Palaeoseismological analyses of northern and central Germany

Northern Germany is an intraplate region and has been regarded as a low seismicity area for a long time. However, historic sources show the occurrence of several significant natural earthquakes in northern and central Germany since the 10th century. In recent years natural earthquakes as well as earthquakes in the vicinity of active gas fields, likely to have been associated with the recovery of hydrocarbons, have been repeatedly instrumentally recorded in northern Germany. In central Germany, which is exposed to a higher earthquake hazard than northern Germany, historically and instrumentally recorded earthquakes accumulate in a N-S trending zone. However, the seismic record of Germany is limited and solely goes back to the year 800 CE. Long periods of seismic quiescence alternating with fault activity for a short geological period of time can falsify the seismic hazard of an intraplate region. Seismic hazard can be underestimated because of seismic quiescence or overestimated because of the detection of periodical clustering, migrating and infrequent seismicity. Therefore, palaeoseismology is the missing link for an accurate assessment of the seismic hazard estimation of a continental low strain area like Germany. Northern and central Germany were repeatedly affected by glaciations and periglacial processes during the Pleistocene. The main difficulty is to distinguish the vast glaciotectonic deformation structures that are present in northern Germany from neotectonic deformation structures. Processes like cryoturbation, depositional loading in water saturated sediments and rapid rates of deposition can generate soft-sediment deformation structures that may also be mistaken for earthquake-induced structures. The analysis of neotectonic activity in northern and central Germany is challenging because recently observed vertical crustal movements along NWSE- striking faults do not commonly correspond to visible morphological features and fault scarps are rapidly destroyed by climatic conditions. Seven WNW-ESE trending major basement faults with a high potential for reactivation due to glacial isostatic adjustment were analysed with regard to neotectonic fault activity. In addition, in central Germany the controversially discussed seismically active part of the Regensburg-Leipzig-Rostock fault system between Leipzig and Cheb and surroundings was analysed with regard to pre-historic activity. Deformation bands and seismites in Palaeogene and Pleistocene deposits exposed in sand and gravel pits are indicators for neotectonic activity. Luminescence dating, shear-wave reflection seismics, electrical resistivity tomography and lineament analysis were applied to support neotectonic activity in the study area. Evidence for neotectonic movements, indicated by the occurrence of deformation bands in Middle to Late Pleistocene sediments, was identified along five of the seven major basement faults that were analysed in northern Germany. Evidence was found at the Aller Fault, the Halle Fault, the Harz Boundary Fault, the Steinhuder Meer Fault and the Osning Thrust. In the area around the Regensburg-Leipzig-Rostock fault system neotectonic movements are indicated by deformation bands in Palaeocene and Middle Pleistocene sediments at fault intersections of mainly NW-SE oriented faults like the Lusatian Thrust and the Finne-Gera-Jáchymov fault system and fault intersections of minor faults in the vicinity to the cities Leipzig and Dresden. It was possible to estimate the timing of neotectonic activity of faulted Pleistocene sediments by means of luminescence dating at two basement faults (Harz Boundary Fault, Steinhuder Meer Fault). The estimated ages of faulted debris-flow deposits at the Harz Boundary Fault (15.2 ± 0.8 and 14.2 ± 0.8 ka ka) point to fault movements after ~15 ka corresponding with the reactivation of the Osning Thrust. The estimated age of growth strata at the Steinhuder Meer Fault (189 ± 5 ka and 158 ± 4 ka) indicates fault movements in Middle Pleistocene Saalian times. At the Harz Boundary Fault shear-wave reflection seismic surveys and electrical resistivity tomography profiles support the neotectonic activity in the Lateglacial. The timing of fault movements implies that the seismicity in northern and parts of central Germany is likely induced by varying lithospheric stress conditions related to glacial isostatic adjustment. For the Harz Boundary Fault and the Osning Thrust this is supported by numerical simulations of Coulomb failure stress variations. Thus, the faults can be classified as glacially-induced faults. Along the Regensburg-Leipzig-Rostock fault system, focal mechanisms of deep-seated earthquakes partly show NW-SE trending nodal planes. The focal mechanisms indicate activity along NW-SE oriented faults that intersect the N-S striking Regensburg-Leipzig-Rostock fault system. This supports the seismotectonic importance of NWSE oriented faults and intersecting faults in the study area of northern and central Germany

Christoffel words and the Calkin-Wilf tree

In this note we present some results on the Calkin-Wilf tree of irreducible fractions, giving an insight on the duality relating it to the Stern-Brocot tree, and proving noncommutative versions of known results relating labels of the Calkin-Wilf trees to hyperbinary expansions of positive integers. The main tool is the Christoffel tree introduced in a paper by Berstel and de Luca

On Christoffel and standard words and their derivatives

We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the aforementioned classes of words. In the case of Christoffel words, the morphisms involved map $a$ to $a^{k+1}b$ (resp.,~$ab^{k}$) and $b$ to $a^{k}b$ (resp.,~$ab^{k+1}$) for a suitable $k>0$. As long as derivatives are longer than one letter, higher-order derivatives are naturally obtained. We define the depth of a Christoffel or standard word as the smallest order for which the derivative is a single letter. We give several combinatorial and arithmetic descriptions of the depth, and (tight) lower and upper bounds for it.Comment: 28 pages. Final version, to appear in TC

Involutions of epicentral words

AbstractEpisturmian sequences, or words, are a natural generalization of Sturmian sequences to arbitrary finite alphabets. In this paper we investigate various combinatorial properties of epicentral words, i.e., palindromic prefixes of standard episturmian words. We consider the action of certain involutions defined on epicentral words. We show that in some cases their fixed points may be characterized in terms of suitable faithful representations of epicentral words. We further show that various previously known results for central Sturmian words may be extended to epicentral words