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The paper is dedicated to the issues of both planar and spatial transformations with respect to the territory affected by mining activities. The planar transformations have been applied among the planar Otto mine coordinate system, St. Stephen Datum of Cadastre Coordinates, and the Datum of Uniform Trigonometric Cadastral Network (hereinafter referred to as JTSK). Here basic transformation characteristics among the above systems are defined. The spatial transformation is performed through a point coordinate conversion between the JTSK and the European Terrestrial Reference System (hereinafter referred to as ETRS89) where conventional relations as well as other conversion possibilities were described. Part of the article is the execution of an experiment of a direct transformation between the St. Stephen Datum of Cadastre Coordinates and the ETRS98 system for the territory of Brno, which was not affected by mining activities. For the above transformation, 8 trigonometric points were used, for which the identity analysis had been done initially. Furthermore, the Interpolation and One Step Transformations were tested, which solve the conversion as divided tasks for both position and heights. The Interpolation Transformation showed better values for residues. The results of the above experiment will be applied for purposes of surveying old mine workings using the GNSS technology. AbstractČlánek je věnován problematice rovinných a prostorových transformací s ohledem na území ovlivněném hornickou činností. Rovinné transformace byly aplikovány mezi rovinným Ottovým důlním souřadnicovým systémem, Katastrálním souřadnicovým systémem svatoštěpánským a systémem Jednotné trigonometrické sítě katastrální (JTSK). Zde jsou definovány základní charakteristiky převodu mezi těmito systémy. Prostorová transformace je realizována převodem souřadnic bodů mezi systémem JTSK a Evropským terestrickým referenčním systémem (ETRS89), kde jsou popsány konvenční vztahy a další možnosti převodu. Součástí článku je realizace experimentu přímé transformaci mezi katastrálním souřadnicovým systémem svatoštěpánským a systémem ETRS98 na území Brna, které není hornickou činností ovlivněno. Pro tuto transformaci bylo použito 8 trigonometrických bodů, u nichž byla původně provedena analýza identity. Testována byla Interpolační transformace a transformace One Step, které řeší převod jako rozdělené úlohy pro polohu a pro výšky. Lepší hodnoty reziduí vykazovala Interpolační transformace. Výsledky experimentu budou použity pro účely vytyčení starých důlních děl technologií GNSS.

This paper discusses a new method for determining co-seismic displacement using the Global Navigation Satellite System (GNSS) for the precise detection of positional changes at permanent stations after an earthquake. Positioning by the Precise Point Positioning (PPP) method is undertaken using data from the GNSS satellites and one designated station. A time series is processed by an anharmonic analysis before and after an earthquake and these one-day solutions increase the accuracy of measurements. The co-seismic static displacement can be precisely detected from the analysed time series before and after the earthquake, which can be used for the verification of seismic models. Reliability of the estimation of the size of the co-seismic offset is given by the mean square error (RMSE) of the shift. In this study, RMSE was determined by two approaches, initially from variances within PPP processing, and secondly when no positional change from the GNSS before or after the earthquake was assumed. The variance of the data in the time series gives a more realistic estimate of RMSE. This dual approach can affect seismological interpretation due to the need for the interpreting geophysicists to determine which case of co-seismic displacement is more probable for any given locality. The second approach has been shown to provide a more realistic co-seismic displacement accuracy in this study.