Systematic measurement of the radioactivity of atmospheric precipitation and evaluation of the artificial radioactivity of the atmosphere

Резюме В статье приводится описание методики измерений искусственной радиоактивности осадков. В результате измерений более 90 образцов бЫло доказано, что здесь мЫ имеем дело с искусственной радиоактивностью, вЫзЫваемой наличием продуктов распада образующихся в результате опЫтов с атомнЫм оружием. Доказательством этого служит прежде всего убЫвание активности испарений с временем. Абсолютная оценка показала, что здесь речь идет об активности порядка 10⁻¹⁰–10⁻⁹ кюру/л. в воде осадков. ПроведеннЫе работЫ показали, насколько важнЫми могут бЫть подобнЫе измерения для метеорологических целей, но в особенности для фпзики облаков и осадков.

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Address: Vojenská lékařská akademie J. Ev. Purkynê, Hradec Králové.

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Address: Geofysikální ústav ĈSAV, odd. meteorologie, Hradec Králové 8.     

On one integral of equations of motion of relative horizontal flow

Резюме Бьул выведен интеграл уравнений двнженид Лагранжа, соответствующжа, соответствуюший чоступательниым, неустойчивым, тошоидальным волнам на границе раздела двух зональнух течений. Внд границы раздела в течение развития волны меняется, превращаясь из обычной трохоиды в циклоиду. Числовые оценки показывают, что рассматриваемые волны цхематичесски соответствуйт коротким воянам на квазистационарных атмосфернын фронтах.

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Dedicated to Professor Bedřich Ŝalamon on his 85th Birthday     

Estimates of fracture parameters of earthquakes

A new estimate of the fracture parameters of earthquakes is provided in this paper. By theMuskhelishvili method (1953) a number of basic relations among fracture-mechanics parameters are derived. A scheme is proposed to evaluate the slip weakening parameters in terms of fault dimension, average slip, and rise time, and the new results are applied to 49 events compiled in the earthquake catalogue ofPurcaru andBerckhemer (1982). The following empirical relations are found in the paper: $$\begin{gathered} \frac{{\tau _B - \tau _f }}{{\tau _\infty - \tau _f }} = 2.339 \hfill \\ {{\omega _c } \mathord{\left/ {\vphantom {{\omega _c } {W = 0.113}}} \right. \kern-\nulldelimiterspace} {W = 0.113}} \hfill \\ \log G_c \left( {{{dyne} \mathord{\left/ {\vphantom {{dyne} {cm}}} \right. \kern-\nulldelimiterspace} {cm}}} \right) = 2 \log L (km) + 6.167 \hfill \\ \log \delta _c (cm) = 2 \log L (km) - 1.652 \hfill \\ \end{gathered} $$ whereG _c is the specific fracture energy,ω _c the size of the slip weakening zone,δ _c the slip weakening displacement,τ _B ?τ _f the drop in strength in the slip weakening zone,τ _∞?τ _f the stress drop,L the fault length, andW the fault width. The investigation of 49 shocks shows that the range of strength dropτ _B ?τ _f is from several doze to several hundred bars at depthh<400 km, but it can be more than 10³ bars ath>500 km; besides, the range of the sizeω _c of the strength degradation zone is from a few tenths of a kilometer to several dozen kilometers, and the range of the slip weakening displacementδ _c is from several to several hundred centimeters. The specific fracture energyG _c is of the order of 10⁸ to 10¹¹ erg cm^?2 when the momentM ₀ is of the order of 10²³ to 10²⁹ dyne cm.     

Self-reversal of spontaneous magnetization of natural cassiterite

Резюме Рассматривается случай экспериментального обнаружения самообращения спонтанной намагниченности на образце естественного касситерита. Самообращение спонтанной намагниченности вызывается, по-видимомы, влиянием различий температурной зависимости намагниченности в отдельных зонах, где обнаруживается повышенная концентрация ионов железа в кристаллической решетке касситерита. Аномальный ход изменений температурной зависимости намагниченности насышения сравнивали как с обычным ходом изменений температурной зависимости намагниченности насышения двух дальнейших образцов касситерита, так и со свойствами естественной остаточной намагниченности. В габлицах приводятся химический состав отдельных образцов и соответствуюшие магнитные характеристики (значения намагниченности насыщения, температуры Кюри и температуры компенсации, а также значения естественной остаточной намагниченности и названия месторождений образцов).

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Address: Bočni II, Praha 4-Spořilov.     

Modeling of the runup heights of the Hokkaido-Nansei-Oki tsunami of 12 July 1993

The Hokkaido-Nansei-Oki earthquake (M _w 7.7) of July 12, 1993, is one of the largest tsunamigenic events in the Sea of Japan. The tsunami magnitudeM _t is determined to be 8.1 from the maximum amplitudes of the tsunami recorded on tide gauges. This value is larger thanM _w by 0.4 units. It is suggested that the tsunami potential of the Nansei-Oki earthquake is large forM _w . A number of tsunami runup data are accumulated for a total range of about 1000 km along the coast, and the data are averaged to obtain the local mean heightsH _n for 23 segments in intervals of about 40 km each. The geographic variation ofH _n is approximately explained in terms of the empirical relationship proposed byAbe (1989, 1993). The height prediction from the available earthquake magnitudes ranges from 5.0–8.4 m, which brackets the observed maximum ofH _n , 7.7 m, at Okushiri Island.     

On the solution of the reverse problem of geodesics with the help of the chord

Резюме Дается вывод формул для вычислений длины хорды, длины и азимутов нормаляных сечений и длины геодезической линии эллипсоида. Применяются тригонометрические функции данных величин и постоянные принятого ргфгргнц-эллипсоида, что является целесообразным при использовании вычислителQjных машин, особенно автоматов. Рабочие формулы рекомендуются в форме (8–11).

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Dedicated to Professor František Fiala on His 85th Birthday

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Address: Veveři 95, Brno.     

Thermomagnetic analysis of magnetite parts of serpentinite samples and results of other investigations

Summary The normal type of serpentinites consists of chrysotile. The magnetite parts are essential parts of the structure of chrysotile serpentinites (primary magnetite). Chrysotile is changed to antigorite by mechanical deformations. The magnetite parts of rock structure are lost and they sat down in the veins of serpentinite rocks (secondary magnetite). In this paper the thermomagnetic diagrams and the results of X-ray investigations of secondary and primary magnetite are described. Some results of susceptibility measurements are given. The secondary magnetite is characterized by a region of oxydation in the interval 280–400° C (secondary magnetite-Fe₂O₃-Fe₂O₃). The oxydation to -Fe₂O₃ is remarkably. On the thermomagnetic diagrams of primary magnetite no typical oxydation region is to be seen. The oxydation: primary magnetite-Fe₂O₃ is very small. The interval of measured susceptibility values amounts to (10–1500)·10^–6 cgs units. The essential variability of the main parts of serpentinite samples is characterized by the great changes of susceptibility values from point to point.The determined values of specific saturation magnetization (Gauss. cm³ g^–1), the X-ray powder data, and some results on remanent magnetization are given.

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Zusammenfassung Die Normaltypserpentinite bestehen aus Chrysotil. Der Magnetit ist Bestandteil der Struktur der Chrysotilserpentinite (primärer Magnetit). Unter dem Einfluß mechanischer Deformationen geht Chrysotil in Antigorit über. Die Magnetitanteile der Gesteinsstruktur gehen verloren und scheiden sich auf Klüften ab (sekundärer Magnetit). In der vorliegenden Arbeit werden die thermomagnetischen Abhängigkeiten und die Ergebnisse von Röntgenuntersuchungen des sekundären und primären Magnetits beschrieben. Es werden einige Ergebnisse der Suszeptibilitätsmessungen angeführt. Der sekundäre Magnetit wird durch einen Oxydationsbereich im Temperaturintervall 280–400° C charakterisiert (sekundärer Magnetit-Fe₂O₃-Fe₂O₃). Die Oxydation zu -Fe₂O₃ ist beträchtlich. Die thermomagnetischen Diagramme des primären Magnetits zeigen keinen typischen Oxydationsbereich. Die Oxydation: primärer Magnetit-Fe₂O₃ ist sehr gering. Das Intervall der gemessenen Suszeptibilitätswerte beträgt (10–1500)·10^–6 CGS-Einheiten. Die starke Veränderlichkeit der Hauptbestandteile der Serpentinitproben wird durch die großen Änderungen der Suszeptibilitätswerte von Punkt zu Punkt gekennzeichnet.Die gemessenen Werte der Sättigungsmagnetisierung (Gauss.cm³ g^–1), der Röntgenuntersuchungen und einige Ergebnisse über die remanente Magnetisierung werden gegeben.

     

不同上覆水氟浓度对湖泊沉积物氟释放与微生物群落的影响

通过模拟沙湖沉积物-水系统,以沙湖原水氟离子（F^-）浓度为1倍浓度（0.69 mg/L）,设置0.5倍浓度、1倍浓度、1倍浓度灭菌、2倍浓度和4倍浓度共5个实验组,探究不同上覆水F^-浓度背景下沙湖沉积物中F^-的迁移.结果表明,沉积物F^-的释放量随上覆水F^-浓度的增加而呈下降的趋势,其中2倍和4倍浓度组的沉积物由释放F^-转变为吸附F^-.碱性水体有利于沉积物F^-的释放,即随着pH增大,F^-释放量也会增加.微生物的Beta多样性层次聚类分析表明,F^-会抑制Paenisporosarcina与Thiobacillus的相对丰度,但对Fusibacter的生命活动具有促进作用.根据各浓度组间优势菌属相对丰度与环境因子的冗余分析可得,Acinetobacter、Thiobacillus相对丰度与pH呈负相关;Fusibacter相对丰度与F^-浓度呈显著正相关,而Thiobacillus的相对丰度则与F^-表现出弱负相关.通过对各浓度组中重要离子的分析发现,0.5倍组和4倍组中F^-的迁移受Ca²⁺、HCO₃^-和SO₄^2-浓度影响较大;相关性分析表明0.5倍浓度组的Ca²⁺、HCO₃^-浓度与F^-浓度呈极显著正相关,而4倍组中F^-浓度和Ca²⁺、HCO₃^-浓度呈负相关,SO₄^2-浓度和F^-浓度的相关性则是0.5倍组呈负相关,4倍组呈极显著正相关.本文在不同上覆水F^-浓度背景下全面探究了沙湖沉积物中F^-释放和迁移机理,为沙湖及其他含氟地表水的氟污染防治提供理论支持.     

Instability of interaction of interplanetary events with the earth's magnetosphere over long periods of time

Summary The position and size of the maximum of a model curve with one maximum during a half year were sought to provide the best linear relation between selected parameters, describing the geoactive event in the interplanetary medium, and the geomagnetic activity indices used and modulated additively by a model curve. The maxima for the separate half-years do not tend to cumulate and thus indicate that the sensitivity of the magnetosphere's reaction to an external stimulus may depend on parameters others than the angle of incidence at the magnetosphere.

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Резюме Искaлось месmоnоложенuе u знaченuе мaксuмумa мо?rt;ельноŭ крuвоŭ с о?rt;нuм мaкрuмумом в mеченuе nолу о?rt;a с целью nолучumь нauлучщее лuнеŭное оmнощенuе меж?rt;у выбрaннымu naрaмеmрaмu, оnuсывaющuмu еоaкmuвное собыmuе в межnлaнеmaрноŭ сре?rt;е, u меж?rt;у uн?rt;ексaмu еомa нumноŭ aкmuвносmu, uсnользовaннымu u мо?rt;улuровaннымu a?rt;?rt;umuвно nрu nомощu мо?rt;ельноŭ крuвоŭ. Мaксuмумы ?rt;ля оm?rt;ельных nолу о?rt;uŭ не nроявляюm mен?rt;енцuю к кумуляцuu u, maкuм обрaзом, свu?rt;еmельсmвуюm о mом, чmо чувсmрвumельносmь реaкцuu мa нumосферы к внещнему сmuмулу можеm зaвuсеmь оm ?rt;ру uх naрaмеmров, a не оm у лa na?rt;енuя нa мa нumосферу.

     

New Approach to the Characterization of M max and of the Tail of the Distribution of Earthquake Magnitudes

We develop a new method for the statistical estimation of the tail of the distribution of earthquake sizes recorded in the Harvard catalog of seismic moments converted to m _W -magnitudes (1977–2004 and 1977–2006). For this, we suggest a new parametric model for the distribution of main-shock magnitudes, which is composed of two branches, the pure Gutenberg-Richter distribution up to an upper magnitude threshold m ₁, followed by another branch with a maximum upper magnitude bound M _max, which we refer to as the two-branch model. We find that the number of main events in the catalog (N = 3975 for 1977–2004 and N = 4193 for 1977–2006) is insufficient for a direct estimation of the parameters of this model, due to the inherent instability of the estimation problem. This problem is likely to be the same for any other two-branch model. This inherent limitation can be explained by the fact that only a small fraction of the empirical data populates the second branch. We then show that using the set of maximum magnitudes (the set of T-maxima) in windows of duration T days provides a significant improvement, in particular (i) by minimizing the negative impact of time-clustering of foreshock/main shock/aftershock sequences in the estimation of the tail of magnitude distribution, and (ii) by providing via a simulation method reliable estimates of the biases in the Moment estimation procedure (which turns out to be more efficient than the Maximum Likelihood estimation). We propose a method for the determination of the optimal choice of the T value minimizing the mean-squares-error of the estimation of the form parameter of the GEV distribution approximating the sample distribution of T-maxima, which yields T _optimal = 500 days. We have estimated the following quantiles of the distribution of T-maxima for the whole period 1977–2006: Q _16%(M _max) = 9.3, Q _50%(M _max) = 9.7 and Q _84%(M _max) = 10.3. Finally, we suggest two more stable statistical characteristics of the tail of the distribution of earthquake magnitudes: The quantile Q _T (q) of a high probability level q for the T-maxima, and the probability of exceedance of a high threshold magnitude ρ _T (m*)  = P{m _k  ≥ m*}. We obtained the following sample estimates for the global Harvard catalog and The comparison between our estimates for the two periods 1977–2004 and 1977–2006, where the latter period included the great Sumatra earthquake 24.12.2004, m _W  = 9.0 confirms the instability of the estimation of the parameter M _max and the stability of Q _T (q) and ρ _T (m*) = P{m _k  ≥ m*}.     

Truncation of the distribution of ground-motion residuals

Recent studies to assess very long-term seismic hazard in the USA and in Europe have highlighted the importance of the upper tail of the ground-motion distribution at the very low annual frequencies of exceedance required by these projects. In particular, the use of an unbounded lognormal distribution to represent the aleatory variability of ground motions leads to very high and potentially unphysical estimates of the expected level of shaking. Current practice in seismic hazard analysis consists of truncating the ground-motion distribution at a fixed number (ε _max) of standard deviations (σ). However, there is a general lack of consensus regarding the truncation level to adopt. This paper investigates whether a physical basis for choosing ε _max can be found, by examining records with large positive residuals from the dataset used to derive one of the ground-motion models of the Next Generation Attenuation (NGA) project. In particular, interpretations of the selected records in terms of causative physical mechanisms are reviewed. This leads to the conclusion that even in well-documented cases, it is not possible to establish a robust correlation between specific physical mechanisms and large values of the residuals, and thus obtain direct physical constraints on ε _max. Alternative approaches based on absolute levels of ground motion and numerical simulations are discussed. However, the choice of ε _max is likely to remain a matter of judgment for the foreseeable future, in view of the large epistemic uncertainties associated with these alternatives. Additional issues arise from the coupling between ε _max and σ, which causes the truncation level in terms of absolute ground motion to be dependent on the predictive equation used. Furthermore, the absolute truncation level implied by ε _max will also be affected if σ is reduced significantly. These factors contribute to rendering a truncation scheme based on a single ε _max value impractical.     

Dependence of amplitudes of seismic body waves on the distance

Резюме Нзменение амплитуд объемных волн с расстоянием было изучено на основании б аемлетрясений, регистрированных 30 сейсмическими станциями в эпицентральных расстояниях<30°. Из рисунков видно, что амплитуды продолных и поперечных волн меняются в изучаемых расстояниях подобным образом, но минимум и максимум кривой (A ^*, Δ) для волнSH подвинуты к ббльшим эпицентральным расстояниям чем в случае воумPH.

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Address: Boční II, Praha 13-Spořilov.     

Feasibility of grain-size analysis methods for determination of vertical hydraulic conductivity of streambeds

Accurate estimation of streambed vertical hydraulic conductivity (K_v) is of great importance in the analysis of water quantity exchange and solute transfer between a stream and its sediments. The paper analyzed the inaccuracy of hydraulic conductivity values of sediments derived from grain-size distribution (K_g), which were determined from eight empirical grain-size methods to represent streambed K_v. In this study, the values of K_v for a streambed were derived using falling-head standpipe permeameter tests conducted at eight study sites in the Elkhorn River, Nebraska, and the tested streambed columns were then collected for grain-size analysis by sieving. These empirical methods were used to calculate the K_g values of the streambed from grain-size distribution data of sediments. Unlike many other studies, this study verifies K_g from grain-size distribution with K_v from permeameter tests on the basis of the same samples of streambed sediments. The K_g values derived from the eight empirical methods were larger than the K_v from permeameter tests; there are five methods that give K_g values of about 3–6 times larger than these K_v. The K_g values from the Kozeny formula followed by the Hazen formula give the largest overestimation error if they are used to represent the K_v of the streambed. The USBR and Shepherd formulas generated K_g values close to K_v, but these K_g values are still larger in general than the K_v values. Moreover, the new values of coefficient C for the empirical formulas were revised so that they can be used to calculate the approximate K_v of a streambed. Among the eight methods, the ratios of the original C values to the average new C range from 1.3 to 5.9. It can be hypothesized that smaller C values must be used in the estimation of K_v for general soil samples if these empirical formulas are used to calculate K_v.     

Study of dynamic behaviour of recession curves

Since Brutsaert and Neiber (1977), recession curves are widely used to analyse subsurface systems of river basins by expressing ? dQ/dt as a function of Q, which typically take a power law form: ? dQ/dt = kQ^α, where Q is the discharge at a basin outlet at time t. Traditionally recession flows are modelled by single reservoir models that assume a unique relationship between ? dQ/dt and Q for a basin. However, recent observations indicate that ? dQ/dt ‐ Q relationship of a basin varies greatly across recession events, indicating the limitation of such models. In this study, the dynamic relationship between ? dQ/dt and Q of a basin is investigated through the geomorphological recession flow model which models recession flows by considering the temporal evolution of its active drainage network (the part of the stream network of the basin draining water at time t). Two primary factors responsible for the dynamic relationship are identified: (i) degree of aquifer recharge (ii) spatial variation of rainfall. Degree of aquifer recharge, which is likely to be controlled by (effective) rainfall patterns, influences the power law coefficient, k. It is found that k has correlation with past average streamflow, which confirms the notion that dynamic ? dQ/dt ‐ Q relationship is caused by the degree of aquifer recharge. Spatial variation of rainfall is found to have control on both the exponent, α, and the power law coefficient, k. It is noticed that that even with same α and k, recession curves can be different, possibly due to their different (recession) peak values. This may also happen due to spatial variation of rainfall. Copyright © 2012 John Wiley & Sons, Ltd.     

Effective Removal of Microorganisms and Biostimulants of Wastewater by the Application of Various Electrolytes

A variety of electrolytes FeCl₃, CaCl₂, CuSO₄, Al₂(SO₄)₃, and LaCl₃ was investigated for their efficiency in removing biostimulants (phosphorous and nitrogen) to improve the water quality. Results show that the removal of PO₄^3– was achieved below the detection limit (BDL) by two electrolytes, CuSO₄ and Al₂(SO₄)₃, and up to 1.0 ± 0.0 mg/L by LaCl₃ from a value of 15.0 mg/L, of the concentration of PO₄^3– in amended water. The turbidity was found to be removed significantly by FeCl₃, CuSO₄, and Al₂(SO₄)₃ by about 5.8 ± 2.6, 9.7 ± 1.0, and 5.4 ± 1.1 nephalometric turbidity unit (NTU), respectively. The removal of the members of Enterobacteriaceae viz., Escherichia coli, Enterobacter spp. Pseudomonas fluorescence, and Pseudomonas spp. was found almost in all the chemical precipitants but their removal was more significant in the water samples treated with CuSO₄, Al₂(SO₄)₃, and LaCl₃. To achieve a complete removal and to sustain the after effects of precipitation, such as recurrence of algal growth, the combination of CuSO₄ and Al₂(SO₄)₃ was investigated. Reduction in the turbidity from 30.83 to <2 NTU, phosphate ion from a value of 1.28 mg/L to BDL and ammonia ion from a value of 44.71 to 36.48 mg/L of natural pond water were observed after the treatment with CuSO₄ and Al₂(SO₄)₃ in combination.     

Modeling of strain dependency of shear modulus and damping of clayey sand

A series of cyclic triaxial tests on clayey sands was carried out and attempts were made to evaluate the strain dependency of shear modulus and damping. Strain dependencies of shear modulus and damping were simply modeled. It was shown that the change in the effective confining stress with loading cycles in the undrained shear test needed to be considered particularly in the large strain range. The consideration could be made by normalizing G with G′₀=AF(e)(σ′_m/σ_mr)ⁿ, the initial shear modulus for the effective confining stress of that particular loading cycle, instead of using G₀. G/G′₀ was expressed by a function of γ as G/G′₀=1/(1+b_gγ) which was almost stress level independent for clayey sands used in this study. The damping ratio was not much affected by the confining stress. The strain dependency of the damping ratio was modeled by h=a_hγ/(1+b_hγ). Effects of load irregularity on the shear modulus were also investigated. The excess pore pressure and the residual strain were generated especially when the major peaks in the irregular loading were applied to the specimen. However, G/G′₀ for the irregular loading could be represented reasonably well by the average curve for the uniform cyclic loading, if the excess pore water pressure and the residual strain were taken into account.     

Determination of the motion of an observation point by microtriangulation when measuring the deformation of dams

Резюме При проверке предпосылок для статических расчетов плотинных стен и при контроле запаса их прочности важное значение имеют геодезические методы. Их применение, однако, часто обусловливается достижением требуемой высокой точности. Препятствием для полного использования некоторых геодезических методов является тоже сравнительно большая продолжительность расчетов. Наиболее трудной задачей при определении триг. методом абсолютных смещений плотины в горизонтальном направлении является определение изменений положения наблюдательных пунктов с помощью сети основных (поверителных) точек. До сего времени применяемые методы, основанные на совместном уравнивании всей сети методом наименьших квадратов и преобразований Гельмерта, требуют большой затраты времени, причем результаты с теоретической точки зрения не вполне надежны. Новый, автором настоящсй статьи предложенный, метод дает возможность простым сравнением измеряемых оснований установить смещенные точки и их смещение постепенно определить путем некоторых вычислительных или графических методов. В результате отпадет как трудопмкое уравнивание всей сети, так и необходимые преобразования. Для лучшего сравнения удобно выбирать для всех пунктов одно и то же начало, достаточно удаленное от плотины. Точность ориентировки повысится в результате повышения числа ориентировочных направлений. Повышение их числа достигается без увеличения затрат путем заделки вторых неподвижных сигналов в устои пунктов. Паралактический угол между подвижным и неподвижным сигналами, который должен быть постоянным, является также ценным контрольным средством качества измерений. Новый метод был с успехом использован на плотине Порабка в Польше. Определение смещенных точек еще перед уравниванием процесс не только существенно ускорит, но и уточнит. На плотине в Жерманицах среднее арифметическое средних ошибок определения точки в IV–VI этапах в одной координате равно ±0,2 μμ, максимальная же ошибка ±0,3 μμ. На плотине Порабка 5 пунктов (устоев) было снабжено двумя центрирующими кольцами с известными расстояниями. С их помощью можно контролировать результаты, полученные различными способами расчетов. Как видно из табл. 8, результаты, полученные при применении нового метода, равноценны и даже более точны, чем результаты, полученные путем совместного уравнивания всей сети по направлениям или углам. В разделе „Графическо-вычислительные методы” приводится сравнение результатов, полученных с помощью ныне применяемых методов с новым графическим постепенным методом. Этот метод выгоден в особенности в тех случаях, когда наперед было определено приблизительное положение смещенной точки (например, прямой засечкой); кроме того, лучше всего проявил себя метод направлений (обратных величин расстояний). Для достижения требуемой высокой точности результатов, необходимы не толяко правильная форма сети и точные измерения, но и пригодный способ расчета. Как практика показывает, упрощения и ускорения расчетов не идут всегда в ущерб точности.

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Address: Praha 1, Dlouhá 13.     

Methods of measurement of ice nuclei concentrations

Summary The actual methods for counting ice nuclei are compared. It appears that the mixing chamber method is most valid.

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Résumé Parmi les méthodes actuelles de mesure du pouvoir glaçogène de l'air, la méthode des chambres à mélange semble la plus valable.

     

Problems of determination of the magnitude-frequency relation

Zusammenfassung Die Fehler in der Bestimmung der N(M)-Funktion werden diskutiert. Fragliche Ergebnisse können schon durch Vernachlässigung manchmal vorkommender nichtlinearer Verteilung der Punkte verursacht werden. Es wird gezeigt, dass auch bei linearer(log N, M) Verteilung verschiedene theoretische Voraussetzungen einzelner Berechnungsmethoden zu nicht vernachlässigbaren Unterschieden in den Ergebnissen führen können. Falls man die N(M)-Funktionen vergleichen will, müssen folgende Bedingungen erfüllt werden: Die Beobachtungsperiode, der Magnitudenbereich, die Klassifikationsgrösse und vor allem die Berechnungsmethode müssen identisch sein.

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Presented at the IASPEI conference, Madrid, Sept. 2, 1969.     

Some aspects of volcanic rocks of the valley of Mexico

Three periods of volcanic activity connected with tectonic events form the geological history of the Valley of Mexico (Mooser 1963, 1969). An igneous rock suite from rhyodacites to andesites (but lacking rhyolites and basalts) can be observed in each period. During the Tertiary epochs — in the Oligo-Miocene and Upper Miocene-Pliocene — we have a more dacitic volcanism, in the Quaternary epoch a more andesitic volcanism. This result was verified by calculating the average of all available and stratigraphically datable chemical analyses byGunn &Mooser (1971) andNegendank (1972). Using the average chemical composition of the Oligo-Miocene, Upper Miocene-Pliocene and Quaternary products the equivalent igneous rocks were computed using theRittmann-norms in theStreckeisen-Q-A-P-F double triangle with the following result (names in parenthesis are those using the classification ofMiddlemost (1973): Quaternary : quartz-latite-andesite (andesite) Upper Miocene-Pliocene : leuco-quartz-latite-andesite (high lime dacite) Oligo-Miocene : leuco-quartz-latite-andesite (high lime dacite) The equal average composition of the two groups of Tertiary volcanic rocks seems to support the theory of a uniform primary andesite magma apart from which of the two possible theories of petrogenesis one favors. The calculated average trace element abundances show high Cr- and Ni-values which suggests that mantle material was involved if we consider the Tertiary products as partial melting products of the lower crust. A more elegant hypothesis seems to be the model ofGunn &Mooser (1971), who consider these volcanic rocks as partial melting products of oceanic tholeiites or their high pressure derivatives in the sense ofRaleigh &Lee (1969).