Doğru hız kestirimi için aylık GPS kampanyalarının performansı üzerine bir inceleme
An investigation on the performance of monthly GPS campaigns for speed estimation
Yazar: SİMGE TEKİÇ RAHMANLAR
Danışman: PROF. DR. ERSOY ARSLAN ; PROF. DR. DOĞAN UĞUR ŞANLI
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Geomatik Mühendisliği Ana Bilim Dalı / Geomatik Mühendisliği Bilim Dalı
Derece: Doktora, 2019
Konu: Jeodezi ve Fotogrametri = Geodesy and Photogrammetry
Dizin: GPS = Global Positioning System ; Hız ölçme = Velocity measurement ; Çok değişkenli zaman serileri = Multivariate time series ; Çoklu lineer regresyon analizi = Multiple linear regression analysis

Özet:
GPS, birçok alanda kullanıldığı gibi yer yuvarının global deformasyonunun belirlenmesinde de kullanılan bir araçtır. Özellikle tektonik hareketin belirlenmesi, buzul sonrası erimenin izlenmesi ve ITRF'ın sıklaştırılması konularında GPS'ten yararlanılmaktadır. Günümüzde yüksek doğrulukta hız belirleme sürekli GPS ölçümleri ile yapılmaktadır. Sürekli GPS ölçümleri için her zaman sabit GPS istasyonu kurma imkânı olmadığı durumlarda kampanya ölçümlerine başvurulmaktadır. Ancak günümüzde var olan, kampanya ölçümlerinden hız belirleyen GPS prosedürleri yeterli doğrulukta hız üretememektedir. 
Bu tezde doğru hız bilgisi üreten GPS kampanya ölçüm ve değerlendirme yöntemleri geliştirilerek, GPS ölçümleri yardımıyla tektonik hareket izlenmiştir. Bu doğrultuda, 1995-2017 yılları arasında 22 yıllık bir zaman dilimini kapsayacak şekilde-yükseklik bileşenine ait yer değiştirme-zaman ilişkisinin R2'si 0,85'ten büyük 24 adet IGS noktası (PALM, ALRT, BAKE, HOFN, HOLM, IQAL, NYAL, PETS, QIKI, RESO, SCOR, THU2, TRO1, AIRA, CHUR, DRAG, SANT, YELL,  SPT0,  ONSA,  NAIN,  KIRU,  ALGO,  BCOV) seçilmiştir.
Bahse konu istasyonların, JPL tarafından GIPSY yazılımı ile analize tabi tutularak türetilen 24 saat oturum süreli GPS baz bileşenlerine ait (doğu, kuzey, düşey) günlük/sürekli zaman serisi elde edilmiştir. Sonrasında, günlük zaman serileri her ayın birinci günü alınarak seyreltilmiş ve aylık/kampanya verisi elde edilmiştir. Sürekli zaman serileri ve kampanya zaman serilerine ait yatay ve düşey hız bilgisi üretilmesinde 1 yıllık ve 6 aylık mevsimsel etki göz önüne alınmış olup, kullanılan matematiksel modelde bilinmeyenler "En Küçük Kareler Yöntemi" ile Matlab R2013a programı aracılığıyla çözülmüştür. 
Tez çalışması sürecinde, düşey bileşende yer değiştirme-zaman ilişkisinde gözlenen eğilim ile buzul sonrası geri çekilmeden kaynaklı kabuk yükselişi arasında bir korelasyon olabileceği araştırılmış, literatür taramaları ile sonuçlar desteklenmiştir. 
Son olarak, kestirilen günlük ve aylık verinin deformasyon oranları 4 farklı varsayıma göre istatistiksel test kullanılarak karşılaştırılmıştır. Diğer bir ifadeyle, ayda bir örneklemeli 24 saat ölçümlü GPS kampanyalarından elde edilen hızlar, doğru olarak kabul edilen ve JPL'den elde edilen sürekli GPS hızlarıyla karşılaştırılmış ve sonuçlar yorumlanmıştır. GPS kampanya süresinin 8-12 saatten 24 saate çıkarılması ve yüksek R2'li (1'e yakın) istasyonlar ile çalışılması sonucunda kampanya GPS ölçümlerinden kestirilen hızların (günlük örneklemeli) sürekli GPS zaman serilerinden elde edilen hızları ile istatistiksel anlamda %95 üzerinde uyuştuğu görülmüştür.

Abstract:
From the first ages of humanity, the shape and dimension of the world has been a subject that attracts the curiosity of mankind. Geodetic science emerged by recognizing this need. Geodesy is a branch of science in the three-dimensional coordinate system, which is used to describe the time-dependent changes in the field of gravitational field, shape and size. This branch of science is examined under two headings. The methods applied until the invention of satellite technology are called classical geodesy and the next developments are named as modern geodesy (satellite geodesy). While the shape of the world can be determined approximately by the methods of measurement called classical geodesy, it was not possible to carry out studies about the change of this shape over time. In particular, the concept of time was integrated into the calculations by means of satellite geodesy. The pioneering methods of satellite geodesy, especially GPS, have created new possibilities and targets that have not yet been achieved by classical geodetic methods and have provided these targets with a fast, efficient and economical way to access. 
 GPS is a tool that is used in many areas as well as to detect the global earth deformation. In particular, GPS is used for determination of tectonic movements, monitoring of post-glacial rebound and realization of ITRF. 
Today, high accuracy speed measurements are done by continuous GPS measurements. Campaign method is used when there is not always the possibility to set up a fixed GPS station for continuous GPS measurements. However, today's GPS procedures that measure speed from campaign measurements do not generate speed data with adequate accuracy.
In this thesis, GPS campaign measurement and evaluation methods, which produce accurate speed data for tectonic movement were developed and the motion was monitored by the help of GPS measurements. 
In this context, 24 IGS monitoring points (PALM, ALRT, BAKE, HOFN, HOLM, IQAL, NYAL, PETS, QIKI, RESO, SCOR, THU2, TRO1, AIRA, CHUR, DRAG, SANT, YELL,  SPT0,  ONSA,  NAIN,  KIRU,  ALGO,  BCOV) that have  greater R2 value than 0,85 for the vertical (up) components of the displacement-time relationship were analysed over a 22-year span between 1995-2017.
A 24-hour session of daily/continuous time series of GPS base components (east, north, up) analysed by JPL with the help of GIPSY program was used in this study. Monthly / campaign data was obtained by sampling the first day of each month of daily time series.
The seasonal effect of one year and six months were taken into consideration when generating of horizontal and vertical velocity component data of continuous and campaign time series. By the help of Matlab R2013a program, unknown parameters in the mathematical model were solved with least squares method.
Speed data obtained from the GPS campaigns, which are sampled 24 hours a month were compared with the continuous GPS speeds obtained from JPL (that accepted as true) and then, the results are interpreted by using confidence intervals. The deformation rates of daily and monthly data were compared by using three different statistical tests. These tests are differ according to the variance is known and unknown, whether the data are obtained in the same or in different sample space.
The confidence intervals (Z90 = 1,645, Z95 = 1,96, Z99 = 2,58) of statistical tests determines if the deformations were within the acceptable range.
According to the Z90 = 1,645 confidence interval; the comparison of campaign data with the continuous data of the AIRA station vertical component and DRAG and NYAL stations latitude component was inconsistent according to the three assumptions. The comparison of campaign data with the continuous data of the AIRA station latitude and longitude components, DRAG station latitude and vertical components, NYAL station longitude and vertical components and ALGO, ALRT, BAKE, BCOV, CHUR, HOFN, HOLM, IQAL, KIRU, NAIN, ONSA, PALM, PETS, QIKI, RESO, SANT, SCOR, SPTO, THU2, TRO1 and YELL stations all components were consistent according to three assumptions. According to the statistical test results, it was found that 96% of the vertical velocity component obtained from the campaign measurements was consistent with the velocity obtained from the continuous data. Similarly, 92% of the horizontal velocity component obtained from the campaign measurements was consistent with the horizontal component velocity obtained from the continuous data.
For Z95 = 1.96 confidence interval; the vertical component of the AIRA station and the longitude component of the DRAG station and latitude component of the NYAL station were incompatible according to three assumptions. The latitude and longitude component of AIRA station, the latitude and vertical component of DRAG station and all components of ALGO, ALRT, BAKE, BCOV, CHUR, HOFN, HOLM, IQAL, KIRU, NAIN, NYAL, ONSA, PALM, PETS, QIKI, RESO, SANT, SCOR, SPTO, THU2, TRO1, YELL were compatible with 3 assumptions. According to the statistical test results, it was found that 96% of the vertical velocity component obtained from the campaign measurements was consistent with the velocity obtained from the continuous data. Similarly, it was found that 96% of the horizontal velocity component obtained from the campaign measurements was consistent with the horizontal component velocity obtained from the continuous data.
For Z99 = 2.58 confidence interval; the comparison of campaign data with the continuous data of the AIRA, ALGO, ALRT, BAKE, BCOV, CHUR, DRAG, HOFN, HOLM, IQAL, KIRU, NAIN, NYAL, ONSA, PALM, PETS, QIKI, RESO, SANT, SCOR, SPTO, THU2, TRO1, YELL all components were compatible with the 3 assumptions. According to the statistical test results, it was found that 100% of the vertical speed component obtained from the campaign measurements was consistent with the speed obtained from continuous data. Similarly, it was found that 100% of the horizontal velocity component obtained from the campaign measurements were consistent with the horizontal component velocity obtained from continuous data.
As a result of working with stations with high R2 value (close to 1),  it was observed that the estimated speeds of the campaign GPS measurements were 95% statistically consistent with the speeds obtained from the continuous GPS time series (daily sampling).
Also, the possible correlation between trend of vertical displacement and crustal rise after glacier withdrawal was also investigated. The results were confirmed by checking with related studies. In this direction, position time series of 34 IGS geodynamics stations with 24-hours period of 1995-2017 were used. By using the Matlab, R2 of vertical velocities were obtained by the least squares method. After this process, R2 values were geospatially modelled around the World by using geostatistical technique named as "ordinary kriging" with ArcGIS program. According to constructed map, continents of South America, Northern Europe and Antarctica, where were affected by glacial retreat, had R2 values close to 1.
To verify the results, the generated map and Milne and Shennan's glacial isostatic adjustment model map were compared by using Geo-referencing Method in ArcGIS program. Glacial retreat rates of 34 IGS points were overlapped with the values in the map.
The results revealed us that the post glacial rebound rates appears to be 88% well-matched with the R2 values. The model proved that the IGS stations which have high R2 values for velocity component was compatible with post glacial rebound in the study of Milne and Shennan. This result showed that it is possible to detect and investigate glacial effects in any region on the Earth with monitoring only vertical speed.
Despite glacial movements modelling is widely used subject among researchers, the withdrawal effect of glaciers cannot be easily forecasted still. Modelling simple is always a good choice for accurate modelling. With low effort and cost, modellers have a chance to investigate the post glacial rebound effect thanks to this basic study. As a result of this study, it has been shown that the deformation of tectonic movement and melting after post glacial effect can be analysed as close to continuous observations with monthly campaigns. 
To sum up, different from other studies, the extension of the observation period to 24 hours provided that risen of estimation accuracy of Horizontal speed from 30-40 percent to 100 levels. Besides, estimation accuracy of vertical speed were increased to 95% level from zero degrees. Campaign observations once a month play an important role in determining the vertical signal. But it will bring heavy costs, labour and time loss to the observer. For this reason, the frequency of campaign measurements should be studied in future studies and the effect of this on speed estimation accuracy should be examined separately.