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Abstract:The Danish astronomer Peter Andreas Hansen, who also worked on theoretical geodesy, provided an original solution for solving the geodetic quadrilateral in which the four angles and the length of one side are known. This procedure, identified in scientific literature as Hansen's problem, has been applied in geodesy but significantly more so when solving various problems related to mining measurements in underground exploitation. Nonetheless, the literature does not cover the determining of the standard deviation of the coordinates of unknown points which are established using Hansen's method. In this paper then, equations are derived to calculate the standard deviation of the coordinates determined by the above mentioned procedure.Key words: geodetic quadrilateral, Hansen's problem, standard deviation Apstrakt: Danski astronom Peter Andreas Hansen, koji se bavio i teorijskom geodezijom dao je originalno rešenje za rešavanje geodetskog četvorougla u kome su poznata četiri ugla i dužina jedne strane. Ovaj postupak koji se u stručnoj literaturi naziva "Hanzenov problem" našao je primenu u Geodeziji, ali znatno više u rešavanju različitih zadataka iz oblasti Rudarskih merenja koji se javljaju pri podzemnoj eksploataciji. Međutim, ono što u literaturi nije obrađeno predstavlja određivanje standardnih odstupanja koordinata nepoznatih tačaka do kojih se dolazi primenom Hanzenovog postupka. U ovom radu izvedene su jednačine za računanje standardnih odstupanja koordinata određenih navedenim postupkom.

Open pit coal mining affects surrounding populated areas, resulting in terrain surface deformation. Surface deformation should be monitored as often as possible to control deformations and prevent potential incidents. This paper analyzes time series deformation estimated from the Sentinel-1 satellite images using the Persistent Scatterer Interferometry method to monitor subsidence rates caused by open pit mining activities. It is possible to measure deformations using classical geodetic methods, but those are rarely used in practice because they are time-consuming and expensive for application in large areas. Using the open access radar images from the Sentinel-1 mission, 513 images from the repository were downloaded between October 2016 and the end of December 2020. We present the processing steps in detail in order to establish a workflow for the automated processing of vertical displacement estimation using open source tools; a total of 402 images were processed: 215 images belonged to the ascending satellite orbit, 187 images belonged to the descending orbit, and 111 images were rejected because of adverse weather conditions. The PS InSAR technique has never been used for the mines of the Republic of Serbia or for land surveying practices related to deformation monitoring. The results based on the Sentinel-1 images were compared with results from geodetic leveling and with neotectonic uplift trends. The trend lines of vertical displacement obtained from PS and corresponding leveling are significantly similar (a Pearson correlation of 85% with a p-value of 0.015). The final evaluation reported results of vertical displacements at the leveling benchmark of −3.4 mm/year with the PS InSAR method and −2.7 mm/year with the leveling method. A comparison of the PS vertical displacements with a settlement model fits reasonably, suggesting that the measurements are valid. As four years of PS time series data is insufficient to establish undisputable conclusions on the neotectonics uplift, extending the time series (covering at least a decade) implies that this approach will become attractive in future neotectonic uplift trend estimations. This study illustrates not only the ability of Sentinel-1 data in mapping vertical deformations, but the obtained results could also be used for geohazard monitoring and land monitoring in general for the area of interest.

Abstract:The development of the crosscut from the aspect of mine surveying is a specific task, since there is no possibility for an independent control of its construction duringthe development. This is primarily related to the long crosscuts where the deviations of the designed direction of crosscut would have significant consequences on safety and technological activities in the mine shaft. In order to avoid errors, it is necessary to perform the preceding analysis of the crosscut accuracy, where the overall standard deviation of the crosscut is calculated. This value must be smaller than the given allowed deviation. The paper presents an a priori evaluation of the accuracy of the crosscut to be developed in the brown coal mine "Soko" for the purpose of ventilating the opening rooms of the eastern part of the deposit. Key words: mine surveying, crosscut, apriori accuracy evaluationApstrakt: Izrada proboja sa aspekta rudarskih merenja je težak i odgovoran posao. Ovo se pre svega odnosi na izradu dužih proboja, s obzirom da u toku njegove izrade ne postoji mogućnost nezavisne kontrole njegove realizacije. Zato je u ovakvim slučajevima neophodna prethodna analiza tačnosti proboja, gde se na osnovu svih potrebnih elemenata, računa ukupno standardno odstupanje proboja koje mora da bude manje od zadatog dozvoljenog odstupanja. U radu je prikazana a priori ocena tačnosti proboja koji treba da se realizuje u rudniku mrkog uglja ,,Soko" za potrebe ventilacije prostorija otvaranja istočnog dela ležišta.

Abstract:The physical surface of the earth has irregular shape which is not mathematically defined, therefore the shape of the Earth is approximated with mathematically defined surfaces such as ellipsoid and sphere. The developing of a global positioning systems, thus and modern navigation systems, as effect produce large amounts of data which contain the problem of homogeneity. This problem could be exceed if all the data are store in the same coordinate system. Hence the need for data transformation from local coordinate systems to the global coordinate systems. Global level implies WGS84 ellipsoid and UTM projection while national coordinate system of Republic Serbia is Gauss-Kruger with Bessel ellipsoid. This coordinate system of Republic Serbia on a global level has a local character. Applying appropriate mathematical models and functions it is possible to transform coordinates from one system to another and vice versa. The paper describes coordinate transformations from Gauss-Kruger coordinate system ellipsoid Bessel to UTM projection WGS84 ellipsoid and vice versa, and also an application which provides transformation of its kind that is made using open source environment. Name of the application is TRANS7_GK_UTM_GK and it can be found and used on the web page of the faculty for Mining and Geology under the link http://gk2utm.rgf.bg.ac.rs with a user guide. Keywords: Gauss-Kruger, Besell, WGS84, UTM, coordinate transformation, r Apstrakt: Fizička površ Zemlje je nepravilnog oblika koja matematički nije definisana zbog čega se oblik Zemlje aproksimira matematički definisanim površima kao što su elipsoid i sfera. Razvojem globalnih sistema za pozicioniranje, samim tim i sistema za navigaciju, za posledicu imamo ogromne količine podataka kod kojih se javlja i problem homogenosti u geoprostornom smislu. Ovaj problem može se prevazići ako bi se svi podaci nalazili u istom koordinatnom sistemu. Odatle i potreba da se podaci iz lokalnih (državnih) koordinatnih sistema transformišu u koordinatne sisteme koji su zastupljeni na globalnom (svetskom) nivou. U svetu je zastupljen elipsoid WGS84 i UTM projekcija, dok je državni koordinatni sistem Republike Srbije, koji posmatrano na globalnom nivou ima ulogu lokalnog karaktera, smešten na elipsoid Besela sa Gaus-Krigerovom projekcijom. Primenom odgovarajućih matematičkih modela i funkcija mogu se transformisati koordinate iz jednog sistema u drugi. U ovom radu prikazan je postupak transformacije iz jednog sistema u drugi, a i aplikacija koja omogućava transformaciju ovakve vrste koja je napravljena pomoću alata i softvera otvorenog koda pod nazivom TRANS7_GK-UTM-GK i dostupna na web adresi Rudarskogeološkog fakulteta na linku http://gk2utm.rgf.bg.ac.rs sa uputstvom za upotrebu.

Transformation between ellipsoids also called datum transformation implies coordinate conversion from one ellipsoid to another ellipsoid, most frequently to be done by Helmert seven-parameter transformation. Transformation parameters involve three rotation, three translation and scale factor and they can be calculated using reference points which are known before and after transformation. Transformation parameters can be obtained with appropriate measurements and in accoradance with measurement uncertainties, they are produce errors of transformed coordinates. This paper describes standard errors of transformed coordinates using Helmert seven-parameter transformation, when switching from ellipsoid WGS84 to Bessel ellipsoid.

Abstract:The task of connecting survey and orienting mine rooms is to obtain the coordinates for the first point of the future underground traverse and the bearing of the first side of the underground traverse on the horizon that is being connected. The task is particularly complex when the connection survey is performed through a single vertical shaft. The accuracy of connection survey and orientation is influenced by the errors in given and measured values, but in addition a question may be asked if the applied calculation method influence the connection precision (accuracy) and if they do to what extent. If the connection through a single vertical shaft is completed by the connection rectangle method, the calculations are most often done by using the Hansen, Weiss or Hause method. This paper presents calculations of standard deviations of unknown values in a connecting rectangle based on the three methods, as well as standard deviations of the bearing of the first side of the underground traverse on an example.