Dependent coordinates in path integral measure factorization

The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group. The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory. The integral relation between the kernels of the original and reduced semigroup are obtained.Comment: LaTeX2e, 28 page

The ISC-GEM Earthquake Catalogue (1904–2014): status after the Extension Project

We outline the work done to extend and improve the ISC-GEM Global Instrumental Earthquake Catalogue, a dataset which was first released in 2013 (Storchak et al., 2013, 2015). In its first version (V1) the catalogue included global earthquakes selected according to time-dependent cut-off magnitudes: 7.5 and above between 1900 and 1918 (plus significant continental earthquakes 6.5 and above); 6.25 between 1918 and 1959; 5.5 between 1960 and 2009. Such selection criteria were dictated by time and resource limitations. With the Extension Project we added both pre-1960 events below the original cut-off magnitudes (if enough station data were available to perform relocation and magnitude recomputation) and added events with magnitude 5.5 and above from 2010 to 2014. The project ran over a 4-year period during which a new version of the ISC-GEM Catalogue was released each year via the ISC website (http://http://www.isc.ac.uk/iscgem/, last access: 10 October 2018). For each year, not only have we added new events to the catalogue for a given time range but also revised events already in V1 if additional data became available or location and/or magnitude reassessments were required. Here we recall the general background behind the production of the ISC-GEM Catalogue and describe the features of the different periods in which the catalogue has been extended. Compared to the 2013 release, we eliminated earthquakes during the first 4 years (1900–1903) of the catalogue (due to lack of reliable station data), added approximately 12&thinsp;000 and 2500 earthquakes before 1960 and between 2010 and 2014, respectively, and improved the solution for approximately 2000 earthquakes already listed in previous versions. We expect the ISC-GEM Catalogue to continue to be one of the most useful datasets for studies of the Earth's global seismicity and an important benchmark for seismic hazard analyses, and, ultimately, an asset for the seismological community as well as other geoscience fields, education and outreach activities. The ISC-GEM Catalogue is freely available at https://doi.org/10.31905/D808B825.</p

The ISC Bulletin as a comprehensive source of earthquake source mechanisms

In this article we summarize the availability of earthquake source mechanisms in the Bulletin of the International Seismological Centre (ISC). The bulletin in its current status contains ∼81 000 seismic events with only one associated mechanism solution and ∼25 000 events with at least two associated source mechanisms. The main sources of earthquake mechanisms in the ISC Bulletin are reported solutions provided by data contributors and ISC-computed focal mechanisms based on first motion polarities. Given the importance of using pre-determined fault plane solutions in different types of studies, here we briefly discuss the methodologies adopted by major data providers to the ISC and investigate the intra-event variability of the source mechanisms. We conclude that the overall agreement among different earthquake mechanisms for the same event as reported by different sources can show a similarity coefficient as high as 80&thinsp;%, based on the rotation angles of their best-fitting double couple solutions, for the majority of the cases. The earthquake source mechanisms discussed in this work are freely available within the ISC Bulletin websearch at http://doi.org/10.31905/D808B830.</p

Frontiers of seismology

The British Seismology Meeting 2019 took place at the University of Edinburgh over three days, 4–6 September. The first British Seismology Meeting, BSM2017, was held in Reading in April 2017 (Lieser et al.2018); there had been earlier seismology meetings in the UK, but no wide-ranging cross-disciplinary meetings since Frontiers of Seismology in Edinburgh 2009 (Sargeant et al.2009). In his welcoming address at BSM2017, Dmitry Stor-chak expressed a wish that it would be the first in a series of such meetings, which he thought should become a regular event, perhaps every two years. At the end of the BSM2017 meeting, Anton Ziolkowski offered the University of Edinburgh as a potential venue for BSM2019.BSM2019: Frontiers of Seismology attracted about 70 scientists from the UK and abroad, to present and discuss seismological research, establish new contacts and strengthen existing links. A feature of the meeting was that all posters were available in a large space adjacent to the lecture theatre for viewing, presentation and discussion for the whole period, including coffee breaks, lunch and evening drinks. Feedback from the meeting was very positive. This article presents a brief summary of each session

Low temperature properties of a quantum particle coupled to dissipative environments

We study the dynamics of a quantum particle coupled to dissipative (ohmic) environments, such as an electron liquid. For some choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first order transition, between strongly and weakly localized regimes.Comment: 10 page

Методика регистрации угловых диаграмм отражения и рассеяния света прецизионных оптических поверхностей

Описано методику реєстрації кутових діаграм відбивання і розсіяння світла і показано, що за індикатрисами розсіяння при оптимальному напрямку спостереження можна оцінити шорсткість оптичних поверхонь за шириною піка, що спостерігається на фоні незмінного п’єдесталу.The technique of registration of angular diagram’s of reflexion and dispersion of light is described and is shown, that on in indicatrix dispersion at an optimum direction of supervision it is possible to estimate a roughness of optical surfaces on width of peak which is observed against an invariable pedestal.Описана методика регистрации угловых диаграмм отражения и рассеяния света и показано, что по индикатрисам рассеяния при оптимальном направлении наблюдения можно оценить шероховатость оптических поверхностей по ширине пика, который наблюдается на фоне неизменного пьедестала

Tsunami hazard assessment of coastal South Africa based on mega-earthquakes of remote subduction zones

After the mega-earthquakes and concomitant devastating tsunamis in Sumatra (2004) and Japan (2011), we launched an investigation into the potential risk of tsunami hazard to the coastal cities of South Africa. This paper presents the analysis of the seismic hazard of seismogenic sources that could potentially generate tsunamis, as well as the analysis of the tsunami hazard to coastal areas of South Africa. The subduction zones of Makran, South Sandwich Island, Sumatra, and the Andaman Islands were identified as possible sources of mega-earthquakes and tsunamis that could affect the African coast. Numerical tsunami simulations were used to investigate the realistic and worst-case scenarios that could be generated by these subduction zones. The simulated tsunami amplitudes and run-up heights calculated for the coastal cities of Cape Town, Durban, and Port Elizabeth are relatively small and therefore pose no real risk to the South African coast. However, only distant tsunamigenic sources were considered and the results should therefore be viewed as preliminary.The Nuclear Structural Engineering (Pty) and the National Research Foundation through the Technology and Human Resources for Industry Programme project (THRIP) TP2011061400009.https://link.springer.com/journal/242019-04-01hj2018Geolog