On the physical meaning of the zonal components of the geopotential

The MacCullagh equation is of key importance in the study of the Earth. It connects the geometrical and the physical properties of the Earth through the geodynamical shape factor J₂. This second zonal geopotential coefficient is closely related to the flattening and to the angular spin velocity of the Earth as well as to its equatorial (A) and polar (C) moments of inertia. Through these moments of inertia the gravitational potential V is connected to the mass density distribution within the Earth.The main target of the present study is to obtain a generalized form of the MacCullagh equation for even orders n ≥ 2 by including the higher order zonal coefficients J_n connected with the higher (n ≥ 2) degree moments of inertia C_n and A_n. The higher the degree n, the higher is the weight of the near-surface (i.e. shallow) mass density distribution in J_n. The second part of this contribution deals with the temporal variations of J_n, dJ_n/dt for n ≥ 2.     

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*}.     

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.     

Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

On the propagation of topographically trapped waves

Abstract

In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL ²/h ³, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l ⁴ f ²/g)^1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q? O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ?O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation.     

Toxicity of the Herbicide 2.4-D-Na to Two Species of Freshwater Prawn of the Genus Macrobrachium

In batch experiments with exposure for 24 to 96 h Macrobrachium naso and M. dayanum were exposed to solutions of the sodium salt of 2,4-dichlorophenoxy acetic acid. The LC_50,96h are 2.397 g/l for Macrobrachium naso and 2.275 g/l for M. dayanum. No mortality was observed in solutions of 2.1 and 1.85 g/l. The differences in toxicity are not dependent on the size of the organisms, but they are species-specific.     

The height of the maximum ionospheric electron density over the MU radar

Ionospheric F₂-layer peak height h_mF₂ variations, as measured over 1986–1995 by the MU radar (34.85°N, 136.1°E) and as calculated with a theoretical model, are discussed. The diurnal variations of the measured peak height for different seasons and levels of solar activity are compared with those estimated from ionosonde M3000F₂ and IRI predictions. Also given are the measured ion drift velocities and meridional neutral winds needed to understand the dynamic behavior of the F₂-layer. It is found that: (1) h_mF₂ is generally higher during periods of the solar maximum than during periods of the solar minimum, and higher in summer than in winter; (2) for the solar maximum, h_mF₂ drops markedly in the morning and in the afternoon, while, for the solar minimum, the h_mF₂ minimum occurs in the morning during summer and usually in the afternoon during winter. In general, the measured h_mF₂ is well reproduced by our model when we use the observed drift velocities and plasma temperatures as inputs. Our modeling study shows that the neutral wind contributes strongly to the diurnal variation of h_mF₂ in winter by lowering the ionization layer by day, particularly for the solar maximum; it also helps to enlarge the day–night difference of h_mF₂ in summer. The northward electromagnetic drifts that usually cancel the neutral wind effect have only a minor effect for the location of the MU radar. Other features of the observed h_mF₂ variations, e.g., the solar maximum–minimum difference, the summer–winter difference, and the morning and afternoon drops, are explained by the basic processes of O⁺ production, loss and diffusion, as influenced by the atomic oxygen concentration and neutral and plasma temperatures.     

Dependence of the power consumed by the magnetosphere on the solar wind parameters

The results of the previous studies, where the expressions were obtained for the electric current, which is generated at the bow shock front and is closed through the magnetosphere, and for the magneto-pause potential as a function of such solar wind parameters as the plasma density and velocity and the IMF intensity, are used. The power (W) consumed by the magnetosphere is equal to the Poynting vector flux S through the magnetopause. According to the special case of the Poynting theorem applied by Heikkila to the-magnetosphere, the energy flux can be expressed in terms of the electric potential (the integration is carried out over the entire surface of the magnetosphere). As a result, the required dependence, which is quadratic with respect to the IMF B _z component, has been obtained for W. It is discussed why the magnetosphere is energy-isolated at the northward IMF B _z component despite this.     

The space and time distribution characteristics of the shear stress field for the sequence of the Wuding earthquake

Follow Chen and Duda's model of spectral fall-off of (3, the dependence of peak parameters of ground motion, peak displacement dm, peak velocity vm and peak acceleration am, upon the environment stress (0-values are studied using near source seismic digital recordings for the sequence of the Wuding, Yunnan, M = 6.5 earthquake, in which, as a new thought, the peak parameters are assumed to be related to the medium Q-value. Three formulae for estimating the environment stress (0-values by the peak parameters of three types of ground motions are derived. Using these formulae, the environment stress (0-values are calculated for the sequence of the Wuding earthquake. The result show that (0-values calculated by the three formulae are constant largely, the averages of (0 are in the range of 5.0～35 MPa for most earthquakes. It belongs to the high-stress earthquakes sequence: the high-stress values are restricted to the relatively small area closely near to the epicenter of the main shock. The fine distribution structure for the contours of the environment stress (0-values is related closely to the strong aftershocks. The analysis of spatial and temporal feature of (0-values suggests that the earthquakes sequence in a rupture process generated at the specific intersection zone of seismo-tectonics under high-stress background.     

Crustal structure of the Peninsular India

Summary Earthquake parameters for the forty aftershocks of the main Koyna earthquake of 10 December, 1967, have been determined. Depths of the foci of the earthquakes have been found to vary between 2 to 17 km. The velocities for the phasesP _g ,P ^*,P _n have been observed to be 5.78±0.00, 6.58±0.04, 8.19±0.02 km/sec, and forS _g ,S ^*,S _n to be 3.42±0.00, 3.92±0.01 and 4.62±0.01 km/sec respectively. A two-layered crustal model has been interpreted for the Peninsular shield with the average thickness of the granitic layer as 20 km and that for the basaltic layer as 18.7 km. A plot of the epicenters suggests a NNE to SSW orientation of the fault.     

Promoting effects of 1975 Haicheng foreshocks on theoccurrence of the mainshock

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Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses

Practical methods for the probability‐based seismic assessment of structures make use of estimates of demands produced by earthquakes of different intensities. The uncertainties associated with these estimates are highly dependent on the variable adopted as the intensity measure (IM, e.g., PGA, spectral acceleration, etc.). This generates the need to compare the efficiency of an originally adopted IMwith that of a new candidate. This implies comparing the dispersion of the demand measure (DM, e.g., maximum interstorey drift ratio, ductility demand, etc.) conditional to each of the two IMs. In order to obtain the demand estimates in a conventional way, a full set of dynamic response analyses should be performed for each IM under scrutiny, i.e., multiple records scaled at several fixed values of each IM. The procedure developed here serves to accelerate this comparison avoiding the effort required to evaluate the dynamic responses of the structure for all the ground motion time histories considered every time that a new IM is adopted. For this purpose, use is made of available results of analyses performed for a different (i.e., the original) IM. Two methods are proposed: the direct method involves performing a regression of the results obtained from the original analyses, taking the candidate IM as the independent variable. The indirect method involves rebuilding the probability density function of the DM given a defined value of the candidate IM by means of the total probability theorem, using the results of the original analyses and certain data relating the two IMs. The proposed methods have been tested by application to several SDOF systems with different periods and different cyclic‐response backbone curves. The conditions affecting their approximation are explored, and some criteria to improve them are identified. The procedure can also be used to determine the optimum value of a parameter to be used in a parameter‐based IM. Copyright © 2004 John Wiley & Sons, Ltd.     

Lateral variations of the modal (a/b) values for the different regions of the world

Several catalogues of global earthquakes reported for the time period from 1900 to 2000 have been compiled to examine lateral variations of the modal (a/b) values as derived from the Gutenberg–Richter empirical law. For this purpose, the world was divided into 27 different seismic regions in terms of tectonic environments. The parameters a and b were calculated using the least-squares method. The modal values computed for each region were used to produce a global map of the modal values using a grid space of 3°. The results show that a and b-values do not always supply much information about tectonic environments of the different regions. It is observed that the modal values estimated for different tectonic regions are consistent with seismicity of the world and represent global seismic sources better than a or b values. The highest modal values have been found in the oceanic subduction zones, and the lowest values in the oceanic ridges. Lowest b values are observed in trenches. These observations suggest that there is a correlation between apparent stresses and b values. Mapping of the modal values provides detailed images of the zones presenting low and high seismic activity and it may be used as a measure of seismic potential sources and relative hazard levels.     

Estimation of the elastic earth parameters using the SLR LAGEOS 1 and LAGEOS 2 data

We present results for the global elastic parameters (k ₂, k ₃) and (h ₂, l ₂) derived from the analysis of Satellite Laser Ranging (SLR) data. The SLR data for two satellites, LAGEOS 1 and LAGEOS 2, collected over a period of two years, from 1 January 2005 to 1 January 2007, from 18 globally distributed ground stations are analyzed using different approaches. The analysis is performed for the two satellites jointly, and the four elastic parameters are estimated. We carry out a sequential analysis and study the stability of the estimates as a function of the length of the data set used. The adjusted final values for k ₂ (0.3011±0.0001) and k ₃ (0.0896±0.0037) and those for h ₂ (0.6146±0.0006) and l ₂ (0.0883±0.0003) for LAGEOS 1 and LAGEOS 2 tracking data are compared to the estimates derived in other studies.     

Daily variability of river concentrations and fluxes: indicators based on the segmentation of the rating curve

The variability of water chemistry on a daily scale is rarely addressed due to the lack of records. Appropriate tools, such as typologies and dimensionless indicators, which permit comparisons between stations and between river materials, are missing. Such tools are developed here for daily concentrations (C), specific fluxes or yields (Y) and specific river flow (q). The data set includes 128 long‐term daily records, for suspended particulate matter (SPM), total dissolved solids (TDS), dissolved and total nutrients, totalling 1236 years of records. These 86 river basins (10³–10⁶ km²) cover a wide range of environmental conditions in semi‐arid and temperate regions. The segmentation—truncation of C–q rating curves into two parts at median flows (q₅₀) generates two exponents (b_50inf and b_50sup) that are different for 66% of the analysed rating curves. After segmentation, the analysis of records results in the definition of nine major C–q types combining concentrating, diluting or stable patterns, showing inflexions, chevron and U shapes. SPM and TDS are preferentially distributed among a few types, while dissolved and total nutrients are more widely distributed. Four dimensionless indicators of daily variability combine median (C₅₀, Y₅₀), extreme (C₉₉, Y₉₉) and flow‐weighted (C*, Y*) concentrations and yields (e.g. C₉₉/C₅₀, Y*/Y₅₀). They vary over two to four orders of magnitude in the analysed records, discriminating stations and river material. A second set of four indicators of relative variability [e.g. (Y*/Y₅₀)/(q*/q₅₀)], takes into account the daily flow variability, as expressed by q*/q₅₀ and q₉₉/q₅₀, which also vary over multiple orders of magnitude. The truncated exponent b_50sup is used to describe fluxes at higher flows accounting for 75% (TDS) to 97% (SPM) of interannual fluxes. It ranges from ? 0·61 to + 1·86 in the database. It can be regarded as the key amplificator (positive b_50sup) or reductor (negative b_50sup) of concentrations or yields variability. C₅₀, Y₅₀, b_50sup can also be estimated in discrete surveys, which provides a new perspective for quantifying and mapping water quality variability at daily scale. Copyright © 2011 John Wiley & Sons, Ltd.     

Model calculations of the total electron content for the system of GPS satellites

The numerical global self-consistent model of the Earth’s thermosphere, ionosphere and protonosphere (GSM TIP), which makes it possible to calculate all the main parameters of the near-Earth plasma, is used to calculate the total electron content (TEC). Calculations have been performed along the radiosignal propagation trajectory between a surface receiving point and a GPS satellite. The TEC value calculated from the satellite data have been compared with such a “true model” TEC value for magnetically quiet conditions of the spring equinox and moderate solar activity. The relative errors in determining the satellite data-based TEC for two European (Troms have been calculated. It has been indicated that an increase in the number of satellites not always results in an increase in accuracy of the TEC value measured on satellites.     

Ray parameters of diffracted long period P and S waves and the velocities at the base of the mantle

The derivation of P and S velocities at the core-mantle boundary (CMB) from long-period diffracted waves by the use of the simple ray-theoretical formulav _CMB=r _c /p (v _CMB=velocity at the CMB;r _c =core radius;p=ray parameter) yields apparent velocity values which differ from the true velocities. Using a dominant period of about 20 sec for calculating theoretical seismograms, we found a linear relation between the apparent velocity and the average velocity in a transition zone at the base of the mantle with fixed velocity on top.The ray parameters determined from long-period earthquake data are found to be 4.540±0.035 and 8.427±0.072 sec/deg for P_diff and S_diff, respectively. These values yield apparent velocities of 13.378±0.103 for P and 7.207±0.062 km/sec for S waves. By means of the theoretical relation between apparent and average velocity and under the assumption of linear variation of velocity with depth, one can invert the apparent velocities into true CMB velocities of 13.736±0.170 and 7.320±0.124 km/sec. These results imply positive velocity gradients at the base of the mantle and hence no significant departures from adiabaticity and homogeneity.Contribution No. 211 of the Geophysical Institute, University of Karlsruhe.     

A statistical study of the interplanetary magnetic field control of sporadic E-layer occurrence in the southern polar cap ionosphere

The influence of the interplanetary magnetic field (IMF) on the occurrence of sporadic E (Es)-layers in the southern polar cap ionosphere has been investigated. We statistically analysed ionogram and Doppler velocity observations made using a HF digital ionosonde located at Casey, Antarctica (66.3°S, 110.5°E; 81°S magnetic latitude) during the two summer campaign intervals 1 January to 18 February, and 1 November to 31 December 1997. The ionogram and Doppler velocity measurements were used to determine the Es-occurrence and electric field vectors (assuming E×B/B² drift), respectively. Concurrent IMF data were obtained from measurements made on board the Wind spacecraft. First, the gross properties of the IMF dependence of Es-formation were obtained: the occurrence rate was higher for negative B_y and/or positive B_z, and lower for positive B_y and/or negative B_z. To reconcile these gross properties with the electric field theory of Es-layer formation, the detailed diurnal variation of both Es-occurrence and the ionospheric electric field were obtained for different orientations of the IMF. The main statistical results are that: (1) the B_y component mainly controls the occurrence of the midnight Es-layers through its influence on the corresponding South West electric field; and (2) the B_z component mainly controls the occurrence of the evening Es-layers. However, the change in the occurrence rate for evening Es-layers was not related to the strength of the associated North West and North East electric fields. The total occurrence of Es-layers depended more on B_y than on B_z, owing to the dominance of B_y-controlled midnight Es-layers in the occurrence distribution. Nevertheless, the dependence of Es-occurrence on B_z was important. We suggest that the increase in Es-occurrence for positive B_z might be explained by the intermittent production of lower F-region ionisation by polar showers and squalls, which also increase in frequency and intensity for positive B_z. The importance of metallic ion transport within the ionosphere is also considered.     

Influences of meteorological and vegetational factors on the partitioning of the energy of a rice paddy field

Observations made in a paddy field were analysed to show the influences of meteorological and vegetational factors on the crop's energy budget. Energy budget in the paddy field was characterized by the major partitioning to latent heat flux LE and by the negative Bowen ratio B mostly in the afternoon. Canopy resistance r_c, estimated with the Penman–Monteith equation, was related to the influences of solar radiation SR, vapour pressure deficit VPD and plant height. The results demonstrated that r_c could not directly account for B but that critical canopy resistance r_cc, defined as the canopy resistance when B = 0, could be used to standardize r_c, and that r_c − r_cc proved to be a good parameter to account for B. Influences of bulk stomatal response on energy partitioning were assessed as follows: the Bowen ratio dropped below zero, while the bulk stomatal aperture dwindled with the increase of VPD. In addition, stomata of a big leaf acted to promote the partitioning to LE against the rise of SR in the condition of higher VPD. Copyright © 2004 John Wiley & Sons, Ltd.     

Factors affecting the measurement of the vertical hydraulic conductivity of a streambed sediment using standpipe tests

The vertical hydraulic conductivity (K_v) of a stream or lake sediment is often determined in the field using standpipe tests. Calculation of K_v is based on the assumption that the hydraulic head in the pipe is equal to that of the stream or lake stage. In this work, a modified equation for K_v is developed for the standpipe test which is applicable when this assumption is not valid. The equation involves not only the hydraulic head at different times but also the difference in the hydraulic head (a) between the groundwater level and river stage. The effects of certain factors on K_v, such as the ratio of the hydraulic head at different times (h₁/h₂), the difference a, and the initial water table height (h₀), are also discussed. The results show that when h₁/h₂ is constant, the relative error (E_r) in K_v increases with the ratio a/h₂. Furthermore, if a/h₂ < 0.05, then for any value of h₁/h₂, E_r is less than 5% using the modified equation. Also, if a/h₂ is large, hydraulic head readings with larger h₁/h₂ ratios must be used to avoid large E_r values. The results of a field test also indicate that the error in K_v decreases as the value of h₀ increases. Copyright © 2013 John Wiley & Sons, Ltd.