Assessment of Satellite Based and Terrestrial Measurement Techniques in Monitoring Vertical Deformations

Transcription

1 Assessment of Satellte Based and Terrestral Measurement Technques n Montorng Vertcal Serdar EROL, Rahm Nurhan ÇELİK, Bhter EROL and Tevfk AYAN, Turkey Keywords: Vertcal Deformaton, GPS, Levellng, Deformaton Analyss, Helmert Varance Component Estmaton SUMMARY Montorng and analyzng deformatons of large structures s ncluded n the man nterest of Geodesy Scence. In deformaton montorng, terrestral technques such as precse levellng and/or space-based technques such as GPS (Global Postonng System) are most commonly used measurement methods. In ths paper, the subject s vertcal deformaton analyss of a large vaduct across a lake. The vaduct s a very attractve test object wth ts geologcal and geotechncal condtons for deformaton research. Wth the am of determnng the deformatons of ths engneerng structure, a control network was establshed and four campagn GPS measurements were carred out. GPS measurements were supported by Precse Levellng Technque. Because of that the heght component s the least accurately determned GPS coordnate, due to geometrc weakness of system and atmospherc errors. Analyss were done accordng to three dfferent approaches; at frst two approaches, deformaton analyss usng the heght dfferences provded from the precse levellng measurements and from the GPS measurements were carred out separately. Then, as the thrd approach, the combned deformaton analyss usng the data from both measurement technques was done. In combnng process of heterogeneous data of two technques, the stochastc nformaton of the measurements was determned by the help of Helmert Varance Component Estmaton technque. In here, the detals about the computaton algorthms of all these three approaches wll be explaned. The results wll be gven both n numercally and graphcally. Interpretatons about the results are gong to be held n the concluson part of the paper too. 1/16 FIG Workng Week 004 Athens, Greece, May -7, 004

2 Assessment of Satellte Based and Terrestral Measurement Technques n Montorng Vertcal Serdar EROL, Rahm Nurhan ÇELİK, Bhter EROL and Tevfk AYAN, Turkey 1. INTRODUCTION AND BACKGROUND Technologc developments affect engneerng applcatons as well as all felds of human lfe. Usng the products of developed technology, very large szes of structures are constructed to serve humanty today. However, montorng these structures aganst destructons of natural effects, such as atmospherc and envronmental factors and perodcally occurred dsasters such as earthquakes, landsldes etc. s very mportant to beng sure on safety of them. Because, when a long perod of tme s consdered, the defects of these effects mght be much more serous. Accordng to ths necessty, much related to human health, montorng deformatons of these engneerng structures and analyzng of them consttutes a man nvestgaton area of geodesy scence. There are several methods to use measurng the deformatons of structures. These methods can be grouped nto two as geodetc methods and non-geodetc methods. The major motvaton of ths study as the subject of ths paper s geodetc methods. Untl 1980 s the deformatons of large engneerng structures were montorng usng conventonal geodetc methods, whch ncludes precson dstance-angle measurements and levellng measurements. After startng to use Global Postonng System (GPS) wth geodetc ams n the world wde, ths satellte based postonng system has also become a domnant technque n deformaton measurements branch of geodesy. GPS technque has benefts of hgh accuracy and smultaneous 3-D postonng; however there are handcaps about vertcal postonng usng ths technque. Because, the heght component s the least accurately determned GPS coordnate, predomnantly due to nherent geometrc weakness and atmospherc errors (Featherstone et al 1998). In most cases of deformaton montorng studes related to large engneerng structures, the requred accuracy level s consderably hgh such as mllmeter. GPS measurement technque satsfes the accuracy requrements for determnaton of D deformatons; on the other hand, the requred accuracy n vertcal may not be satsfed by usng ths technque, because of the nsuffcences mentoned above. Therefore, usng GPS measurement technque n deformaton measurements wth mllmeter level accuracy requres some specal precautons that ncrease the measurement accuracy n GPS observables va elmnatng or reducng some error sources such as usng forced centerng equpments, applyng specal measurng technques lke rapd statc method for short baselnes or desgnng specal equpments for precse antenna heght readngs (Erol and Ayan 003). In some cases, even these specal precautons mght be nsuffcent to reach the necessary accuracy level; at that tme to support GPS measurements wth a precse conventonal method such as precse levellng measurements would be very useful as an mprovng soluton. FIG Workng Week 004 Athens, Greece, May -7, 004 /16

3 All these summary nformaton, gven here untl now, s to mply the necessty and reason of ths study. The am of ths study s analyzng the vertcal deformatons of an engneerng structure usng GPS and Levellng measurements data. Durng the analyss, three dfferent approaches were appled. In the frst and second approaches, heght dfferences from precse levellng measurements ( H) and from GPS measurements ( h) were used n the analyzng algorthm separately, but n the thrd approach the combnaton of heght dfferences ( h and H) were used n the deformaton analyzng procedure. In combnng process of two observables groups ( h and H), Helmert Varance Component Estmaton Technque s used durng the determnng the weghts of observables as the stochastc part of the model. The theory, applcaton steps and results wll be explaned among the detals of followng sectons.. THEORY OF DEFORMATION ANALYSIS The conventonal deformaton analyss s managed n three steps n geodetc networks. In the frst step, the measurements, carred out n t 1 and t measurement epochs, are adjusted separately accordng to free adjustment method; outlers and systematc errors are detected and elmnated n ths step. In the second step, global test procedure s carred out and by ths test t s ensured that f the network ponts, assumed as stable, stayed really stable n the t = t t 1 tme nterval or not. In the global test, after the free adjustment calculatons of the networks (epochs) separately, the combned free adjustment s appled to both epoch measurements. Durng the combned free adjustment computaton, the postons of the assumed stable ponts, are gven as one-sngle group of ponts for both epochs, on the other hand the postons of the deformaton ponts n the t 1 nstant are assumed as f one group of ponts and the postons n the t nstant are assumed as another group of ponts. In addton to ths, n combned free adjustment, the partal-trace mnmum soluton s appled for the stable ponts ( tr( Q stable, stable ) = mn ) (Ayan 198; Ayan et al. 1991, Erol and Ayan 003). After determnng a group of stable ponts as the results of global test, the deformaton ponts are handled one by one and t s nspected that f ther postons are changed or not (Ayan 198, Ayan et al. 1991, Erol and Ayan 003)..1 Deformaton Analyss Usng Heght Dfferences.1.1 Deformaton Analyss wth Levellng Measurements To test the changes of heghts n ponts of a control network, measurements are carred out n duratons of t 1 and t. The network s adjusted separately by usng these measurement groups. Durng these calculatons, free network adjustment method s used and t s assumed that all of the pont heghts are changed. To use the same pont heghts as the approxmate values n both adjustment computatons s purposed. In the calculatons, outlers are elmnated and calculatons are repeated. It s amed that the measurement precson and network geometry are to be the same durng the both perod (Erol and Ayan 003). 3/16 FIG Workng Week 004 Athens, Greece, May -7, 004

4 The second step of analyss s called as global test. Wth ths test, t s determned f there s any vertcal dsplacement n a pont or a group of pont n the t = t t1 nterval. For carryng out the global test, the free adjustments of the measurements n duraton of t 1 and t and thereafter the combned free adjustment of two groups of measurements are employed. Ω = T 1 v1 P1 v1 Ω = T v P v Ω = v G T G P G v G Ω 1 S 01 = (1) f1 Ω S 0 = () f Ω G S 0G = (3) f G In the equatons, f 1, f, f G demonstrate the degree of freedom after the frst, the second and the thrd adjustment computatons correspondngly. As t s understood, equaton 1 belongs to free adjustments computatons of the frst epoch, equaton belongs to free adjustments computatons of the second epoch and equaton 3 belongs to the combne free adjustments. From these results that are found out n equaton 1, equaton, and equaton 3, the test value T G s determned as gven below. Ω + 0 = Ω1 Ω f 0 = f1 + f r = f G f 0 T G (Ω (Ω Ω G 0 ) / r = (4) / f ) 0 0 Ths test value s ndependent from the datum and ft to the F-dstrbuton wth n an assumpton. T G test value, s compared wth the crtcal value, chosen from the Fsherdstrbuton table accordng to r and f 0 degrees of freedom for S=1-α=0.95 confdence level. There after, f T < F, t s accept that the H 0 null hypothess that s mpled wth G r, f0,1 α H 0 : d H H1 = 0 = s true for the ponts of whch heghts assumed as f not changed. On the contrary, f TG > Fr, f0,1 α, t s sad that the ponts, whch had been chosen as stable were changed ther heghts. Then, the combned free adjustment and global test are repeated agan and agan as all of the ponts, whch had been assumed stable, are beng leaved out from the assumed stable ponts lst one by one, because each of them mght be responsble for the deformaton of the network composed by stable ponts. By ths way, the real stable ponts, whch are not changed ther postons durng the t tme nterval, are determned (Erol and Ayan 003). The followng step of the analyss s the localzng of heght changes. For dong ths, T H test values are calculated for the every network ponts, except the stable ponts, and they are compared wth F crtcal value that s gven from the Fsher dstrbuton table agan (Erol and Ayan 003). 4/16 FIG Workng Week 004 Athens, Greece, May -7, 004

5 d = H H 1 Ω Q T 1 0 dd S 0 = TH f0 r S0 d d Q = Q + Q (5) = dd H1H1 HH If the TH > Fr, f0,1 α, t s sad that the heght of the pont changed sgnfcantly. Otherwse, t s resulted that d heght dfference s not a dsplacement but t s caused by the random measurement errors (Erol and Ayan 003)..1. Deformaton Analyss wth GPS Derved Heght Dfferences Determnng vertcal deformatons usng GPS derved heght dfferences s based on the same calculaton algorthm as deformaton analyss wth precse levellng data, whch s explaned above very detal. In the algorthm, the ellpsodal heght dfferences (dh j ), whch were derved from the GPS baselne solutons, are used as measurements. Also, the stochastc nformaton of measurements comes from the GPS baselne solutons as m 0 (apror varance) and Q (cofactor value of heght dfference). From these values, m dh j dh j dh = m j 0Qdh jdh s j calculated as varance of GPS derved heght dfferences. The weght of GPS derved heght m0dh j dfferences s calculated as P dh =. In ths equaton s m 1 j 0dh = n the case study. j m.1.3 Combned Deformaton Analyss FIG Workng Week 004 Athens, Greece, May -7, 004 dh j In ths approach, heght dfferences, derved from both measurng technques, are used together and deformaton analyss s appled accordng to results of evaluaton of combned data groups. A very mportant pont that has to be consdered n the frst step of ths approach s that the both measurements groups derved from both technques do not have the same accuracy. And so, the stochastc nformaton between these measurements groups relatve to each other has to be derved. In ths study, for computng the weghts of both measurement groups derved from GPS measurements and levellng measurements respectvely, Helmert Varance Component Estmaton (HVCE) Technque have been used. Varance Analyss was developed at the very begnnng of 0 th century and frstly was appled to heterogeneous data n 1907 by F.R. Helmert (Grafarend 1984). So far, varance analyss technque has been appled to a lot of felds and the problems related to Geodesy and Photogrammetry Engneerng has become the frst among these felds. The purpose of varance component estmaton s to fnd realstc and relable varance components of the measurements to construct correctly the a pror covarance matrx of them. The method dvdes the measurements nto dfferent groups, and then smultaneously estmates the varance components for each group. Before a least square soluton s used, the a pror covarance matrx has to be estmated (Kızılsu 1998). Varance analyss technque has an ncreased mportance especally after satellte based measurement technques have become wdely used n geodetc applcatons. Because, satellte based measurements and terrestral measurements are used together wth n a same project to 5/16

6 serve the same purpose. However, wth ths am, when combnng these measurements s necessary, the correlaton between them and dfferent weghts of each measurement group causes problems n the computaton algorthms. Because of that t s dffcult to put together the measurements, whch doesn t have the same accuracy. In general, the weghts are derved expermentally n the laboratory envronments to use whle combnng these knds of measurements. However, these expermental processes could be dscussed, because, researches are shown that there are consderable dfferences between the weghts, computed accordng to varance analyss and expermental ones. A full dervaton of the technque and computatonal model of varance component estmaton are gven n Welsch 1978, Grafarend The summary of the mathematcal model s gven below (Kızılsu 1998). The Helmert equaton, Hσ = c (6) Matrx expresson of equaton 6 s: h h h 11 1 u1 h h h 1... u...h...h...h 1u u uu σ σ σ 1... u = c 1 c... c u where, u s number of measurement groups T c = v P v (8) h = n Tr(N N ) + Tr(N N N N ) (9) 1 1 h j = Tr(N N jn N ), ( j) (10) N s global normal equaton matrx ncludng all measurements, n s number of measurements n th measurement group, P s assgned weght matrx for th group, N s normal equaton matrx for th group, v s resduals of th group measurements, and σ s estmate of the true value of the varance factor. In here, as t s seen that, c s a functon of P (weght matrx) and P s also a functon of σ. And because of ths herarchy, Helmert soluton needs an teratve computaton. Step by step computaton algorthm of Helmert Varance Component Estmaton s as gven below: The Frst Step : Before the adjustment, a unque weght s selected for each measurement groups. At the begnnng, the weghts for each measurement groups can be chosen equal P = P =... = P 1) ( 1 u = (7) 6/16 FIG Workng Week 004 Athens, Greece, May -7, 004

7 The Second Step : By usng the a-pror weghts, normal equatons ( N1, N,...,N u ) for each measurement groups separately and general normal equaton (N) are composed. In here, the general normal equaton s the summaton of normal equatons such as N = N + N N u The Thrd Step : Adjustment process s started, unknowns and resduals are calculated. 1 T x = N d, (d = A Pb) (11) v = A x b v 1 u 1 u 1... (1)... = A x b u The Fourth Step : Helmert equaton s generated (Equaton 6). The Ffth Step : Varance components n Helmert equaton (σ1,σ,...,σ u ) and new weghts are calculated. P + 1 = P / σ (13) The Sxth Step : If the varance component ( σ ) for all groups ( = 1,,...,u) s equal to one, then the teratons wll be over. If t s not, then t goes to the second step and computatons are carred on usng the new weghts. The teratons are contnued untl the varances reaches to one ( σ 1) (Kızılsu 1998). = 3. NUMERICAL EXAMPLE 3.1 Defnton of the Study In ths study, the vertcal deformatons of hghway vaduct, Karasu, were nvestgated usng GPS measurements data and precse levellng data. As the longest vaduct of Turkey (160m), Karasu s located n the west of Istanbul n one part of the European Transt Motorway. Whle t s consdered the hydrologc and geologc condtons of the area, where the vaduct was bult, t s better understood the reason of choosng ths vaduct as the example for nvestgatng the structural deformatons of a constructon, because ths vaduct cross over the lake and pers of the buldng are n the water. The deformaton measurements of Karasu nvolved four measurement campagns. The frst campagn was n June 1996, the second n March 1997, the thrd n October 1997 and the last one was n Aprl These four campagns were ncluded GPS measurements and precse levellng measurements. Wth the am of nvestgatng the deformatons of ths structure, a well desgned local geodetc network was establshed, and t was measured usng GPS 7/16 FIG Workng Week 004 Athens, Greece, May -7, 004

8 technque accordng to desgned sesson plan. Also, precse levellng measurement technque was carred out between network ponts. The network had 6 reference ponts, were set around the vaduct and 4 deformaton ponts on the buldng of the vaduct especally establshed on the pers (as t s seen n the fgure 1(a)) where thought to be most stable places on the structures. (a) Fgure 1 : In (a) one of the 4 deformaton ponts establshed on a per of the vaduct s shown, n (b) also one of these ponts s seen durng the GPS sesson. Vaduct has two tracks and 4 of deformaton ponts, the 1 of them are n the northern track and other 1 of them are n the southern track as t s seen n the fgure. The constructons of these deformaton ponts were bult as approprate for the forced centerng nsttutons (see (b) fgure 1 (a)-(b)). And reference network ponts were constructed as pllar and so they also had these nstrumentaton systems to avod the centerng errors (Erol and Ayan 003). Fgure : The confguraton of the geodetc network (Çelk et al. 001). 8/16 FIG Workng Week 004 Athens, Greece, May -7, 004

9 3. Evaluatng of Deformaton Analyss Approach Resultant graphcs of three deformatons analyss approaches are gven below. Northern Track - Levellng dh n mm Ponts dh 1- dh -3 dh 3-4 (a) Southern Track - Levellng dh n mm Ponts dh 1- dh -3 dh 3-4 (b) Fgure 3 : Heght dfferences between consecutve epochs for each pont n the northern track (a) and southern track (b) of the vaduct accordng to the frst approach results (deformaton analyss usng heght dfferences from levellng measurements) 9/16 FIG Workng Week 004 Athens, Greece, May -7, 004

10 Northern Track - GPS dh n mm Ponts dh 1- dh -3 dh 3-4 (a) Southern Track - GPS dh n mm Ponts dh 1- dh -3 dh 3-4 (b) Fgure 4 : Heght dfferences between consecutve epochs for each pont n the northern track (a) and southern track (b) of the vaduct accordng to the second approach results (deformaton analyss usng heght dfferences derved from GPS measurements) 10/16 FIG Workng Week 004 Athens, Greece, May -7, 004

11 Northern Track - Levellng+GPS dh n mm Ponts dh 1- dh -3 dh 3-4 (a) Southern Track - Levellng+GPS dh n mm Ponts dh 1- dh -3 dh 3-4 (b) Fgure 5 : Heght dfferences between consecutve epochs for each pont n the northern track (a) and southern track (b) of the vaduct accordng to the thrd approach results (deformaton analyss usng heght dfferences derved from both GPS measurements and levellng measurements) 3.3 Interpretng of the Results As t s mentoned prevously, the deformaton analyss was carred out nto three approaches. At frst data from both measurement technques were processed for each epoch separately. Thus, the results from ndependent solutons for each epoch were compared. Ths was necessary for gettng nformaton about the qualty of data, revealng possble nherent problems and to get apror nformaton about nstable ponts and by ths way to determne a sutable strategy for analyss. As the result of ths preparaton process, t was seen that precse levellng measurements made very benefcal support to GPS measurements. Because by the help of levellng, t s 11/16 FIG Workng Week 004 Athens, Greece, May -7, 004

12 become possble to check the heghts from GPS measurements and antenna heghts problems occurred durng GPS sessons were able to be clarfed. Ths s very consderable contrbuton of levellng measurements to GPS measurements n deformatons montorng. After these processes, deformaton analyses were carred out by usng heght dfferences from levellng measurements, from GPS measurements and also by usng combnaton of heght dfferences from both GPS and levellng measurements respectvely. In general meanng, the results were confrmed each other. In the results, t was surprsngly found that the maxmum heght changes were n pont and pont 4 (as t s seen n the graphcs), whch were assumed as stable at the begnnng of the project and even though that ther constructons are pllar. Accordng to analyss of precse levellng data, on the contrary of the stuaton n pont and pont 4, there weren t seen any changes n heghts n the deformaton ponts on the vaduct. On the other hand, accordng to the second approach (usng GPS derved heght dfferences) n some ponts on the vaduct, heght changes were reported. In the thrd approach, as a result of the Helmert Varance Component Estmaton t was computed that the weght of heght dfferences from levellng equals to 30 tmes over of the weght of GPS derved heght dfferences. Ths result was reached n the thrd teraton step. Accordng to derved weghts of the heterogeneous data group, deformaton analyss was repeated. Results of three approaches can be compared accordng to graphcs (see fgure 3, 4, and 5). In the graphcs, heght changes accordng to consecutve measurement campagns are seen. The pont groups of each track of the vaduct are shown n separate graphcs. Therefore, for the result of each approach, there are two graphcs as northern track and southern track. As the graphcs of the frst, the second and the thrd approaches are compared, t s seen that the results of the thrd approach s closer to the frst approach. Ths smlarty shows that t s not relable enough to use GPS measurements wthout specal precautons for the GPS error sources, such as multpath, atmospherc effects, antenna heght problems etc., n vertcal deformaton analyss of engneerng structures. So, as the result of ths study, t s suggested to support GPS technque wth levellng measurements n montorng vertcal deformatons. Accordng to nvestgatng result of the second approach, t was seen changes n heghts of some ponts on the vaduct. However, whle the frst and thrd approaches are consdered, t s understood that these changes, seemed to be deformatons on the object pont of the vaduct accordng to results of the second approach, were not sgnfcant and caused by the error sources n GPS measurements especally antenna heght problems. In general revew of graphcs, all ponts ncludng reference and deformaton ponts, have smlar characterstc of movements between consecutve epochs. Maxmum movements were recorded n pont and pont 4 and these movements were nterpreted as deformaton. The movements recorded n deformaton ponts on the vaduct ddn t mean deformaton snce they are not sgnfcant regardng to accuracy acheved. However, at a frst glance, t was surprsng to found deformatons n pont and pont 4 that had been chosen as reference ponts, after geologcal and geophyscal nvestgatons, the 1/16 FIG Workng Week 004 Athens, Greece, May -7, 004

13 orgn of these results was captured. Accordng to that the area s a marsh area that ths characterstc mght wden also underneath of these two reference ponts, and 4. The uppermost sol layer n the regon s not seemed to be stable and the foundatons of the constructons of the reference ponts are not founded as deep as the pers of the vaduct and so they are affected the envronmental condtons easly. And these condtons supported the results of the analyss that n the object ponts on the vaduct, there were not exposed any sgnfcant movements. On the other hand, t s possble to menton about the correlaton between vertcal movements n two reference ponts, and 4, and wet/dry seasons, because the uplft and snkng movements of these reference ponts seems very synchronc as related to seasonal changes n amount of water (see the gven graphcs n fgures 3, 4 and 5). 4. CONCLUSION AND REMARKS In ths study, vertcal deformatons of a large hghway vaduct were nvestgated wth three dfferent deformaton analyss approaches. The man motvaton was testng the performance of GPS as a satellte based precse postonng system n determnng vertcal deformatons as beng aware of geometrcal weakness of ths system and error sources affects ts vertcal postonng accuracy. To determne the performance of t, the results of analyss of the data derved from GPS are compared wth the results of analyss of precse levellng measurements. As the thrd approach, data groups, ellpsodal heght dfferences from GPS and orthometrc heght dfferences from precse levellng measurements were combned, and they were used n the deformaton analyss computatons. These heterogeneous data were combned accordng to HVCE technque n ths deformaton analyss approach, and as the result of ths technque, the weghts of precse levellng heght dfferences as proportonal to the weghts of GPS derved heght dfferences was calculated as 30. The results of ths study, experenced wth measurements of Karasu vaduct, are thought to be very mportant remarks for vertcal deformaton analyss studes usng GPS measurements. As the frst remark, GPS measurement technque can be used for determnng vertcal deformatons wth some specal precautons for elmnatng GPS error sources. These nclude usng forced centerng mechansms to avod centerng errors, usng specal equpments for precson antenna heght readngs, usng specal antenna types to avod multpath effects etc. Also, durng the data processes t s necessary to clear the cycle slps from the data, and to consder nsuffcences of the used tropospherc and onospherc models. However, even though these precautons, to provde better results n vertcal deformaton analyss, GPS measurements have to be supported wth Precse Levellng measurements. It was seen that precse levellng technque gves more successful and relable results accordng to GPS technque n determnaton of vertcal deformatons, whle the frst and the second analyss approaches were compared each other. And usng the combnaton of GPS measurement technque and precse levellng technque gves better results than usng just GPS measurement technque as t can be seen n the thrd deformaton approach. Hence, usng the combnaton of levellng measurements and GPS measurements together n deformaton analyss algorthm gves better and more relable 13/16 FIG Workng Week 004 Athens, Greece, May -7, 004

14 results n vertcal deformaton analyss. And on the other hand, levellng provdes an opportunty to check antenna heghts errors and by ths way t helps to ncreases the qualty of GPS data, and accordng to ths, usng levellng measurements as an auxlary technque durng the deformaton measurements n addton to GPS s also be benefcal for the D deformaton analyss wth GPS measurements. REFERENCES Ayan, T. (198) General Revew of Deformaton Analyss n Geodetc Networks, I.T.U. Journal, Vol l, Istanbul, Turkey (n Turksh) Ayan, T., Tekn, E., Denz, R., Külür, S., Toz, G., Çelk, R. N., Özşamlı, C. (1991) Determnng Landsldes n the Regon of Büyükçekmece Gürpınar Vllage Usng Geodetc Methods, Techncal Report, February 1991, Istanbul Techncal Unversty, Istanbul, Turkey (n Turksh) Çelk, R. N., Ayan, T., Denl, H., Özlüdemr, T., Erol, S., Özöner, B., Apaydın, N., Erncer, M., Lenen, S., Groten, E. (001) Montorng Deformaton on Karasu Vaduct Usng GPS and Precse Levellng Technques, 001, Kluwer Academc Publsher, Netherlands Erol, S. (1999) Deformaton Measurements and Analyss n Karasu Vaduct Usng GPS Technque, MSc Thess, June 1999, Istanbul Techncal Unversty, Insttute of Scence and Technology, Istanbul, Turkey (n Turksh) Erol, S., Ayan, T. (003) An Investgaton on Deformaton Measurements of Engneerng Structures Wth GPS And Levellng Data Case Study, Internatonal Symposum on Modern Technologes, Educaton and Professonal Practce n the Globalzng World, 6-7 November 003, Sofa, Bulgara Featherstone, W. E., Denth M. C. and Krby J. F. (1998) Strateges for the Accurate Determnaton of Orthometrc Heghts from GPS, Survey Revew 34, 67 (January 1998), pp Grafarend, E.W. (1984) Varance-Covarance Components Estmaton, Theoretcal Results and Geodetc Applcatons, 16 th European Meetng of Statstcans, Marburg, 1984 Kızılsu, G. (1998) Precson Analyss for Lageos I and Lageos II PhD Thess, Istanbul Techncal Unversty, Insttute of Scence and Technology, Istanbul, Turkey (n Turksh) Welsch, W. (1978) A posteror Varanzenschatzung nach Helmert, AVN, 85, 55 63, 1978 BIOGRAPHICAL NOTES Serdar EROL (Research Assstant) The author graduated from the Geodesy and Photogrammetry Engneerng Department of Istanbul Techncal Unversty (ITU) n June In January of 1998, he started to study as Research Assstant n Geodesy Dvson of ITU. He graduated Geodesy and Photogrammetry Engneerng Master Program of Insttute of Scence and Technology at ITU n June He studed Montorng and Analyzng of Karasu Vaduct Usng GPS Measurements as hs MSc thess. He attended to Doctorate Program of Geodesy n Insttute 14/16 FIG Workng Week 004 Athens, Greece, May -7, 004

15 of Scence and Technology of ITU n the year of Stll, he s studyng hs PhD thess wth the subject of Deformaton Analyss Usng GPS and Precse Levellng Measurements and employed as a research assstant at ITU. Hs scentfc nterests nclude Deformaton Analyss, GPS Measurements and Data Processng, Hardware of Computers. Rahm Nurhan ÇELİK (Assocate Professor) The author graduated from the Geodesy and Photogrammetry Engneerng Department of Istanbul Techncal Unversty (ITU) n June After that, he has got MSc. Degree from Geodesy and Photogrammetry Engneerng Program from ITU n 1989 and PhD degree from Surveyng Department of New Castle upon Tyne Unversty, England, n He has been workng as lecturer snce 1987 at ITU and now he s Assocate Professor. He supervsed 9 MSc Thess and PhD Thess up to know. He drected and studed a lot of research projects. He has been char of Turksh Chamber of Surveyng and Cadastre Engneers between 000 and 00. He also has got membershps of organzaton comtes and scentfc comtes of a lot of actvtes and symposums such as Young Surveyor Days and Earthquake Symposum n Kocael. Hs scentfc nterests nclude Geodesy, Navgaton, GPS, Informaton Systems, GIS, Qualty Standards, Industral Measurement Technques, Image Processng, Computers, Programmng and Practcal Investgatons. Bhter EROL (Research Assstant) The author graduated from the Geodesy and Photogrammetry Engneerng Department of Istanbul Techncal Unversty (ITU) n June In December of the same year, she started to study as Research Assstant n Geodesy Dvson of ITU. She graduated Geodesy and Photogrammetry Engneerng Master Program of Insttute of Scence and Technology at ITU n June 000. She studed Montorng of Large Buldngs by Precson Inclnaton Sensors as her MSc thess. She attended to Doctorate Program of Geodesy n Insttute of Scence and Technology of ITU n the year of 000. Stll, she s studyng her PhD thess wth the subject of Determnng local precse geod models usng GPS/Levellng data and developng geod computaton software for usng n practcal applcatons and employed as a research assstant at ITU. Her scentfc nterests nclude geodetc data modelng, geod determnaton, deformaton montorng of engneerng structures, geodetc networks, programmng of geodetc computatons. Tevfk AYAN (Professor Doctor) The author graduated from the Surveyng and Cadastre Engneerng Department of Yıldız Techncal Unversty (YTU) n After that, he has got MSc. Degree from Geodesy department from YTU n 1967 and PhD degree from Geodesy Department of Karlsruhe Unversty, Germany, n He has been workng as lecturer snce 1971 at YTU and than ITU and now he s Professor. He supervsed a lot of master and doctoral thess on geodetc network desgn, optmzaton, GPS measurements and deformaton analyss etc. He drected and studed a lot of research projects. He has been char of Turksh Chamber of Surveyng and Cadastre Engneers between 1996 and He also has got membershps of 15/16 FIG Workng Week 004 Athens, Greece, May -7, 004

16 organzaton comtes and scentfc comtes of a lot of actvtes and symposums. Hs scentfc nterests nclude theory of errors and adjustment, geodesy, deformaton measurements and analyss, GPS and trangulaton networks. CONTACTS Res. Assst. Serdar Erol Istanbul Techncal Unversty, Geodesy Department ITU Insaat Fakultes, Jeodez Anablm Dal Maslak-Istanbul TURKEY Tel Fax Emal erol@tu.edu.tr Web ste: Assoc. Prof. Rahm Nurhan Çelk Istanbul Techncal Unversty, Geodesy Department ITU Insaat Fakultes, Jeodez Anablm Dal Maslak-Istanbul TURKEY Tel Fax Emal celkn@tu.edu.tr Web ste: Res. Assst. Bhter Erol Istanbul Techncal Unversty, Geodesy Department ITU Insaat Fakultes, Jeodez Anablm Dal Maslak-Istanbul TURKEY Tel: Fax: Emal bhter@tu.edu.tr Web ste: Prof. Dr. Tevfk Ayan Istanbul Techncal Unversty, Geodesy Department ITU Insaat Fakultes, Jeodez Anablm Dal Maslak-Istanbul TURKEY Tel Fax Emal: ayan@tu.edu.tr Web ste: 16/16 FIG Workng Week 004 Athens, Greece, May -7, 004