Three-dimensional inverse problem for inhomogeneous transversely isotropic media

Summary The basic formula used in the presented paper gives the relation between the P wave travel-time perturbation and the perturbation of an inhomogeneous transversely isotropic medium, expressed by four perturbations of elastic parameters and by two angles of orientation of the axis of symmetry of transverse isotropy in space. The travel time perturbation is computed along the ray in the unperturbed inhomogeneous isotropic medium. Four elastic parameters and two angles are parametrized in the model under study and a system of equations for many rays is constructed. The equations are linear in the sought elastic parameters and nonlinear in the sought angles, and the iterative Levenberg-Marquardt algorithm is thus used to solve them. The theoretical 3-D inverse problem was solved in the presented numerical example. The data, simulating teleseismic data, were computed in the direct problem and then inverted. The results indicate the applicability and limitation of the presented algorithm in real problems.

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a a, unaa n¶rt;aa am, ¶rt;am mu ¶rt; uu u na u uu ¶rt;¶rt; nn umn ¶rt;, a m nuu naamau u ¶rt; au umauu u umuu nn umnuu nmam. u u na um ¶rt; a aa ¶rt;¶rt; umn ¶rt;. nu naam u ¶rt;a a naamuua ¶rt;u u nma uma au ¶rt; u . au u n um nu naama u u n um a umauu umuu, nm un m umamu aum a-aa¶rt;ma ¶rt; u u. am nu¶rt; ¶rt; m u nu. nu muu ¶rt;a aaa a na a¶rt;aa u am ¶rt;a a. mam naam auu u mu nuu nu¶rt;uma a a.

     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.     

Study of the velocity conditions in the earth's crust in the regions of the Bohemian massif and the carpathian system along international profiles VI and VII

u¶rt;m n uu ¶rt;u m n u ma n¶rt;aa, nu m¶rt;u u ¶rt;uau. n nuu uu ¶rt;u m n ¶rt;a¶rt; nu NoNo VI, VII. u au u n m a (x, H), ¶rt;auu an¶rt;u ¶rt;u m ¶rt; m¶rt; nu, u mua m nuu (H), aamuu an¶rt;u m a mua ¶rt;¶rt; uu ¶rt;uua u a. u a ¶rt;u m (x, H) amm ¶rt;uuu (u) a m¶rt; nu. m¶rt; u, auuu aau, om aamuam muau an¶rt;u ¶rt;u m, uu , n m u m nu aamuu a nmu, am ma a¶rt;am aa uu ¶rt;u m. aa u a¶rt;u n nu NoNo VI u VII u umuu ¶rt;a. mua m nu (H) num m ¶rt;u amu aua u anam um, ¶rt;a amu ¶rt;aua u ¶rt;- nma (nu No VII). ma ¶rt; ¶rt; aua, maa numa nm m u numa nm ma¶rt;um, a unaa nuu umnmauu a¶rt;uu ¶rt;uau amu aua.     

On one formulation of the frontal wave problem

u nu m¶rt;a a u ¶rt; u amu ¶rt; au amm u a m amuu ma. ¶rt; au mam ¶rt; nma a¶rt;au.     

Determination of the geopotential scale factor from satellite altimetry

Summary The geopotential scale factor R ₀ =GM/W ₀ has been determined on the basis of satellite altimetry as R _{0=(6 363 672·5±0·3) m} and/or the geopotential value on the geoid W ₀ =(62 636 256·5±3) m ² s ^–2 . It has been stated that R ₀ and/or W ₀ is independent of the tidal distortion of surface W=W ₀ due to the zero frequency tide.

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¶rt;a nmu amumuu u ama amnmuaa R ₀ =GM/W ₀ =(6 363 672,5±0,3) m u/uu aunmuaa a nmuu¶rt;a W ₀ =(62 636 256,5±3) m² s^–2. m, m R ₀ u/uu W ₀ auum m nm amu a a nuu ¶rt;au nmu W=W ₀ .

     

Temperature-time dependence of the electrical conductivity of garnets

aam mam uu mn¶rt;muaamuu n¶rt; u u nua ua —aam auumu m mnam (200–1000°, ₂ 10^–1 a). aa¶rt;u, m um na¶rt;a uu a n¶rt;u auumu mn¶rt;mu m mnam, u¶rt;m auumu ¶rt;a mn¶rt;mu mnam u n¶rt;m mu mnam uma.     

On the further generalization of trochoidal frontal waves

Summary A non-linear model of trochoidal waves is presented which represents a geometrical and kinematical generalization of Gerstner's waves and of the results of[2–4].

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¶rt;aam ¶rt; mu¶rt;a , ma m u ma u am[2–4] mu umuu u uamu mm ¶rt;u.

     

On the accuracy of location of local shocks on the territory of Czechoslovakia and adjacent areas

Summary The calculation procedures for determining epicentre parameters of weak near shocks with foci in Poland are discussed and tested for explosions with known epicentres.

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m m¶rt; ¶rt; n¶rt;u num a uu m num nmua n auauu, u mu a mumuu u, n muu ¶rt;au uu mau. au mam nam (a. 4) nu nuuu na 71 u m ¶rt;u n¶rt; ¶rt; a auu ¶rt;a [11].

     

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.

     

Simple model for long-range forecasts of AT500 hPa level fluctuations

Summary A forecast model to predict the fluctuations of level AT 500 hPa in a selected grid of points is derived. The solution of the compensation equation is sought in the form of a trigonometric polynomial in three idependent variables. It constitutes the basis of a numerical solution of the prediction problem with the use of a high-speed computer. A three-month forecast of the altitude fluctuation of level 500 hPa is evaluated by means of the daily values of the correlation coefficient. The results are satisfactory and the general evaluation shows the model to be prospective.

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¶rt;um nmua ¶rt; ¶rt; na au m AT 500a a uum m m. u au nauu um u¶rt; mu mu nua m m auu n. m u u nmu a¶rt;au a . u¶rt;um a m na au m 500a nu nu m au uuma uu. mam m anumu, u nu ¶rt; n¶rt;mam nnmu.

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List of symbols used * coupling coefficient between two conjugate atmospheric elements - * ageostrophicity coefficient of the atmospheric system - Coriolis' parameter (=2 sin) - , * geographic latitude, geographic longitude - *, geopotential reference and pressure levels - , * compensation and coupling frequencies - integration field over the entire atmospheric system - A** constant (A*=2 ²(*+*)) - A _r ,B _r ,C _r ,D _r constants related to subsystem -r- - A _s ,B _s ,C _s ,D _s constants related to subsystem -s- - B** constant (B**= ⁴(*²+2**)) - C _r constant (i=1, 2, 3, 4) - E _k ,E _v ,E _p energies of the atmospheric system: kinetic, internal and potential - K transformation constant - m total number of generalized frequencies - R(T) frequency characteristics of the numerical band filter - r0(t),r1(t) daily values of the correlation coefficient - Q heat - x, y coordinates in the reference plane - t time - _p ² Laplace's differential operator in thep-system     

Anomaly of geomagnetic variations in the southeastern margin of the Bohemian Massif

Summary Magnetic variations were recorded along three profiles crossing the southeastern margin of the Bohemian Massif. The data were processed in order to get induction vectors (Wiesevectors) and in-phase and out-of-phase induction vectors (Schmucker-vectors). Several events of field variations were separated into external and internal parts. The same events were also treated by a physical-statistical approach. Taking into account these results, we were able to delineate a zone of electrical inhomogeneity. It is in close relation to the Moravo-Silesian lineament. The depth of the internal anomalous field source was estimated at 20 to 25 km.

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¶rt;a u uuau n uu n nu, nu — u. u¶rt;uu ( u), n u u n¶rt; u n u¶rt;uu ( ), n ¶rt;u n uau u u u n au ¶rt; uu-uuu ¶rt; u ¶rt;¶rt;u na¶rt; nu -uu . ¶rt; au uu a n a u n¶rt; 20–25 .

     

Induction vector estimates in the Bohemian Massif and in the transition zone to the Carpathians

u¶rt;m mam m u¶rt;uu n n mau au u n¶rt; anama. am m auu u au am aua ¶rt;a, m m unam ¶rt; u¶rt;au ua aau mn¶rt;mu n.     

Effects of the imf sector structure in the midlatitude troposphere and stratosphere

Summary The data on geopotential heights and temperatures at 7 pressure levels between 1000-10 hPa above Berlin(52.5 °N, 13.4 °E) are analysed for the winters of 1963–1973. No demonstrable effect of the interplanetary magnetic field sector boundary crossing (IMF SBC) is found in the lower and middle stratosphere, but there is a demonstrable effect in the middle troposphere at the 500 hPa level. This effect is less important than the IMF SBC effect in the tropospheric vorticity area index and seems to be of a different type.

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auum ¶rt;a nnmua m u mnam a 7 nm ¶rt;au ¶rt; 1000-10 a a¶rt; u(52,5 °.., 13,4 °.¶rt;.) ¶rt; u 1963–1973. ua ¶rt;aam m nu mau nam aum n( ) ¶rt;a amu u u ¶rt; mam, ma m a¶rt; ¶rt; mn a 500 a. mm m a, m u¶rt; na¶rt;u aumu am, u am m ¶rt; muna.

     

Deep structure of the bohemian massif from phase velocities of Rayleigh and Love waves

Summary Phase velocities of Rayleigh and Love waves have been measured between the broadband seismic stations KHC (Kaperské Hory, South Bohemia) and KSP (Ksi, Lower Silesia), a profile that nearly coincides with the Interactional DSS Profile VII. The data for both wave types were separately inverted into models of shear-wave velocity versus depth. Novotný's model KHKS 82[1] for the DSS Profile VII was used as a start model. While the crustal section of Novotný's model is compatible with both of our data sets, our Rayleigh-wave data require smaller shear-wave velocities, on the average by 0.24 km/s, in the top 180 km of the mantle. The average difference between Novotný's model and our Love-wave model in that depth range is only 0.06 km/s. If our identification of the observed Love waves as the fundamental mode is correct, this result indicates the presence of polarization anisotropy in the uppermost mantle.

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u a mu u a ¶rt; unu uuu mauu (an , a u) u S (, ua uu). u - S nuuum mmmm ¶rt;a¶rt; nu VII . a ¶rt; u mun m¶rt; umua ¶rt;u auumu mu nn mu. am mam¶rt;u a unaa ¶rt; S 82 m[1] ¶rt; nu VII . a am ¶rt;u m aua uu aau au ¶rt;a, ¶rt;a au ¶rt;a ¶rt; mm uu m nn — ¶rt; a 0,24 / 180 uma amuu. ¶rt;a aua ¶rt; ¶rt; m u a ¶rt; ¶rt; a m ¶rt;uanau n¶rt;mam 0,06 /. u aa u¶rt;muuau a¶rt;a a a ¶rt;ama ¶rt;a m nau, m mm mam u¶rt;ummm numuu nuau aumnuu amuu.

     

Travel time curves for complex inhomogeneous slightly anisotropic media

Summary The linearization approach is used to compute the travel times in inhomogeneous slightly anisotropic media. The basic formulae are outlined and their accuracy demonstrated in comparison with the exact solution based on the zero-order ray theory and the Backus formula (1965). The linearization is extended also to complex media with curved interfaces. The computer program for calculating travel times in 2D, inhomogeneous, slightly anisotropic, complex media is briefly described. The numerical results obtained for a realistic situation and various types of waves are presented to enable the effects of anisotropy and the effects of inhomogeneity on the resulting travel times to be compared.

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na uauua n¶rt;¶rt; ¶rt; ama¶rt;aa , anmau aaumn ¶rt;a. ¶rt; u n¶rt; au m u n muu nuuuu u m¶rt; aa (1965). a uauua n¶rt;¶rt; ¶rt; a ¶rt; uuuauau a¶rt;a. am nuaa uuma naa ¶rt; ama¶rt;a ¶rt; ¶rt;. u mam ¶rt; a mun ¶rt;am m um m aumnuu u m ¶rt;¶rt;mu a a anmau .

     

Iterative geophysical tomography

Summary The algorithm of iterative geophysical tomography is presented. The medium is approximated smoothly by means of B-splines. The tww-point problem of ray computation is solved with the aid of paraxial approximation. The parameters of the medium are obtained from the iterative algorithm of minimizing the quadratic form. Two numerical 2-D examples are given.

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u¶rt; au umamuuu mauu. ¶rt;a annuuaa n nu nu -na. ma na aa a nu nu naaua annuauu. aam ¶rt; n a umamu aua uuauauu a¶rt;amu . am nu¶rt; ¶rt;a 2-D u nua.

     

The periodicity of aurorae in the years 1001–1900

Summary The sequence of aurorae, observed at latitudes up to 55° between the years 1001 and 1900 was processed by methods of spectral analysis. The same methods were applied to parts of various duration of this interval. The periods predominant in the time series under investigation were determined. In all the selected parts of the interval, these periods are always located within the same frequency band. Their position is related to the periods corresponding to mutual conjunctions of the large planets.

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¶rt; n uu, a¶rt;au a uma ¶rt; 55° nu¶rt; 1001–1900, ama nu nu m¶rt; nma aaua. a n¶rt; ¶rt; am a ¶rt;u m umaa. u n¶rt; na¶rt;au nu¶rt; u¶rt;a ¶rt;a. mu nu¶rt; ¶rt; a am umaa ¶rt;a a¶rt;m ¶rt;ua ¶rt;uaan amm. nu mum nu¶rt;au, mmmuu au u u nam.

     

Characteristics of the mid-latitude ionosphere suitable for modelling ionospheric filtration of ULF waves

Summary An approximate method of one-dimensional modelling of the plasma of the Earth's ionosphere is demonstrated for purposes of studying the ionospheric filtration of ULF waves (micropulsations). Apart from the basic local parameters, characterizing the plasma, also derived local characteristics have been defined, i.e. the mass of the so-called effective ion and its effective collision frequency . Drawing on existing empirical models of the mid-latitude ionosphere, vertical profiles (50 km h 1000 km) were determined of the characteristics N_e N_i, v_e, and for the daytime and nighttime mid-latitude ionosphere under low and enhanced solar activity, which can be used to study the ionospheric ULF filter.

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aa nu uum m¶rt; ¶rt;a ¶rt;uau na ¶rt; u ¶rt; nmm uu u umauu (unau). ¶rt; u mu naamau na n¶rt; mu m aamumuu — aa m. a. mu ua, , u mua amma mu, . a mu nuuu ¶rt; ¶rt;um u u n¶rt; mua nuu (50 h 1000 ) aamumu N_e N_i, v_e, u ¶rt; u u ¶rt;u um nu u u amumu. ¶rt;u nam nu uuu u uma.

     

Thermally driven hydromagnetic instabilities in a non-constantly stratified layer

Summary The convection in a rapidly rotating electrically conducting, fluid horizontal layer of non-constant stratification, permeated by an inhomogeneous magnetic field, is studied. In this connection, a temperature model of the layer is constructed, which creates a structure such that part of the layer is unstably and a part stably stratified. The results obtained are applied to the conditions in the fluid Earth's core.

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¶rt;m u m aa mn¶rt; u¶rt;uma , m um nm mamuuau u a¶rt;um ¶rt;¶rt; aum n. uaa nu m mna ¶rt; nu¶rt;um uu ma mm, nu m am mamuuum mau, a am — mau. mam unm ¶rt; aaua n, nu¶rt;u u¶rt; ¶rt; u.

     

Is there any relation between the sun's motion and global seismic activity?

Summary The seismic energy released by global earthquake activity with time was correlated with F=||, where || is the absolute value of the change of the Sun's acceleration with time. For deep earthquakes and probability P=0.95, the coefficient of correlation was found to be around 0.4. For shallow earthquakes, the dependence was not proved.

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¶rt;a u uu (1900–1982.) ua ¶rt; F=||,¶rt; || am au uu u a. mu (h>60 ) u ¶rt; mmu =0.95 uum uu ¶rt;muam0.45. nm mu auum a n¶rt;m¶rt;a.