The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.     

Geoarchaeological evidence on a Late Bronze Age earthquake,Ohrid Basin (North Macedonia)

Geoarchaeological investigations on the northeastern shore of Lake Ohrid revealed 3.5 m thick deepwater lacustrine sediments overlying terrestrial vegetation macrofossils, worked wood and abundant potsherds dated to the Late Bronze Age (LBA). Distinct contact of deepwater sediment with the sub-aerial weathered limestone bedrock point to a sudden increase in lake level. According to radiocarbon data, catastrophic flooding occurred shortly after 1214 yr bc. Because the area is located in a highly active seismic zone, we propose that this event was caused by tectonically induced, metre-scale coseismic subsidence related to faults bordering the Ohrid alluvial plain. Moreover, this event coincides well with a dramatic switch in the habitation and settlement strategy in the region. More important, however, is the finding that the age of the proposed massive tectonic event and change in habitation lies within the interval of the proposed ‘earthquake storm’ in the eastern Mediterranean dated to 1225–1175 bc. As the Ohrid-Korça zone belongs to the same tectonic province, a relationship between the abovementioned earthquakes and the proposed event can be expected. This research therefore might provide the first direct evidence of a large-scale earthquake event linkable to the LBA collapse of Europe's first urban civilisation in the Aegean.     

Robotic telescopes for high energy astrophysics in Ondřejov

We report on two small aperture robotic telescopes called BART and D50 operated in Ondřejov. Both telescopes are capable of automatic observation of gamma ray burst (GRB) optical afterglows. Coordinates of GRBs are taken from alerts distributed via Internet. Telescopes observe other interesting high energy sources when there is not any alert. The smaller telescope BART has aperture D = 254 mm. The bigger telescope D50 has a primary mirror of diameter D = 500 mm. Both telescopes are controlled by free software package RTS2 and are accessible through Internet. We describe the two telescopes and related software and show some results such as our first observed optical counterpart of GRB.     

Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.