the residual of the measured range for each SLR observation and to form the partial derivates of the range with respect to parameters to be solved for that affect the orbit and also parameters related to the station such as station coordinates and ERP's. The program forms the observation and normal equations and carries out a least squares solution for the parameters. It also computes the unit variance factor and covariance matrix of the parameters in order to quantify their precision. The variance component estimation technique has been introduced into the parameter estimation program RGODYN. The modified program is called RGOVCE (Royal Greenwich Observatory Variance Component Estimation) Besides the input files used in RGODYN, the program RGOVCE is also controlled by a file (GROUP. DAT) which defines the initial standart deviations of the laser stations, the required number of groups and the name of the stations in any individual group. Hence only the initial standard deviations are supplied to the program. In order to compute the observation residuals, the program RGOVCE is rerun with the estimated parameters.