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# Earthquake magnitude relationships in the region of the Carpathian-Pannonian Basin

Acta Geodaetica et Geophysica Hungarica
Author: T. Zsíros

In the region of the Carpathian-Pannonian Basin (44–50N; 13–28E) 81 earthquakes have moment magnitude (M w); 61 of them are crustal events (focal depth <65 km) while 20 earthquakes belong to the intermediate focal depth region of the Vrancea (Romania) zone. For crustal events the regression of moment magnitude (M w) on local magnitude (M l) shows a better fit for large magnitudes using a second order equation against to a linear relationship, and the actual quadratic formula based on 61 events is the following: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\begin{gathered} M_w = 1.37( \pm 0.28) + 0.39( \pm 0.18)M_l + 0.061( \pm 0.026)M_l^2 \hfill \\ (M_w :1.9 - 5.5;M_l :1.4 - 5.5). \hfill \\ \end{gathered}$ \end{document}.In the intermediate focal depth Vrancea zone of the south-eastern bend of the Carpathians (44.5–46.5N; 25.5–28.0E) the number of body wave magnitudes is the largest one (20) among the local (8), the surface wave (14) and the duration (17) magnitudes. The linear relationship between the moment (M w) and the body wave (M b) magnitudes has the following form: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $M_w = 1.20( \pm 0.08)M_b - 0.76( \pm 0.40)(M_w :4.1 - 7.7;M_b :3.8 - 7.3).$ \end{document}.The relationships of the different (M l, M s, M b, M d) magnitudes are also presented in the paper.

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# Order of magnitude of multiple Fourier coefficients of functions of bounded p-variation

Acta Mathematica Hungarica

## Abstract

For a Lebesgue integrable complex-valued function f defined over the n-dimensional torus
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}^n$$ \end{document}
:= [0, 2π)n, let
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\hat f$$ \end{document}
(k) denote the Fourier coefficient of f, where k = (k 1, … k n) ∈ ℤn. In this paper, defining the notion of bounded p-variation (p ≧ 1) for a function from [0, 2π]n to ℜ in two diffierent ways, the order of magnitude of Fourier coefficients of such functions is studied. As far as the order of magnitude is concerned, our results with p = 1 give the results of Móricz [5] and Fülöp and Móricz [3].
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# Application of time- and magnitude-predictable model in the Central Himalaya and vicinity for estimation of seismic hazard

Acta Geodaetica et Geophysica Hungarica
Authors: H. Paudyal, D. Shanker, H. Singh, and V. Singh

Time dependent seismicity investigation in six seismogenic sources of Nepal and its adjoining areas in the Central Himalaya reveal that there is intermediate time clustering of the moderate size shallow earthquake in each seismogenic source. The inter-event times, between the successive shallow mainshocks, of the magnitude equal to or larger than certain cut-off magnitudes for each of these sources are used for long-term earthquake hazard prediction corresponding to individual sources of the region. For the hazard estimation, the following relations have been established here as: log T t = 0.46 M min +0.07 M p +0.02 log m 0 −2.38, and M f = 0.78 M min −0.25 M p −0.04 log m 0 + 4.32, where T t is the inter-event time measured in years; M min is the moment magnitude of the smallest mainshock considered; M p is the magnitude of preceding main shock, M f is the magnitude of the following mainshock and m 0 is the moment rate in each source per year. The value of σ = 0.22 and multi-correlation coefficient, R = 0.62 for the first equation and σ = 0.30 and R = 0.59 for the second equation are estimated.Based on these relations and using the magnitude and time of occurrence of the last main shocks in each seismogenic source, time dependent conditional probabilities of the next shallow main shocks during the next 10, 20 and 30 years as well as the magnitude of the expected main shocks are forecast.

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# Investigate the magnitude of differences in total metabolizable protein among different genotypes of barley grown for three consecutive years

Cereal Research Communications
Authors: K. Hart, B. Rossnagel, and Peiqiang Yu

Several genotypes of barley have been developed by Crop Development Center. However, no quantitative evaluation of true protein supply to ruminants has been done in terms of protein degradation balance (PDB) and total metabolizable protein supply (or total truly absorbed protein in the small intestines). The objective of this study was to determine the magnitude of difference in terms of total metabolizable protein supply of five CDC feed-type barley cultivars in comparison to Canada’s most widely grown malting cultivar AC Metcalfe. Six, two row cultivars of spring sown barley, included AC Metcalfe, CDC Cowboy, CDC Dolly, CDC Helgason, CDC Trey and McLeod were grown in the research field of University of Saskatchewan, Saskatoon, SK, Canada for three consecutive years. The quantitative predictions were made in terms of: 1) Rumen synthesized microbial protein truly absorbed in the small intestine (AMCP); 2) Rumen undegraded protein truly absorbed in the small intestine (ARUP); 3) Endogenous protein in the digestive tract (AECP); 4) Total metabolizable protein supply in the small intestine. The results showed that CDC barley variety differed (P < 0.05) in AMCP ranging from 34 to 40 g/kg DMand AECP, but had no difference (P > 0.05) in ARUP with average of 48 g/kg DM. Total metabolizable protein ranged (P < 0.05) from 85 to 92 g/kg DM. In conclusion, CDC barley variety affected total predicted metabolizable protein supply, but not to large extend. All the barley varieties had negative degraded protein balance value.

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# Seismicity of the Bánát region

Acta Geodaetica et Geophysica Hungarica
Author: T. Zsíros

In the seismic source zone of Bánát more than 600 earthquakes are known since 1773 among them six events with magnitude of 5.0–5.7 measured on the surface magnitude scale. The macroseismic reinterpretation of the April 2, 1901 earthquake yields epicentral intensity of VII on the European Macroseismic Scale, and a focal depth value of 12 km. Based on empirical relations the maximum rupture area is estimated as 50–55 km 2 and the maximum displacement along the fault is about 16 cm in the Bánát seismic zone due to the MS = 5.7 event occurred on July 12, 1991. The average recurrence that we may expect an earthquake of M ≥ 3.4 every 1 year, an earthquake of M ≥ 4.3 every 10 years and an earthquake of M ≥ 5.3 every 100 years in the studied source zone. The probabilistic seismic hazard assessment predicts 1.3–2.1 m/sec 2 peak ground accelerations, and 6.7–7.3 maximum (theoretical) earthquake intensity values with 10% chance of exceedance for an exposure time of 100 years in the region.

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# Review of the historical seismicity in the western and southwestern territory of Romania (Banat Seismic Region)

Acta Geodaetica et Geophysica Hungarica
Author: E. Oros

The seismicity of the western and southwestern territory of Romania, called in this paper Banat Seismic Region (BSR) is analyzed for the historical period using a new regional Parameter Earthquakes Catalogue (Oros et al. 2007). The catalogue comprises a number of 709 earthquakes occurred between 1443 and 1970, the 269 of which being new recorded events. The magnitudes/intensities (epicentral or maximum observed) range between 2.2 and 5.7 ( M m , M s , m b , MLH or M W ) and 3.0–8 EMS, respectively. Some of the major events re-evaluated on instrumental basis (historical seismograms collected by the author as partner into the EuroSeismos project) show larger values of magnitudes than the previous ones. The space distribution of the epicenters displays an obvious clustering trend well correlated with the tectonics and geology (faults and fault systems, structures). The time distribution displays an apparent migration of the seismic activity between different sources zones, e.g. before 1900 the activity concentrates within the northwestern and southeastern areas of BSR and after 1900 the activity groups mainly in the central part of the region.

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# Seismicity of Kecskemét area

Acta Geodaetica et Geophysica Hungarica
Author: T. Zsíros

In the small seismic source zone of Kecskemét 203 earthquakes are known between 1739 and 2006, and about 90 percent of them have a magnitude value not more than 3.0, however the strongest event on July 8, 1911 has 5.6 surface-wave magnitude. Concerning the latter earthquake the maximum (epicentral) intensity I = VIII (EMS) was observed in the area enclosed by Kecskemét, Katonatelep and Hetényegyháza locations. The quake caused significant damage to buildings (I ≥ VI EMS) on about 6 thousands square kilometres and was felt (I ≥ III EMS) on some 85 thousands square kilometres. The focal depth is estimated as 11 km directly from the individual intensity data points. During the earthquake liquefaction (sand crater) occurred in the epicentral area and some electromagnetic effects were also observed. Studying the source dimensions we conclude the rupture area is between 40 and 67 square kilometres and the maximum displacement along the fault is estimated to 14–20 centimetres for the Kecskemét earthquake of July 8, 1911. A probabilistic seismic hazard assessment predicts 1.1–1.5 m/s 2 peak ground accelerations, and 6.6–7.1 maximum (theoretical) earthquake intensity values with 10% chance of exceedance for an exposure time of 100 years in the studied area.

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# A new ground motion model - Methodological approach

Acta Geodaetica et Geophysica Hungarica
Author: G S Stamatovska

The investigations presented in this paper were aimed at empirical definition  of ground motion under Vrancea earthquakes.  They were based on the recorded accelerogrammes from the occurred strong Vrancea earthquakes of 1977, 1986 and 1990 obtained from the accelerographs installed in the territory of former Yugoslavia, Romania and Bulgaria. A methodological approach to empirical prediction of ground motion parameters under strong earthquake effects was developed and empirical attenuation laws of horizontal peak ground acceleration (PGA) were defined.  A new empirical mathematical model was applied. In this model the amplitudes of strong ground motion are in function of earthquake magnitude, epicentral distance, focal depth, azimuth of the instrument location in respect to  the radiation pattern and the ratio between the semi-axes of the seismic field  ellipse. Through the so called non-homogeneity function of the region, the model indirectly involves the effect of the focal mechanism and the non-homogeneity of the region through which the seismic waves propagate.  The mathematical model applied in these investigations contributed to the  empirical definition of the attenuation laws that play an important role in seismic  hazard analyses and hence in evaluation of the seismic hazard a country or a  region is exposed to.  The results obtained from these investigations are important not only for   Macedonia but for the entire Balkan region and beyond.  The presented methodology and the applied mathematical model of functional relationships are of a particular importance since they are different from the empirical models of strong ground motion that have so far been applied in the world.

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# On the Order of Magnitude of Fourier Transforms

Acta Mathematica Hungarica
Authors: M. Bagota, D. Giang, and F. Móricz
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# On the average order of magnitude of Dirichlet series

Acta Mathematica Hungarica
Author: G. Halász
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