Distribution of Maximum Earthquake Magnitudes in Future Time Intervals, Application to the Seismicity of Japan (1923-2007)

We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and Generalized Extreme Value distribution (GEV). We obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration tau. This distribution can be characterized by its quantile Qq(tau) at any desirable statistical level q. The quantile Qq(tau) provides a much more stable and robust characteristic than the traditional absolute maximum magnitude Mmax (Mmax can be obtained as the limit of Qq(tau) as q tends to 1, and tau tends to infinity). The best estimates of the parameters governing the distribution of Qq(tay) for Japan (1923-2007) are the following: Form parameter for GEV = -0.1901 +- 0.0717; position parameter GEV(tau=200)= 6.3387 +- 0.0380; spread parameter for GEV(tau=200)= 0.5995 +- 0.0223; Q_0.90,GEV(tau=10)= 8.34 +- 0.32. We also estimate Qq(tau) for a set of q-values and future time periods in the range for tau between 1 and 50 years from 2007. For comparison, the absolute maximum estimate Mmax from GEV, which is equal to 9.57 +- 0.86, has a scatter more than twice that of the 90 percent quantile Q_{0.90,GEV}(tau=10) of the maximum magnitude over the next 10 years counted from 2007.Comment: 15 pages + 10 figure

On the Correct Use of Statistical Tests: Reply to "Lies, damned lies and statistics (in Geology)"

In a Forum published in EOS Transactions AGU (2009) entitled "Lies, damned lies and statistics (in Geology)", Vermeesch (2009) claims that "statistical significant is not the same as geological significant", in other words, statistical tests may be misleading. In complete contradiction, we affirm that statistical tests are always informative. We detail the several mistakes of Vermeesch in his initial paper and in his comments to our reply. The present text is developed in the hope that it can serve as an illuminating pedagogical exercise for students and lecturers to learn more about the subtleties, richness and power of the science of statistics.Comment: 7 pages and 1 figure: This text expands considerably the short text published under the same title in Eos Transactions AGU, Vol. 92, No. 8, page 64, 22 February 201

Rigorous statistical detection and characterization of a deviation from the Gutenberg-Richter distribution above magnitude 8 in subduction zones

We present a quantitative statistical test for the presence of a crossover c0 in the Gutenberg-Richter distribution of earthquake seismic moments, separating the usual power law regime for seismic moments less than c0 from another faster decaying regime beyond c0. Our method is based on the transformation of the ordered sample of seismic moments into a series with uniform distribution under condition of no crossover. The bootstrap method allows us to estimate the statistical significance of the null hypothesis H0 of an absence of crossover (c0=infinity). When H0 is rejected, we estimate the crossover c0 using two different competing models for the second regime beyond c0 and the bootstrap method. For the catalog obtained by aggregating 14 subduction zones of the Circum Pacific Seismic Belt, our estimate of the crossover point is log(c0) =28.14 +- 0.40 (c0 in dyne-cm), corresponding to a crossover magnitude mW=8.1 +- 0.3. For separate subduction zones, the corresponding estimates are much more uncertain, so that the null hypothesis of an identical crossover for all subduction zones cannot be rejected. Such a large value of the crossover magnitude makes it difficult to associate it directly with a seismogenic thickness as proposed by many different authors in the past. Our measure of c0 may substantiate the concept that the localization of strong shear deformation could propagate significantly in the lower crust and upper mantle, thus increasing the effective size beyond which one should expect a change of regime.Comment: pdf document of 40 pages including 5 tables and 19 figure

Characterization of the frequency of extreme events by the Generalized Pareto Distribution

Based on recent results in extreme value theory, we use a new technique for the statistical estimation of distribution tails. Specifically, we use the Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for peak-over-threshold values in the form of the Generalized Pareto Distribution (GPD). Useful in finance, insurance, hydrology, we investigate here the earthquake energy distribution described by the Gutenberg-Richter seismic moment-frequency law and analyze shallow earthquakes (depth h < 70 km) in the Harvard catalog over the period 1977-2000 in 18 seismic zones. The whole GPD is found to approximate the tails of the seismic moment distributions quite well above moment-magnitudes larger than mW=5.3 and no statistically significant regional difference is found for subduction and transform seismic zones. We confirm that the b-value is very different in mid-ocean ridges compared to other zones (b=1.50=B10.09 versus b=1.00=B10.05 corresponding to a power law exponent close to 1 versus 2/3) with a very high statistical confidence. We propose a physical mechanism for this, contrasting slow healing ruptures in mid-ocean ridges with fast healing ruptures in other zones. Deviations from the GPD at the very end of the tail are detected in the sample containing earthquakes from all major subduction zones (sample size of 4985 events). We propose a new statistical test of significance of such deviations based on the bootstrap method. The number of events deviating from the tails of GPD in the studied data sets (15-20 at most) is not sufficient for determining the functional form of those deviations. Thus, it is practically impossible to give preference to one of the previously suggested parametric families describing the ends of tails of seismic moment distributions.Comment: pdf document of 21 pages + 2 tables + 20 figures (ps format) + one file giving the regionalizatio

Cultural Influences upon Soviet-Era Programmatic Piano Music for Children

The Russian Revolution and the ensuing Union of Soviet Socialist Republics (USSR) spawned an era of Soviet music education that resulted in generations of gifted musicians. Soviet-era piano composers contributed to the emergence and the development of a unique style of piano training, a Soviet piano school, represented by great pianists and music educators known all over the world. Recent research on Soviet-era piano music focuses on non-programmatic piano compositions. The research conducted in this work appears to be the first to produce a comparative overview of major programmatic piano compositions for children written during the Soviet era. In Cultural Influences Upon Soviet-Era Programmatic Piano Music For Children, the author offers an examination of Soviet-era music history, traditions, aesthetics, as well as the influences of Soviet cultural and political forces upon the creation and development of extra-musical imagery and narratives in Soviet-era programmatic piano music. This work discusses the role of musical meaning, expressed through extra-musical imagery and narratives, which is conveyed by the means of imagination, fantasy, and creativity in programmatic piano compositions. This research examines the role of culture, and the use of cultural references and the cultural toolkit in children’s music education and piano instruction. It also studies the major Soviet-era composers and programmatic piano compositions, and offers a comparative overview of the main categories of extra-musical imagery and narratives that are prevalent among the character pieces composed over the course of Soviet cultural history. The Soviet-era composers reflected the Soviet culture and history in their programmatic piano compositions by using extra-musical imagery and narratives that capture children’s imagination and motivate them in their musical education and piano training. This work identifies an important collection of Soviet-era programmatic piano compositions for the use in children’s musical education as well as in future research. The concepts discussed in this paper and the comparative overview of the Soviet-era programmatic piano compositions and their categories represent a valuable source for piano instructors to understand the historical development, significance, and expressive intentions of the network of symbols and narratives that underlies much of the Soviet piano repertoire, to help achieve success with their students

He lived for the sake of people. To the 180th anniversary of the Ekaterinoslav zemstvo doctor V.T. Skrylnikov (1837-1898) (part 2).

The second part of the essay about zemstvo doctor, V.T. Skrylnikov elucidates his fruitful activity in the field of balneology: study and popularization of therapeutic properties of the so-called "Timofeev clay", publication of his "Seasonal Bulletin of Slaviansk mineral water ". We describe recent years of the doctor’s life, complicatedwith the disease and severe family affairs. The grateful memoriesof his fellow doctors about himare listed

He lived for the sake of people. To the 180th anniversary of the Yekaterinoslav zemstvo doctor V.T. Skrylnikov (1837-1898).

For the first time the article introduces to the reader biography of one of the founders of the Yekaterinoslav Medical Society, a local doctor, author of numerous scientific papers on medicine and hygiene VasiliyTimofeevich Skrylnikov. The first part provides previously unknown details about his origin, the work as the head of the free zemstvo clinic, highlights his proposals in the field of sanitary service of the city Yekaterinoslav, wide publishing activities. The aspects of V.T. Skrylnikov’s service on guardianship of orphans, and the initiative to create Yekaterinoslav Department of Russian society of public health are touched upon