The accuracy assessment of InSAR measurements and reducing data points

Yapay Açıklıklı Radar İnterferometrisi (InSAR), yeryüzü topografyasının ve  deformasyonun belirlenmesi için yeni bir jeodezik tekniktir ve yersel ölçümlere ihtiyaç duymaz. InSAR ölçü sadece uydu bakış doğrultusunda bilgi verir. Bu ölçüler yörünge, topografya veya atmosfer kaynaklı hataları içerisinde barındırabilir. Bu ölçülerin doğruluğu İzmit Depremi örnek verisi üzerinde test edilmiştir. İzmit depremiyle ilgili olarak bu bölgedeki GPS noktalarındaki ölçümlerle aynı noktalardaki InSAR ölçüleri karşılaştırılmış, aradaki fark yaklaşık ±4 cm bulunmuştur. InSAR ölçülerinin çözülmesi sırasında başlangıç noktası kaynaklı hatalardan kurtulabilmek amacıyla aynı noktalar arasındaki göreli farklar incelenmiştir. Bu durumda farkların ortalaması ±2 cm’dir. Aradaki farkın nedeninin hem GPS hem de InSAR’ın kendi içerisinde barındırdığı hata kaynakları hem de GPS ölçülerinin deprem sonrası hareketleri içermemesine rağmen, InSAR ölçülerinin elde edildiği deprem sonrasına ait görüntünün depremden 1 ay sonrasına ait olması nedeniyle deprem sonrası hızlı hareketleri içermesi olduğu değerlendirilmiştir. InSAR ölçüleri çok yoğun olması nedeniyle, hesaplama yükü çok ağırdır. Ayrıca bu ölçülerin GPS ve nivelman gibi başka jeodezik yöntemlere ait ölçü gruplarıyla kullanılmaları durumunda çok baskın olmaktadırlar. Bu nedenle seyrekleştirilmelerine ihtiyaç vardır. InSAR ölçülerinin seyrekleştirilmesi üzerine yeni bir algoritma geliştirilmiş, bu algoritmanın sık kullanılan quadtree algoritması ile karşılaştırması yapılmıştır. Yeni algoritmanın quadtree algoritmasına göre InSAR veri kümesini 2/3 oranında daha az noktayla daha doğru bir şekilde temsil ettiği hesaplanmıştır. Bu seyrekleştirme algoritmasının yapılacak çalışmalarda kullanılabileceği değerlendirilmiştir. Anahtar Kelimeler: GPS, InSAR, doğruluk, nokta seyrekleştirme. Interferometric Synthetic Aperture Radar (InSAR) is a new geodetic technique for determining earth topography and deformation and it does not need any land survey. InSAR uses Synthetic Aperture Radar (SAR ) images which are in the region of microwave of electromagnetic spectrum It is a method in which phase component of SAR images are differenced and effects other than the deformation are removed to determine deformation. These phase difference images are called interferograms. In interferograms every 2π cycle of phase corresponds to one wavelength deformation in line of sight (LOS). To determine absolute deformation these cycles have to be unwrap namely added over each other. InSAR measurements can include many types of errors. These errors can be caused by orbit, digital elevation model or atmosphere. Not  many  studies has been interested on the accuracy of these measurements. In this study the accuracy of InSAR measurements are tested for İzmit Earthquake by GPS measurements Firstly, The interferogram was constructed by ERS-1 SAR images. Because of the inadequacy of the phase unwrapping algorithm, every cycle of the interferogram was digitized. The measurements at GPS points were compared with the InSAR measurements at the same points for İzmit Earthquake. 11 GPS points lay over the interferogram. The comparison was made for north and south of North Anatolian Fault (NAF) separately, 8 of the GPS points stay north of the NAF, 3 of them south. For the aim of comparison, the deformation of GPS in 3 dimensions was projected on LOS of InSAR measurements. For the North of the NAF, the average of the differences is 38 mm and all the differences are in the same direction. The reason for this difference is thought to be the postseismic deformation which was included by InSAR measurements but not by GPS measurements. For South of the NAF the average of the difference is 94 mm and al the differences are in the same direction. The main reason for this differences is the beginning point that is chosen to unwrap phase. It can be seen that the GPS point which is near the beginning point but out of the InSAR measurements coverage area has a 91mm displacement in LOS. This means that the beginning point has a 91 mm shift. In this case the difference for the South of the NAF is only 3 mm. Another test was held to check the accuracy. It was taking in to account the double differences between GPS points. By this namely, differencing displacement between two GPS points and checking InSAR measurements at those point, we can get rid of unwrapping beginning point error. The average of differences is 20 mm and Standard deviation is ±7mm. InSAR measurements are highly dense compared with other geodetic observations. For calculation convenience, this huge number of data points is reduced by different approaches. One of the most used is quadtree algorithm. Quadtree algorithm, divides the data in quadrants and checks the rms value for each quadrant. If the rms value of a quadrant bigger than a threshold value determined at the beginning, algorithm goes on dividing that quadrant to another quadrants. If the rms value is smaller than the threshold value, the algorithm stops for that quadrant. This algorithm generally gives good results but it does not take in to account the natural patterns that exist in data. In this study a new algorithm is investigated which takes into account the patterns in a data set and can represent the data by smaller number than quadtree. In this new developed algorithm contour lines are created for the data with the selected interval taking into account the slope of the data. Then, these contour lines are simplified by the commonly used Douglas-Poiker algorithm. And all the vertices of the simplified contour lines are converted to data points. And for other purposes such as weighting all of these data points are associated with the points in the original dataset that each of them represents.  To test the results this new algoritm was compared with quadtree algorithm for İzmit earthquake interferogram. The data set was sampled by quadtree and newly developed algorithm. And by these sampled points, the original data set was tried to be constructed again. Differences are taken with the reconstructed dataset and original dataset for two algorithms. It was observed that the new algorithm represents the original data more accurately with 2/3 less points if  compared  with the quadtree. Keywords: GPS, InSAR, accuracy, data reduction