Gravity topographic corrections computed from a square grid of height points

Summary Computation of terrain corrections from a map with a square grid of mean height points

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uu mnauu nna n am ¶rt;u m u¶rt; a¶rt;am mu m nm.

     

Analytical continuation of the gravity field for a two-dimensional body using an infinite series

Summary A procedure is derived which enables the analytical continuation of a two-dimensional gravity field to be expressed in the form of an infinite series. For this purpose, an apparatus is used which represents the two-dimensional analogy of Bicadze-type integrals.

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nuaa m¶rt;ua na aum aaumu n¶rt;u ¶rt;aumau n u¶rt; ¶rt;a. nm annaam n¶rt;mau ¶rt; aau uma muna ua¶rt;.

     

On the propagation of wave from a cylindrical cavity

Summary This paper discusses the disturbance produced in an infinite layer of non-homogeneous elastic material characterised by =0 ⁿ and =0ⁿ(n>0) where and are the density and shear modulus respectively of the material, due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the radius vector is shown graphically and compared with the corresponding homogeneous case.     

Étude statistique des crochets magnétiques à Tamanrasset

Résumé On compare, en premier lieu, les crochets magnétiques donnés par le Bulletin de l'I.A.G.A. avec les crochets visibler sur les enregistrements de Tamanrasset entre 1949 et 1957. 33% des crochets sont retrouvés, et on étudie leur fréquence. Celle-ci suit le cycle solaire, esdt minimum l'hiver et plus élevéc l'après-midi que le matin. L'obíssance à la loi deMcNish ne semble pas prouvéc. L'amplitude la plus probable est de 7 . — On étudie ensuite des phénomènes ressemblant aux crochets (faux crochets) et caractérisés par une allure bien définie des dérivéesdH/dt etdD/dt. Leur fréquence ne suit pas le cycle solaire, est minimum à l'équinoxe et uniforme dans le cours de la journée. L'amplitude la plus probable est de 7 à 10 , et la durée de développement de l'ordre de 5 minutes. La direction du vecteur perturbation est NNW ou SSE, avec prédominance du SSE, ce qui correspond dans l'ionosphère à un courant WSW-ENE. L'existence des faux crochets peut expliquer certaines confusions dans l'identification des crochets.

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Summary First of all, we compare the magnetic crochets given by the I.A.G.A.-Bulletin with the crochets we can see on Tamanrasset records between 1949 and 1957. We find out 33% of these crochets and we study their frequency. It follows the solar cycle, it is minimum during winter and greater in the afternoon than in the morning. Obedience toMcNish law does not seem to be proved. The more probable amplitude is 7 . — Then we study phenomena looking like crochets (false crochets) which are caracterised by a well definite feature ofdH/dt anddD/dt. Their frequency does not follow solar cycle, it is minimum et equinox and level during the course of the day. The more probable amplitude is from 7 to 10 , and the development plasts about 5 minutes. The direction of disturbance vector is NNW or SSE, with predominance of SSE, which sould correspond to a WSW-ENE stream in the inosophere. The existence of false crochets may explain some confusions when we identify crochets.

     

On the use of stress values as an exploration tool

Summary This paper discusses the possibility of using readily available isallo stress lines referring to the compressional angle , as an exploration tool. It is shown that inhomogeneities in the Earth will produce anomalies in the isallo stress lines. Conversely, stress anomalies can be interpreted in terms of inhomogeneities in the Earth. The stress anomalies produced by a simple inhomogeneity are discussed which serves to illustrate the idea.

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Zusammenfassung Die Arbeit diskutiert die Möglichkeit, bestimmte (isallele) Spannungslinien, die sich auf den Kompressionswinkel beziehen, zur geophysikalischen Prospektion heranzuziehen. Es wird gezeigt, dass gewisse Inhomogeneitäten in der Erde Spannungsanomalien hervorrufen. Umgekehrt wird auch gezeigt, dass Spannungsanomalien auf gewisse Inhomogeneitäten in der Erde schliessen lassen können, was zur Prospektion gebraucht werden kann. Als Beispiel werden die Anomalien, die durch eine einfache Inhomogeneität hervorgerufen werden, rechnerisch diskutiert.

     

Predictive spectral analysis of short records using maximum entropy

Summary A method of spectral analysis based on the prediction of the signal by means of AR parameters is proposed. The essence of this method ranks it between the classical methods of spectral analysis and the method of maximum entropy. For sufficiently high SNR its resolution is higher than that of the classical methods. The new method enables power and phase spectra of the signal to be determined, and provides a better determination of the power spectrum amplitude. than the method of maximum entropy. A regularization procedure is presented which abolished the instability of the prediction filter, obtained by the least-squares method.

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¶rt; n nma aaua, a a n¶rt;aauu uaa n amu naam. mm n m ¶rt;au aumu auu m¶rt; nma aaua nuu u¶rt; u m¶rt;a aua mnuu. n a¶rt;am n aa nm n au auuu m¶rt;au nu aau n ¶rt;mam u mu ua . nm mu ua n¶rt;m a¶rt;, m¶rt; aua mnuu. muu m m¶rt;a aua mnuu n¶rt; n nma aaua nm n¶rt;m m a nm ua. aam n¶rt;aa uma um m¶rt; auu a¶rt;am, m unaa uau ¶rt; ¶rt;u mu am u.

     

Some results of calibrating CG-2 gravimeters (sharpe) by the tilt method

am mam mauau m amaua aaum CG-2¶rt;u muna No; 174-G, 181-G u 228-G nuu m¶rt;a aa. mama mauau aum, m num mum mm 1. 10^–4 u n¶rt;um um a. a a¶rt;a ¶rt; a auum ama uum mauaum m mnam.     

On one application of Ertel's theorem

u nu m¶rt;a a u u¶rt;a u u m ma, m mam uauu ¶rt; nm u. aa ¶rt; na nuam m umu uu u a¶rt;u uu m.     

Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

The thermal field of the lithosphere in the region of mid-ocean ridges modelled on the basis of known surface temperature and heat flows

Summary The possibility of solving the stationary heat equation with the convective term is demonstrated in the case that the velocity field of the continuum, and the temperature and heat flow on the Earth's surface are known, and that an assumption is made about the magnitude of heat flows on another part of the boundary of the two-dimensional region being investigated, whereas no boundary condition is imposed on the remainder of the region's boundary. The problem has been solved numerically for a kinematic model of the lithosphere in the region of mid-ocean ridges, based on the assumption of a broad deflected convective flow moving at a distance of more than about 150 km from the ridge modelled as a plate.

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aaa m u maua au na mna a, ¶rt;a um n m mua u a nmu u um mnama u mn nm. a ¶rt; amuau aamua ¶rt; amu ¶rt;um n¶rt;nu uu mn nma a a ma amuau a u a¶rt;a. ma na a u m¶rt; a ¶rt; uamu ¶rt;u um amu ¶rt;u-auu m, a a n¶rt;mauu u ma mu nma a amu m ma nau 150 ¶rt;u auma nm.

     

A new dissipation model based on memory mechanism

Summary The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.List of symbols unidimensional stress - unidimensional strain - Q ^–1 specific dissipation function - c(t) creep compliance - m(t) relaxation modulus - c ₀ instantaneous compliance - m equilibrium modulus - (t) creep function - relaxation function - () spectral distribution of retardation times - spectral distribution of relaxation times - c ^*() complex compliance - m ^*() complex modulus - tang loss-tangent     

Normal gravity model of phobos

Summary The normal gravity field of Phobos defined by the sum a) of the gravitational potential of a homogeneous tri-axial ellipsoid representing the body of Phobos, b) of the potential of its centrifugal forces, c) of the constant part in the tidal-forming potential due to Mars, has been investigated. The radius-vector of the equipotential surface representing the normal model, as well as the gravity on it, have been derived. The long-term variations in the figure parameters and in gravity, due to the tidal evolution of the Mars—Phobos system, have been derived.

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¶rt;m a n u mmu a, ¶rt;a a) nmuaa ¶rt;¶rt; m unu¶rt;a, n¶rt;ma m a, ) nmuaa m u, ) nm amu nuua nmuaa m aa. ¶rt; au a¶rt;ua-ma nmu, n¶rt;ma ¶rt;a a ¶rt;, u u u mmu a n¶rt;. auauu naam u u u u mmu, a nuu u um a—.

     

A stochastic differential equation approach to soil moisture

The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDE's), one representing the so-called surplus state of the moisture and the other the deficit condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively.The solutions to these SDE's are not in close-form but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions.To illustrate the model, climatic parameters representing the surplus and deficit cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model.     

On the meridional form of baroclinic waves in a two-layer quasi-geostrophic model

Summary It is shown that in laterally bounded two-layer models of the atmosphere the only permissible meridional variation of the wave solutions is of the form sin(/D) whereD is the lateral width.     

Accuracy of integral migration transformation in dependence on space-time sampling

Summary The accuracy of wave field extrapolation is studied with respect to the discretization of field data and integral extrapolator. Assuming a far-field approximation of the Rayleigh-Sommerfeld solution for a two-dimensional scalar wave equation, the minimum and the maximum transmitted frequency are expressed as functions of the sampling intervals t, x, and the half-width x₀ and angle _a of the migration aperture. The theoretical limitation of the transmitted frequency band is tested on numerical examples.

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aamuam mm manuu auumu m ¶rt;umuauu n u uma manu nama. ¶rt; u uma u -¶rt;a ¶rt; ¶rt; a au, ¶rt; nuuuu ¶rt;a n mu ¶rt; uua u aua n¶rt;aa amm a uu m a -nmam ¶rt;umuauu t u , nuu ₀ u a _a uau anm. mu n¶rt;u amm ¶rt;uanaa mmua a u nua.

     

Power-law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/¹⁺. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10^–bm and on the increase ~ 10^–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother     

On some effects connected with electromagnetic induction in a rotating earth

muu aamuam mauma u¶rt;u, aa uauu n aum n aa , ma n¶rt;mam ¶rt;¶rt; n¶rt;u a. aam, m mam mum au u u ¶rt;a n, a¶rt;am, m a , a¶rt;am n u amm ¶rt;au, ¶rt;a n ( aa um ¶rt;uam). a aamuam u m maua ¶rt;¶rt; aum n a au ¶rt;¶rt; n¶rt; aa. a am uu n S_q auau a m au u u n m mu, m na a, mum a¶rt;a au a¶rt;u mu au u.     

On the algebraic structure of particle motion in a field of turbulence

Summary The motion of particles in a turbulent flow is described by means of algebraic physics. The initial concepts are structurally ordered groupoids, algebras of observables, logically dependent on them, with couplings and the non-canonic transition between two Hamiltonians. The non-canonic transition leads to the substitution of time t by a new parameter. Its real counterpart gives the lower limit of the size of the time step in the differential equation of transfer, based on the semi-empirical image of turbulent diffusion.

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uu amu mm muu nua ¶rt;mau aau uuu. ¶rt;u nmuu m mm n¶rt;nnu¶rt;, uu m u auu a a¶rt;a u u auu n¶rt; ¶rt; ¶rt;aumuaau. auu n¶rt; nu¶rt;um a u t naam. ¶rt;mum aa n¶rt;m uau aa am au na, nua a nnuu au mm ¶rt;uuu.

     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

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¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Primary ionization coefficients for dry and moist air; secondary ionization coefficients for a water surface

Summary A comparison has been made between the Townsend primary ionization coefficient, , for dry air and for air with humidities typical of those in the atmosphere. is defined as the number of new electrons produced by an electron per centimeter of drift in a field. A range of field/pressure ratios,E/p ₀, of 40 to 100 V (cm torr)^–1 was employed. The variation of with humidity is very small.Over the range ofE/p ₀ from 50 to 100 V (cm torr)^–1, the secondary ionization coefficient, , of a water surface has been found from sparking potential data to be typically 2×10^–4. represents the fraction of primary ionizing collisions that ultimately result in the production of additional electrons at the surface.