Abstract. The Satellite Radar Interferometry is one of the common methods that allow to measure the land subsidence caused by the underground black coal excavation. The interferometry images processed from the repeat-pass Synthetic Aperture Radar (SAR) systems give the spatial image of the terrain subjected to the surface subsidence over mining areas. Until now, the InSAR methods using data from the SAR Systems like ERS-1/ERS-2 and Envisat-1 were limited to a repeat-pass cycle of 35-day only. Recently, the ESA launched Sentinel-1A and 1B, and together they can provide the InSAR coverage in a 6-day repeat cycle. The studied area was the Upper Silesian Coal Basin in Poland, where the underground coal mining causes continuous subsidence of terrain surface and mining tremors (mine-induced seismicity). The main problem was with overlapping the subsidence caused by the mining exploitation with the epicentre tremors. Based on the Sentinel SAR images, research was done in regard to the correlation between the short term ground subsidence range border and the mine-induced seismicity epicentres localisation.

The development of generalisation (simplification) methods for the geometry of features in digital cartography in most cases involves the improvement of existing algorithms without their validation with respect to the similarity of feature geometry before and after the process. It also consists of the assessment of results from the algorithms, i.e., characteristics that are indispensable for automatic generalisation. The preparation of a fully automatic generalisation for spatial data requires certain standards, as well as unique and verifiable algorithms for particular groups of features. This enables cartographers to draw features from these databases to be used directly on the maps. As a result, collected data and their generalised unique counterparts at various scales should constitute standardised sets, as well as their updating procedures. This paper proposes a solution which consists in contractive self-mapping (contractor for scale s = 1) that fulfils the assumptions of the Banach fixed-point theorem. The method of generalisation of feature geometry that uses the contractive self-mapping approach is well justified due to the fact that a single update of source data can be applied to all scales simultaneously. Feature data at every scale s < 1 are generalised through contractive mapping, which leads to a unique solution. Further generalisation of the feature is carried out on larger scale spatial data (not necessarily source data), which reduces the time and cost of the new elaboration. The main part of this article is the theoretical presentation of objectifying the complex process of the generalisation of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions, Salishchev measures, and Banach theorems ensure the uniqueness of the generalisation process. Their application to generalisation makes this process objective, as it ensures that there is a single solution for portraying the generalised features at each scale. The present study is dedicated to researchers concerned with the theory of cartography.

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Abstract. In this article, topics regarding the technical and legal aspects of creating digital underground mining maps are described. Currently used technologies and solutions for creating, storing and making digital maps accessible are described in the context of the Polish mining industry. Also, some problems with the use of these technologies are identified and described. One of the identified problems is the need to expand the range of mining map data provided by survey departments to other mining departments, such as ventilation maintenance or geological maintenance. Three solutions are proposed and analyzed, and one is chosen for further analysis. The analysis concerns data storage and making survey data accessible not only from paper documentation, but also directly from computer systems. Based on enrichment data, new processing procedures are proposed for a new way of presenting information that allows the preparation of new cartographic representations (symbols) of data with regard to users' needs.

Determining the correct height of mountain peaks is vital for tourism, but it is also important as a reference point for devices equipped with GPS (Global Positioning System), e.g., watches or car navigation systems. The peak altitude data are part of geographic and geodetic information. As more modern technologies and equipment become available, their precisions should increase. However, verification of peak heights is usually only conducted for the highest, well-known mountains—lower peaks or mountain passes are rarely verified. Therefore, this study focuses on an investigation of 12 altitude points on a section of the longest and most famous touristic trail in Poland (the Main Beskid Trail), located in the Orava–Żywiec Beskids Mts (Mountains). The aim of this research is to measure and verify the heights of the 12 selected mountain peaks, in addition to evaluating the chosen methods based on the quality of the obtained data and determining their suitability and opportunities for use in further research. Measurements were obtained at the most specific height points—on the 12 highest points of the summits. This study compares two modern measurement techniques: the global navigation satellite system (GNSS) and light detection and ranging (LiDAR). The obtained results were later compared with those widely used on the internet and in printed materials (period covered: 1884–2015). This analysis demonstrates that lesser-known objects are rarely the subject of remeasurement and significant altitude errors may occur, primarily because the heights originated from a source in the past when modern methods were not available. Our findings indicate that the heights of the peaks presented in cartographic materials are inaccurate. The assumed heights should be corrected by direct measurements using modern techniques.